Suppose that the speed at which cars go on the freeway is normally distributed with a mean of 66 miles per hour (mph) and standard deviation 10 mph. Letxxbe the speed for a randomly selected car. Round all answers to 4 decimal places where possible.What is the z-score for a car that is caught going 60 mph? The z-score =What is the probability of randomly choosing a car on the freeway and it going below 60 mph?P(x≤60)=P(x≤60)=What is the z-score for a car that is caught going 86 mph? The z-score =What is the probability of randomly choosing a car on the freeway and it going above 86 mph?P(x≥86)=P(x≥86)=If a highway patrol woman only wants to catch the top 1% of all cars on the freeway , then what speed does the car on the freeway need to be going in order for her want to catch the speeder? mph

Answer:

?

Step-by-step explanation:

Answer:

8 hours

Step-by-step explanation:

Given data

Commission= 5%

Sales= $3,200

Total earnings= $240

Let us find the amount in commission earned

=5/100*3,200

=0.05*3,200

=$160

Hence 240-160=$80

$80 is the amount earned yesterday

we are told that per hour is $10

Hence $80 will be earned for

=80/10

=8 hours

The arc length of the graph of the function \(\(y = \frac{3}{2}x^{2/3}\)\) over the interval [8, 64] is approximately  109.602 units.

To find the arc length, we use the formula:

\(\[ L = \int_{a}^{b} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx \]\)

where a and b represent the interval limits. In this case, a = 8 and b = 64 . To calculate \(\( \frac{dy}{dx} \)\), we differentiate the function with respect to x :

\(\[ \frac{dy}{dx} = \frac{3}{2} \left(\frac{2}{3}\right)x^{-1/3} = \frac{1}{x^{1/3}} \]\)

Substituting this into the formula, we have:

\(\[ L = \int_{8}^{64} \sqrt{1 + \frac{1}{x^{2/3}}} \, dx \]\)

Evaluating this integral gives us the arc length of approximately 109.602 units.

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The expression cos (125°) - cos 55° cos 35° cos 55° can be written as cos (55°) + cos (55°) cos (35°) cos (55°).

cos (125°) can be rewritten as cos (180° - 125°). Similarly, cos (35°) can be rewritten as cos (180° - 35°). Therefore, the expression can be written as:

cos (180° - 125°) - cos (55°) cos (180° - 35°) cos (55°)

Simplifying further, we have:

cos (55°) - cos (55°) cos (145°) cos (55°)

Since 145° is the supplement of 35°, we can rewrite it as:

cos (55°) - cos (55°) cos (180° - 35°) cos (55°)

Now, cos (180° - 35°) is equal to -cos (35°). Therefore, the expression becomes:

cos (55°) + cos (55°) cos (35°) cos (55°)

Hence, the expression as a function of an acute angle is:

cos (55°) + cos (55°) cos (35°) cos (55°)

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Answer:

For the dot to dot, the slope is 8/4

simplified = 2

Step-by-step explanation:

Answer:

2x +5y = -15

Step-by-step explanation:

We need to find the slope

m = (y2-y1)/(x2-x1)

   = (-7--1)/(10- -5)

   = (-7+1)/(10+5)

   -6/15

  -2/5

The point slope form

Y+7= -2/5 (x - 10).

Distribute

y + 7 = -2/5x + 4

Add 2/5 x to each side

2/5x +y +7 = 4

Subtract 7 from each side

2/5x +y = -3

Multiply each side by 5

5(2/5x +y) = -3*5

2x +5y = -15

This is standard form Ax + By = C where A is a positive integer

Answer:

It’s linear!

Step-by-step explanation:

linear is a straight-line relationship between two variables.

After solving, the height of the building is 15.19 m tall.

In the given question, a baseball dropped from the roof of a tall building takes 3. 1 seconds to hit the ground.

We have to find the height of the building.

Initial Velocity, denoted as u, is the velocity at time interval t = 0. It is the speed at which motion first occurs.

Initial velocity u=0

Time t=3.1 seconds

Let height of the cliff is h.

So s=ut+at^2/2

Now putting the value

s = 0+(9.8×3.1)/2

s = 30.38/2

s = 15.19 m

Hence, the height of the building is 15.19 m tall.

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Answer:

30x^5y^5

Step-by-step explanation:

What is the product of 10x4 y2 and 3xy3 ?

30x^5y^5

There was no control group for comparison answers.

There was no control group to compare the results to change in blood flow could have been caused by something else .

The movement of blood through the vessels from arteries to capillaries and then into veins is referred to as blood flow.

There are two blood circulatory systems in the human body, which are linked: The systemic circulation transports blood to organs, tissues, and cells, supplying them with oxygen and other vital substances. The pulmonary circulation is where fresh oxygen enters the bloodstream.

As the heart beats, blood is pumped through a network of blood vessels known as the circulatory system. The vessels are flexible tubes that transport blood to all parts of the body.

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Answer:

One of the answers is HL, and the other answer is ΔBCA ≅ ΔDEC, or ΔCAB ≅ ΔCDE.

Step-by-step explanation:

Only right angles use HL as a postulate theorem.

In this method, we first initialize the first two terms of the series as 'a' and 'b' respectively. We then print the first two terms separately. After that, we use a loop to generate and print the remaining terms of the series.

Here is a method in Python to print the Fibonacci series up to a given number of terms 'n':

```
def fibonacci(n):
   # Initialize the first two terms of the series
   a, b = 0, 1
   # Print the first term
   print(a)
   # Print the second term
   if n >= 2:
       print(b)
   # Generate and print the remaining terms
   for i in range(2, n):
       # Compute the next term in the series
       c = a + b
       # Update the values of a and b
       a, b = b, c
       # Print the next term
       print(c)
```

Inside the loop, we first compute the next term of the series as the sum of the previous two terms (i.e. 'a' and 'b'). We then update the values of 'a' and 'b' to prepare for the next iteration. Finally, we print the next term of the series.

You can call this method with the desired value of 'n' to print the Fibonacci series up to the given number of terms. For example:

```
fibonacci(7)
```

This would print the Fibonacci series up to 7 terms: 0, 1, 1, 2, 3, 5, and 8.

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Answer:

17

Step-by-step explanation:

5x+2

(5*3)+2

15+2

17

Answer: 11, 16, 26, 41

Step-by-step explanation:

The probability that monofilament cables will be discovered during the next ten years and that both discoveries will occur within the next twenty years are, respectively, 0.811 and 0.833.

X = time taken to discover Negative gravity

Y = time taken to discover Monofilament Cables

X follow exponential distribution with mean = 10

Y follow exponential distribution with mean = 6

a)P(Y < y) = 1- e^(-y/mean)

 P(Y < 10)

= 1 - e^(-10/6)

= 0.8111

The probability monofilament cables will be discovered within the next 10 years is 0.8111

b)P(X <20 ,Y < 20)= P(X < 20)P(Y < 20)

= (1 - e^(-20/10)) (1 - e^(-20/6))

= 0.8338

The probability both discoveries will take place within the next 20 years

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The correct answer is option 3. Sample Statistics. the symbols p-hat, x bar and s represent Sample Statistics which is a term for all symbols collectively.

When it is not possible to analyze the entire population, all of the aforementioned symbols are referred to as "sample statistics" because they are calculated from a "random sample" taken from the "population."

The entire population is used to calculate what is known as "population parameters," which are fixed measurements.

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Complete Question:

What do the symbols p-hat, x bar and s represent?

The statement about the sequence that is true is (c) It is neither arithmetic nor geometric.

The sequence is given as

-10, -3, -10, -3, -10, ...

Test for arithmetic sequence:

An arithmetic sequence is any seqeunce that has a common difference

The sequence -10, -3, -10, -3, -10, ... does not have a common difference

This is so because the first two terms are repeated through out

Test for geometrics equence:

A geometric sequence is any seqeunce that has a common ratio

The sequence -10, -3, -10, -3, -10, ... does not have a common ratio

This is so because the first two terms are repeated through out

Hence, the true statement is (c)

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The number 437.184 can be rounded or estimated as  437 if estimated to the tenths.

In mathematics, estimation implies approximating or rounding numbers. This is commonly used to make calculations simpler or to apply maths to real life. For example, 8 oranges divided by 6 people is equal to 1.33; however as calculating 0.33 when cutting oranges might be quite difficult it is better to estimate it as 1.

The general rule is that if a number is above five you should estimate it to the next unit, but if the number is below 5 you should estimate it to 0. Here is an example:

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Answer:

Step-by-step explanation:

The no of different ways in which these restaurants can be visited

= ¹⁵P₁₅

= 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

= 1.30 x 10¹²

b ) Each combination takes 1 week and 50 weeks in  a year to work

No of years to take to try all the combination

= 1.30 x 10¹² / 50

= 2.615 x 10¹⁰ years .

To answer this question, we need to use the information given in the problem. We know that 52% of all adults are shareholders, so the probability that a randomly selected adult owns shares of stock is 0.52.

To find the probability that a randomly selected adult did not own shares of stock, we can subtract this probability from 1 (since the sum of the probabilities of all possible outcomes must equal 1).

So, the probability that a randomly selected adult did not own shares of stock is:

1 - 0.52 = 0.48

Now, we can see that the information about shareholders having some college education is not needed to answer this question.

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Answer: The correlation between variables must be significant

Step-by-step explanation: In order to make reliable predictions using the equation of a regression model, the correlation Coefficient between the dependent and independent variables must be significant (that is a correlation Coefficient value close to either 1 or - 1). This is because the range of value of the correlation Coefficient is between - 1 to +1 and the closer the correlation Coefficient value is to either of these numbers, depicts the strength of the relationship which exists between them hence, enabling us to make good and accurate predictions which are close to the actual value.

Regression Analysis is a statistical and reliable process for making predictions using the regression model.

The correct option is:

Option B. The correlation between variables must be significant

The regression line can be explained as:

1. The correlation coefficient between the dependent and independent variables must be significant.

2. The correlation coefficient value should be near 1 or -1.

3. Thus, the values closer to - 1 and +1 will depict the strength of the relationship between the coefficient values.

Thus, regression lines help to predict accurate and reliable results that are close to the actual value.

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To find the teaching year for all 218 teachers at High School A, we need to use the concept of weighted averages.

Let the mean teaching year for the 200 teachers be x. Then the total teaching years for the 200 teachers would be 200x.

Since we know that there are 18 additional teachers with a mean teaching year of 2.5, the total teaching years for these teachers would be 18 x 2.5 = 45.

Thus, the total teaching years for all 218 teachers would be 200x + 45.

To find the mean teaching year for all 218 teachers, we divide the total teaching years by the total number of teachers:

(mean teaching year) = (total teaching years) / (total number of teachers) = (200x + 45) / 218

Therefore, the mean teaching year for all 218 teachers at High School A would be (200x + 45) / 218.

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After reflection of the coordinate from point S to S'', the final coordinate is (-1, 5).

Reflection of an object along a coordinate plane is a transformation that produces a mirror image of the object with respect to the given plane. This transformation involves flipping the object across the plane while keeping the distances and angles between its points intact.

In the given problem, we can approach the transformation as;

The given point S(1, -5) is reflected over the y - axis, this makes the coordinate of y-axis remain the same while the value of the x-axis changes to negative, The new coordinate will become S'(-1, -5).

When the new coordinate S'(-1, -5) reflects over the x-axis, the value of the y - coordinate changes to negative while the x - axis does not change. The final coordinate is S''(-1, 5).

Therefore, the location of point S" is described by the ordered pair (-1, 5).

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Answer:

$800 in interest

Step-by-step explanation:

T = A(1 + rt)

T = 2,000(1 + .05(8))

T = 2,000(1.4)

T = 2800

2800 - 2000 = 800

Answer:

(12,-6)

Step-by-step explanation:

Answer:

(12,-6)

Step-by-step explanation:

When dilating points, you multiply both coordinates (x and y) by the scale factor.

The point we are given is: (4,-2) and the scale factor is 3.

Multiply each coordinate by the scale factor of 3.

X-coordinate: 4

     4* 3= 12

New X-coordinate: 12

Y-coordinate : -2

    -2 * 3= -6

New Y-coordinate: -6

Our new x-coordinate is 12 and y-coordinate is -6. Therefore, our point is (12,-6). So, the image of point (4,-2) after a dilation of 3 is (12, -6).

The median is the midpoint of the distribution. it is the number such that half of the observations fall above it, and half fall below it.

The following statement is correct.

The median M of a distribution is the number at which half of the observations are smaller and half are greater.

For skewed distributions or distributions containing outliers, the median is the most useful metric of central tendency. For example, in highly skewed income distributions, the median is frequently utilised as a measure of central tendency.

For normal distributions, the mean is employed. For skewed distributions, the median is typically utilised. The mean is not a reliable tool since it is heavily impacted by outliers. Because it is far more robust and comprehensible, the median is better suited for determining central tendency from skewed distributions.

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Answer:Continuous play hitting the ball back and forth between opposite teams is called a _____.

a

side-out

b

double hit

c

rally

d

fault

Step-by-step explanation: