the amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 20 minutes and a standard deviation of 7 minutes. find the probability that a randomly selected athlete uses a stairclimber for (a) less than 17 minutes, (b) between 20 and 27 minutes, and (c) more than 30 minutes.

The method of resection involves measuring the angles between known points and the point you want to locate.

Here are the general steps-

1. Set up your instrument (Wolfpack) and measure the distances (R1, R2, R3, R4) between the known points and the point you want to locate.
2. Measure the angles (Alpha, Beta, Gamma) between the known points and the point you want to locate.
3. Calculate the coordinates of the point using trigonometry and the measured angles and distances.

To calculate the coordinates, you can use the following formulas:

\(x = (R1 * cos(Alpha) + R2 * cos(Beta) + R3 * cos(Gamma)) / 3\)

\(y = (R1 * sin(Alpha) + R2 * sin(Beta) + R3 * sin(Gamma)) / 3\)

I recommend using the measurements and formulas provided above to perform the calculations based on your specific data.

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For a student who participate in a wide variety of extra-curricular memorial high school, the probability of the union of being either a freshman or senior is equals to the 0.50.

We have students who attend memorial high school have a wide variety of extra-curricular activities.

Probability of student who likely to join the dance team = 38% = 0.38

Probability of student who likely to participate in the school play = 18% = 0.18

Probability of students who likely to join the yearbook club = 42% = 0.42

Probability of students who likely to join the marching band = 64% = 0.64

Also, students have equal probabilities of being freshmen, sophomores, juniors, or seniors.

So, the probability ( a student is senior )

= 1/4 = 0.25

The probability ( a student is freshman )

= 1/4 = 0.25

We have to determine the union of being either a freshman or senior. Now, the probability of the union of disjoint or independent events is the sum of their individual probabilities.

So, probability ( a student is freshman or senior) = P( freshman ∪ senior )

= P( freshman) + P( senior)

= 0.25 + 0.25 = 0.50

Hence, required probability is 0.50.

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1.  You would need to wrap approximately 17.5 million hamburgers to make your first one million dollars.

2.  There are approximately 6.82 miles in 1.2 × 10^4 yards.

3.  The speed of light is approximately 108,000 km/hr.

4. The cost of 16 onions is approximately $5.82.

5. It would take approximately 337.5 minutes to drive from San Francisco to Los Angeles.

6.The cost to drive from San Francisco to Los Angeles would be approximately $196.20.

To calculate the number of hamburgers you need to wrap to make one million dollars, we'll start by calculating your earnings per hour.

Earnings per hour = Salary per 2 weeks / (2 weeks * 8 hours per day * 5 days per week)

Earnings per hour = $840.34 / (2 * 8 * 5) = $840.34 / 80 = $10.50425 per hour

Next, we'll calculate how many hours it would take to earn one million dollars:

Hours to earn one million dollars = $1,000,000 / Earnings per hour

Hours to earn one million dollars = $1,000,000 / $10.50425 = 95,227.4597 hours

Now, we'll calculate the number of hamburgers you need to wrap:

Hamburgers = Hours to earn one million dollars * Hamburgers per hour

Hamburgers = 95,227.4597 * 184 = 17,516,671.5668 hamburgers

Rounded to 3 significant figures, you would need to wrap approximately 17.5 million hamburgers to make your first one million dollars.

To convert yards to miles, we'll divide the given number of yards by the number of yards in a mile:

Miles = 1.2 × 10^4 yards / 1,760 yards per mile

Miles = 6.81818182 miles

Rounded to 3 significant figures, there are approximately 6.82 miles in 1.2 × 10^4 yards.

To convert the speed of light from cm/s to km/hr, we'll multiply the given value by conversion factors:

Speed in km/hr = 3.0 × 10^10 cm/s * (1 km / 10^5 cm) * (3600 s / 1 hr)

Speed in km/hr = 3.0 × 10^10 * 10^-5 * 3600

Speed in km/hr = 108,000 km/hr

The speed of light is approximately 108,000 km/hr.

To calculate the cost of 16 onions, we need to find the cost per pound and then convert it to the cost of 16 onions:

Onions per pound = 3 onions / 1.5 lb = 2 onions per pound

Cost per pound = 33 cents per kilogram * (2.20462 lb / 1 kg) = 72.75246 cents per pound

Cost of 16 onions = 16 onions * (1 pound / 2 onions) * Cost per pound

Cost of 16 onions = 8 pounds * 72.75246 cents per pound

Cost of 16 onions = 582.01968 cents

Rounded to dollars, the cost of 16 onions is approximately $5.82.

To calculate the time it takes to drive from San Francisco to Los Angeles, we'll divide the distance by the average speed:

Time = Distance / Speed

Time = 405 miles / 72 mi/hr

Time = 5.625 hours

To convert hours to minutes, we'll multiply by 60:

Time = 5.625 hours * 60 minutes/hour

Time = 337.5 minutes

It would take approximately 337.5 minutes to drive from San Francisco to Los Angeles.

To calculate the cost of driving from San Francisco to Los Angeles, we'll calculate the number of gallons of gasoline needed and then multiply it by the cost per gallon:

Gallons of gasoline = Distance / Fuel efficiency

Gallons of gasoline = 405 miles / 8.15 miles per gallon

Gallons of gasoline = 49.693788 gallons

Cost = Gallons of gasoline * Cost per gallon

Cost = 49.693788 gallons * $3.95/gal

Cost = $196.2012266

Rounded to 2 decimal places, the cost to drive from San Francisco to Los Angeles would be approximately $196.20.

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The distance QS is approximately 42.178 km, rounded to three significant figures.

1. Point P is due North of point Q.

2. The ship is at point S.

3. The distance PS is 29 km.

4. The bearing of the ship from point P is 062°.

5. The bearing of the ship from point O is 036°.

To find the distance QS, we need to use trigonometry and the angles given. We'll start by finding the length of PS and the angle SPQ.

Step 1: Finding the length of PS

Since PS is a straight line, its length is given as 29 km.

Step 2: Finding the angle SPQ

The bearing of the ship from point P is 062°. Bearing angles are measured clockwise from the north, so the angle SPQ is the supplement of the given angle. The supplement of 062° is (180° - 062°) = 118°.

Step 3: Calculating the distance QS

To find the distance QS, we can use the sine rule, which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. The formula is:

(QS / sin(SPQ)) = (PS / sin(SQP))

Rearranging the formula, we get:

QS = (sin(SPQ) / sin(SQP)) * PS

Now let's substitute the values into the formula:

QS = (sin(118°) / sin(62°)) * 29 km

Using a scientific calculator, we can calculate the value of the expression:

QS ≈ 42.178 km

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Answer:

50 degrees

Step-by-step explanation:

50 degrees because angle 2 is its vertical angle

If the given point is p(x, y) and change the sign of its x coordinates and y coordinates, then the new location will be on third quadrant

The coordinates of the point p = (x, y)

In the graph, there are four quadrants.

In first quadrant the x axis value and y  axis value will be positive. In second quadrant the value of x will be negative and y will be positive. In the third quadrant the value of and y will be negative. In fourth quadrant the value of x will be positive and y will be negative

Here at first both x and y are positive and it will be on first quadrant. The the sign of the x coordinates and y coordinates will change sign. So both of them will be negative.

Therefore, the location of will be on third quadrant

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Answer: 1:1

Step-by-step explanation:

True, often top standard management prefers to use the same marketing mix globally because it leads to significant cost savings. This approach streamlines management processes and allows for more efficient resource allocation.

True. This is because Standard the marketing mix in across all markets reduces the need for customization and adaptation, which can be time-consuming and costly. By using a consistent approach, top management can achieve significant cost savings. However, it's important to note that this approach may not always be effective, as cultural and market differences can require customization in order to effectively reach and resonate with local consumers.
Standardization allowed companies to continue to produce a variety of products despite the reduced variation. At the same time, the process is simple and the production and purchasing cost is reduced. This creates a perfect win-win situation for everyone involved.

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Answer: 5/13

Step-by-step explanation: cos is adj/hyp giving us a 12 for adj and 13 for hyp. Tan is Opp/Adj confirming 12 is the adj and 5 being the Opp. Sin is Opp/Hyp giving us 5/13. Hope it helps

Answer:45 76 97 790 9786 99780 533455 6687878

Step-by-step explanation:

The indefinite integral is: (t^2)i + (t)j + (3t)k + C

To find the indefinite integral of the given vector function (2ti + j + 3k) with respect to t, we need to integrate each component separately.

Step 1: Integrate the i-component with respect to t:
∫(2t) dt = t^2 + C1

Step 2: Integrate the j-component with respect to t:
∫(1) dt = t + C2

Step 3: Integrate the k-component with respect to t:
∫(3) dt = 3t + C3

Now, combine the integrated components and the constants of integration (C1, C2, C3) to form the final result:

Your answer: (t^2)i + (t)j + (3t)k + C

Here, C = (C1)i + (C2)j + (C3)k is the constant of integration in vector form.

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Answer:20.3

Step-by-step explanation:

Answer: 69.7 inch

Step-by-step explanation:

Given

A television is advertised as 83 inch TV(diagonal length)

The height of the TV is 45 inches

Suppose, width is x

Using Pythagoras theorem, we can write

\(\Rightarrow 83^2=45^2+x^2\\\Rightarrow x^2=83^2-45^2\\\Rightarrow x^2=6889-2025\\\Rightarrow x=69.7\ \text{inch}\)  

Answer: 69.7

Step-by-step explanation:

Answer:

(i)  2² · 3 · 7

(ii)  3024

(iii) k = 16

(iv) 12 cm

Step-by-step explanation:

The first few prime numbers are:  2, 3, 5, 7, 11, 13, 17, ...

To find which prime numbers multiply together to make 84, start by dividing 84 by the first prime number, 2:

⇒ 84 ÷ 2 = 42

As 42 is not a prime number, we need to divide again:

⇒ 42 ÷ 2 = 21

As 21 is not a prime number, we need to divide again.  

21 is not divisible by 2, so let's try dividing by the next prime number, 3:

⇒ 21 ÷ 3 = 7

As 7 is a prime number, we can stop.

Therefore, 84 is the product of:

⇒ 84 = 2 · 2 · 3 · 7

As 2 appears two times, we can write this using exponents:

⇒ 84 = 2² · 3 · 7

Lowest Common Multiple (LCM):  The lowest multiple shared by two or more numbers.

Prime Factors Method of finding LCM

Step 1

Find the prime factorization of each number.

From part (i):            84 = 2² · 3 · 7

Given in part (ii):    432 = 2⁴ · 3³

Step 2

Write each number as a product of primes, matching primes vertically where possible:

\(\begin{array}{ r c c c c c c c ccccccccc}84&=& 2 & \cdot & 2 & \cdot & & & & & 3& \cdot & & & && 7\\\\432 &=& 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3\\\\\cline{1-17} \\\sf LCM & = & 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3 &\cdot & 7\end{array}\)

Step 3

Bring down the primes in each column then multiply the factors to get the LCM:

⇒ LCM = 2 · 2 · 2 · 2 · 3 · 3 · 3 · 7

⇒ LCM = 2⁴ · 3³ · 7

⇒ LCM = 3024

From part (ii) we know that the prime factorization of 432 is:

432 = 2⁴ · 3³

A perfect cube is a number multiplied by itself three times.

One of the factors of 432 is a perfect cube → 3³.

Therefore,

\(\begin{aligned}432 & = 2^4 \cdot 3^3\\\\\implies \dfrac{432}{2^4} & = 3^3\\\\\dfrac{432}{16} & = 3^3\end{aligned}\)

So we need to divide 432 by 2⁴ to get the perfect cube 3³.

Therefore,

⇒ k = 2⁴

⇒ k = 2 · 2 · 2 · 2

⇒ k = 16

To find the largest possible length of the side of the square, we need to find the greatest common factor of 432 and 84.

Prime Factors Method of finding GCF

Step 1

Find the prime factorization of each number.

From part (i):            84 = 2² · 3 · 7

Given in part (ii):    432 = 2⁴ · 3³

Step 2

Write each number as a product of primes, matching primes vertically where possible:

\(\begin{array}{ r c c c c c c c ccccccccc}84&=& 2 & \cdot & 2 & \cdot & & & & & 3& \cdot & & & && 7\\\\432 &=& 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3\\\\\cline{1-17} \\\sf GCF & = & 2 & \cdot & 2 & \cdot & & & & & 3& & & & && \end{array}\)

Step 3

Bring down the primes in the columns where both numbers have the factor, then multiply the factors to get the GCF:

⇒ GCF = 2 · 2 · 3

⇒ GCF = 12

Therefore, the largest possible length of the side of the square is 12 cm.

Answer:

Explanation: We have to find the resultant velocity of the pedestrian, the sketch of the scenario is as follows:

The resulting rate is as follows:

Answer:

D. linear; y = –x – 1

Step-by-step explanation:

Linear; y=-x - 1

The slope is negative since it’s decreasing. So it’s not the first equation. It’s not a quadratic equation because there is no forming U shape for this data. It’s not a exponential function because the slope is not 3 and a exponential function is in the form y=a(b)^x

...............................................................................................................................................

Answer:

The correct answer is D) linear; y = –x – 1

Step-by-step explanation:

To find this, use any values in the table and it will produce a true statement. This is how we check to see if a model is correct. See the two examples below for proof.

(4, 5)

y = -x - 1

-5 = -4 - 1

- 5 = -5 (TRUE)

(0, -1)

y = -x - 1

-1 = 0 - 1

-1 = -1 (TRUE)

B. The statement is true.

Answer:

Vowel= 0.2

Number= 0.5

Step-by-step explanation:

Vowel: There are a total of 5 sample spaces known as A,E,I,O,U. From those 5, there is one randomly selected letter e. This will also be known as 1/5, 20% or 0.2.

Number: There are a total of 2 sample spaces known as 1,2. Out of those two numbers, there will be one random number selected known as 2. This is known to be 1/2, 50% or 0.5

Step-by-step explanation:

We can express the inequality in

- 9p = 40.5

p = 40.5 / - 9

p = -4.5

So Now

p > - 4. 5

Answer:

To simplify the expression (-3+1)+(-4-i), we can perform the addition operation within the parentheses first:

(-3+1)+(-4-i) = -2 + (-4-i)

Next, we can simplify the addition of -2 and -4 by adding their numerical values:

-2 + (-4-i) = -6 - i

Therefore, (-3+1)+(-4-i) simplifies to -6-i.

Step-by-step explanation:

Answer:

B. 16/25

Step-by-step explanation:

6

10

+

4

100

=  

6 × 10

10 × 10

+

4

100

=  

60

100

+

4

100

=  

60 + 4

100

=  

64

100

=  

64 ÷ 4

100 ÷ 4

=  

16

25

Answer:

\(\huge\boxed{\sf \frac{16}{25} }\)

Step-by-step explanation:

\(\displaystyle \frac{6}{10} +\frac{4}{100}\)

To equalize the denominator, we will have to multiply the fraction 6/10 by 10.

\(\displaystyle =\frac{6 \times 10}{10 \times 10} +\frac{4}{100} \\\\\ =\frac{60}{100} +\frac{4}{100}\)

Now, that the denominator is equal, we can add both the fractions.

\(\displaystyle= \frac{60+4}{100} \\\\=\frac{64}{100}\)

Divide both numerator and denominator by 2.

\(\displaystyle = \frac{64 \div 2}{100 \div 2} \\\\= \frac{32}{50}\)

Divide again.

\(\displaystyle= \frac{32 \div 2}{50 \div 2} \\\\= \frac{16}{25} \\\\\rule[225]{225}{2}\)

As per the concept of probability, there are 4,717,440 number of passwords are possible.

Probability:

In statistics, probability refers the favorable outcome of the particular event.

Given,

A password to a computer consists of 6 characters: a digit, a letter, a digit, a letter, a digit, and a letter in that order, where the numbers from 1 through 9 are allowed for digits.

Here we need to find how many different passwords are possible.

Total number of characters = 6

According to this, each password would have

5 digits of 10 digits: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], and

one of 26 letters: [A to Z].

Here there is no repeats are allowed, and assuming only upper case letters are valid and the letter is the last character, then we can form 10*9*8*7*6 * 26 = 786,240 such passwords.

If the repetition is allowed then number of possible passwords is

786,240 * 6 = 4,717,440.

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Answer:

y = 10 and x =18

Step-by-step explanation:

From the parallelogram,

DH + HF = DF

x+2 + 2y = DF

Also DH = HF

x+2 = 2y

x - 2y = -2 .... 1

Also GH = HE

3x-3 = 5y+1

3x - 5y = 1 + 3

3x-5y = 4 .... 2

Solve  1 and 2 simultaneously

x - 2y = -2 .... 1 * 3

3x-5y = 4 .... 2 * 1

_____________

3x-6y = -6

3x-5y = 4

Subtract

-6y + 5y = -6-4

-y = -10

y = 10

Substitute y = 10 into 1

x- 2y = -2

x - 2(10) = -2

x - 20 = -2

x = -2+20

x = 18

Hence y = 10 and x =18

the answer is x=-1/3

Normal quantile plot is a graph of points (x,y) where each x-value is from the original set of sample data, and each y-value is the corresponding Z-score that is a quantile value expected from the standard normal distribution.

What is a Normal Quantile Plot?

A normal quantile plot is a graphical tool used to determine whether a data set is normally distributed or not.

It plots sample data versus a theoretical normal distribution.

In general, the points on the plot should form a straight line if the data is normally distributed. If the data is not normally distributed, the points on the plot will not form a straight line.

A normal quantile plot can be used to evaluate the following:

The normal quantile plot of the residuals is the most important diagnostic tool for examining whether the assumptions of a linear regression model have been met.

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Answer:

13 cm

Step-by-step explanation:

just took the test

The correct value of the inequality as solves is x > 14 , and the error made by the student was that he directly divided the RHS by 7.

To simplify the equation we will multiply 7 on both the sides.

Then we will get the result as 7x > 98

Thus, we can say that the new inequality will be x > 14 ,

Hence , the mistake made by the student was that he didn't divided both the sides by 7 but only one side.

So a result, he obtained the incorrect result x>2.

Inequality is a concept in mathematics and uses symbols such as > , < , <= , >= etc.

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The probability that more than but fewer than have a personal computer is 0.0166.

A random sample of households is selected (N) = 172.

P = 0.6 (60% of households have personal computers).

First, we need to check the conditions of normality that Np and N(1-p) both are greater than or equal to 5.

Np = 172*0.6 = 103.2

N(1-p) = 172*0.4 = 68.8

Both the conditions are met and we can use the z table to estimate the required probabilities.

Z = (x-mean)/SD

Mean = Np = 172*0.6 = 103.2

SD = √Np(1-p) = 6.4249513617

We will use continuity correction here,

In continuity correction;

P(X>=X) = P(X>x-0.5)

P(x<=X) = P(x<x+0.5)

P(X<X) = P(X<x-0.5)

P(X>X) = P(X>X+0.5)

P(X1<X<X2) = p(x1-0.5<X<X2+0.5)

P(52<X<89)

By continuity correction,

P(51.5<X<89.5) = P(X<89.5)-P(X<51.5).

P(X<89.5)

Z = (89.5-103.2)/6.42495 = -2.13

From the z table,

P(z<-2.13) = 0.0166

P(X<51.5)

Z = (51.5-103.2)/6.42495 = -8.05

From the z table,

P(z<-8.05) = 0.0000

The required probability is 0.0166-0.0000 = 0.0166

The probability that more than but fewer than have a personal computer is 0.0166.

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