Piotr has run the first 24 miles of a race which means he is 85% finished. How long is the race?

Answer:

27π

Step-by-step explanation:

First, find the area as though the circle were complete.

A = πr²

A = π(6)²

A = 36π

Now, if you look at the diagram, you can see that the chunk missing forms a 90 degree angle.  In a circle, there is 360 degrees in total.  This means that only 3/4 of the circle is left.  Multiply the area by 3/4.

36π × 3/4 = 27π

The area is 27π.

To eliminate the parameter in the pair of parametric equations x = t - 3 and y = t^2 + 5, the correct equation is y = x^2 - 6x - 14.

To eliminate the parameter t and express y in terms of x, we can substitute the expression for x in terms of t into the equation for y.

Given x = t - 3, we can rearrange it to obtain t = x + 3.

Substituting this value of t into the equation for y = t^2 + 5, we get:

y = (x + 3)^2 + 5.

Expanding this equation, we have:

y = x^2 + 6x + 9 + 5,

y = x^2 + 6x + 14.

Therefore, the correct equation that eliminates the parameter t and expresses y in terms of x is y = x^2 + 6x + 14.

The other options presented (Oy = x^2 - 14, Oy = x^2 + 6x + 14, Oy = x^2 + 14) are not correct as they do not correspond to the elimination of the parameter t and the substitution of x in terms of t in the equation for y.

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To find the weight that represents the 85th percentile of newborn babies given the data. The weight that represents the 85th percentile of newborn babies in the given data is 8.4 pounds.

Follow these steps:
1. Arrange the data in ascending order: 5.5, 6.3, 6.4, 6.5, 6.7, 7.2, 7.7, 7.7, 7.7, 7.7, 7.7, 8.0, 8.1, 8.6, 9.3
2. Determine the total number of data points (n): There are 15 data points in the provided dataset.
3. Calculate the 85th percentile rank (R) using the formula: R = P * (n+1), where P is the desired percentile (0.85 in this case). R = 0.85 * (15+1) = 0.85 * 16 = 13.6
4. Since the calculated rank (13.6) is not a whole number, we will interpolate between the two closest data points. In this case, the 13th and 14th data points. The 13th data point is 8.1, and the 14th data point is 8.6.
5. Interpolate the 85th percentile weight using the following formula: Weight = Weight at lower rank + (R - lower rank) * (Weight at higher rank - Weight at lower rank)
Weight = 8.1 + (13.6 - 13) * (8.6 - 8.1) = 8.1 + 0.6 * 0.5 = 8.1 + 0.3 = 8.4.

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Answer:

8.9

Step-by-step explanation:

8.94427191

Answer:

8.9

Step-by-step explanation:

8.94427191 the number 1 spot to the right of the decimal point is tenths. the number is 9 the number to the right of that is 4. unless that number 2 digits to the right of the decimal point is 5 or over the 9 stays the same

The linear cost function representing the cost C(x) to produce x items is C(x) = 4992 + 23.30x. The linear revenue function representing the revenue R(x) for selling x items is R(x) = 27.20x.

In a linear cost function, the fixed cost represents the y-intercept and the variable cost per item represents the slope of the line.

In this case, the fixed cost is $4992, which means that even if no items are produced, there is still a cost of $4992.

The variable cost per item is $23.30, indicating that an additional cost of $23.30 is incurred for each item produced.

To obtain the linear cost function, we add the fixed cost to the product of the variable cost per item and the number of items produced (x).

Therefore, the cost C(x) to produce x items can be represented by the equation C(x) = 4992 + 23.30x.

Part 2 of 4 (b): The linear revenue function that represents the revenue R(x) for selling x items is R(x) = 27.20x.

In a linear revenue function, the selling price per item represents the slope of the line.

In this case, the selling price per item is $27.20, indicating that a revenue of $27.20 is generated for each item sold.

To obtain the linear revenue function, we multiply the selling price per item by the number of items sold (x).

Therefore, the revenue R(x) for selling x items can be represented by the equation R(x) = 27.20x.

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Answer:

4/20=1/5

Step-by-step explanation:

The total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.

To find the total amount of money earned by Nora over 21 years, we need to calculate the salary for each year and then sum them up.

In the first year, Nora's salary is $40,000.

In the second year, her salary will be increased by 3%, so it will be:

$40,000 + 3% of $40,000 = $40,000 + $1,200 = $41,200.

In the third year, her salary will again increase by 3%, so it will be:

$41,200 + 3% of $41,200 = $41,200 + $1,236 = $42,436.

We can continue this process for each year, adding 3% of the previous year's salary to calculate the next year's salary.

To calculate the total amount of money earned over the 21 years, we need to sum up the salaries for each year. Here's the calculation:

Total = $40,000 + $41,200 + $42,436 + ... (21 terms)

To simplify the calculation, we can use the formula for the sum of an arithmetic series:

Total = (n/2) * (2a + (n - 1)d)

where:

n = number of terms (21 in this case)

a = first term ($40,000)

d = common difference (3% of the previous year's salary)

Plugging in the values:

Total = (21/2) * [2(40,000) + (21 - 1)(0.03)(40,000)]

Simplifying further:

Total = (21/2) * [80,000 + 20(0.03)(40,000)]

= (21/2) * [80,000 + 2,400(40,000)]

= (21/2) * [80,000 + 96,000]

= (21/2) * 176,000

= 21 * 88,000

= 1,848,000

Therefore, the total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.

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The value of Expected value, variance, and standard deviation of y of given probability distribution is 6.4, 9.76 and 3.12 respectively.

To compute the expected value of y, denoted E(y), we use the formula:

E(y) = Σ [y × f(y)]

Using the given probability distribution, we have:

E(y) = (2 × 0.20) + (4 × 0.30) + (7 × 0.40) + (8 × 0.10) = 1.6 + 1.2 + 2.8 + 0.8 = 6.4

Therefore, the expected value of y is 6.4, rounded to 1 decimal place.

To compute the variance of y, denoted Var(y), we use the formula:

Var(y) = E(y^2) - [E(y)]^2

where E(y) is the expected value of y, and E(y^2) is the expected value of y squared. To find E(y^2), we use the formula:

E(y^2) = Σ [y^2 × f(y)]

Using the given probability distribution:

E(y^2) = (2^2 × 0.20) + (4^2 × 0.30) + (7^2 × 0.40) + (8^2 × 0.10) = 1.6 + 3.6 + 19.6 + 6.4 = 31.2

Substituting this and the previously calculated E(y) into the formula for Var(y), we get:

Var(y) = E(y^2) - [E(y)]^2 = 31.2 - 6.4^2 = 31.2 - 40.96 = 9.76

Therefore, the variance of y is 9.76, rounded to 2 decimal places.

we take the square root of the variance to find the standard deviation:

σ = √Var(y) = √9.76 = 3.12

Therefore, the standard deviation of y is 3.12, rounded to 2 decimal places.

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____The given question is incomplete, the complete question is given below:

The following table provides a probability distribution for the random variable y 2 4 7 f(u) 0.20 0.30 0.40 0.10 8 a. Compute E(y) (to 1 decimal). 5.2 b. Compute Var(y) and ơ (to 2 decimals). Var(y)

Answer:

350

Step-by-step explanation:

1 percent of the grade is 3.5, multiply that by 100, then you will get 350.

Answer: t = d/s

Step-by-step explanation:

Time = Distance/Speed
Substitute values in
E.g.
Jenny went for a drive in her new car. She drove for 8 miles at a speed of 4 miles per hour. For how many hours did she drive?

8/4 = 2 hours

The resultant velocity of the boat can be calculated using vector addition. The magnitude of the resultant velocity is found by considering the boat's speed and the current's speed, while the direction is determined by the angle made by the boat's path with respect to the shore. (a) 13.65 km/hr (rounded to two decimal places). (b)  64.7° (rounded to one decimal place)

a) To find the resultant velocity of the boat, we can use vector addition. The boat's velocity in calm water is 16 km/hr, and the current's velocity is 3 km/hr. Since the boat is heading into the current, we need to subtract the current's velocity from the boat's velocity to determine the resultant velocity.

Using the concept of vector addition, we can use the Law of Cosines to find the magnitude of the resultant velocity:

Resultant velocity = √(boat velocity^2 + current velocity^2 - 2 * boat velocity * current velocity * cos(angle))

= √(16^2 + 3^2 - 2 * 16 * 3 * cos(35°))

≈ √(256 + 9 - 96 * 0.819)

≈ √(256 + 9 - 78.624)

≈ √(186.376)

≈ 13.65 km/hr (rounded to two decimal places)

b) To find the resultant direction of the boat with respect to the shore, we need to determine the angle between the resultant velocity vector and the shore. This angle is equal to the angle made by the boat's path with respect to the shore.

Using the Law of Sines, we can find the angle:

sin(angle) / resultant velocity = sin(boat angle) / boat velocity

Substituting the values, we have:

sin(angle) / 13.65 = sin(35°) / 16

Solving for angle, we find:

angle ≈ arcsin((sin(35°) / 16) * 13.65)

≈ arcsin(0.608 * 13.65)

≈ arcsin(8.3028)

≈ 64.7° (rounded to one decimal place)

Therefore, the resultant direction of the boat with respect to the shore is approximately 64.7°.

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Answer:

What is x-2+5x = 6x-2

What is -4x-10+6x = 2x-10

What is 7+10x+4x-8 = -4x+9

Step-by-step explanation:

Answer:

B Is the right one that the answer

Answer:no idea mate sorry

Step-by-step explanation:

Answer:

Total time = 19 minutes.

Step-by-step explanation:

Given the following data;

Time to shower = 720 seconds

Time to eat breakfast = 420 seconds

To find the total time in minutes;

Total time = 720 + 420

Total time = 1140 seconds

We know that 60 seconds equals a minute.

Total time = 1140/60

Total time = 19 minutes.

Therefore, it will take Andrew 19 minutes to take a shower and eat breakfast.

Answer:

Step-by-step explanation:

Given lines

The lines are same as both have same slope and y-intercept.

Correct statement is following:

Answer:

C. They are lines that lie exactly on top of one another because they have the same slope and the same y-intercep

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

The image shows a large rectangle with a similar, smaller triangle inside of it. The small leg on the small rectangle is 4, and the small leg on the large rectangle is 12. This tells me that the scale factor is 3.

If the scale factor is 3, then

\(6*3=6+6x\)

Simplify

\(18=6+6x\\12=6x\\x=2\\\)

Answer:

x^2+x

Step-by-step explanation:

Use the distributive property: x*x+x*1=x^2+x

Step-by-Step Solution:

Finding the product means to find what the expression would equal if it was multiplied.

In this equation, we need to multiply x to x, and 1.

x(x) + x(1) = x² + x

Step-by-step explanation:

Area of triangle=1/2 × base × altitude

base=7/2 ft

altitude=8/5ft

Subtitute values in formula:

Area=1/2*7/2*8/5 square.ft

Area=56/20 square.ft

Note:if you need to ask any question please let me know.

Answer:

it is c

Step-by-step explanation beacuse

Answer:

4

Step-by-step explanation:

Notice each side was increased by 4 times

You can set up a ratio of

\(\frac{new}{old}\)

then reduce or divide

The term that makes the differential equation\(y′+y^2=t^4e^t\)nonlinear is:

d) The y² term makes the differential equation nonlinear.

A linear differential equation consists of one variable, its derivative, plus a few additional functions. A linear differential equation has the conventional form dy/dx + Py = Q, which includes the variable y and its derivatives. In this differential equation, P and Q are functions of x or numerical constants.

A non-linear differential equation is a differential equation that is not a linear equation in the unknown function and its derivatives.

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Given that, Margaret drove to an appointment at 50 miles per hour. Her speed on her return was 40 miles per hour. The trip back took one quarter of an hour longer.

The question is asking to determine the distance Margaret drove to her appointment in miles. The formula used to solve the problem is as follows;

distance = speed × time Given that the distance to and from the appointment are the same. Distance to the appointment (going) = Distance from the appointment (returning)Distance = Distance Going = Distance Returning Let's determine the time it took Margaret to drive to her appointment using the formula above. Distance = speed × time Distance Going = 50 mph × t (where t represents time)Distance Going = 50tThe time it took her to drive back is (t + 0.25) since the return took one quarter of an hour longer. Distance = speed × timeDistance Returning = 40 mph × (t + 0.25)Distance Returning = 40t + 10Using the formula Distance = Distance Going = Distance Returning50t = 40t + 10Subtract 40t from both sides.50t - 40t = 10t = 10Thus, t = 1The distance going to the appointment is;Distance Going = 50tDistance Going = 50 × 1Distance Going = 50 , Margaret drove 50 miles to her appointment.Answer: Margaret drove 50 miles to her appointment.

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We can estimate that approximately 442 infants in the sample completed the hepatitis B vaccine series.

In the study by Henning et al. (1992) published in the American Journal of Public Health, it was found that 66 percent of a sample of 670 infants had completed the hepatitis B vaccine series. This means that out of the 670 infants in the sample, 66% of them had received all three doses of the hepatitis B vaccine.

To calculate the actual number of infants in the sample who had completed the hepatitis B vaccine series, we can multiply the sample size by the percentage:

Number of infants who completed vaccine series = 0.66 * 670 = 442.2

Since we cannot have a fraction of an infant, we can round this number to the nearest whole number to obtain an estimate of how many infants in the sample completed the vaccine series. Therefore, we can estimate that approximately 442 infants in the sample completed the hepatitis B vaccine series.

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Answer:

the answer is D

Step-by-step explanation:

i just did the test

Answer:

D

Step-by-step explanation:

Answer: No

Step-by-step explanation:

Points inserted are

\((1\ \frac{1}{2},4), (2,4), (5,4)\\\)

As all the points have the same y-coordinate, therefore, they must lie on the same horizontal line of \(y=4\)

So, the ingested points are not correct.

Points maybe \((1,2), (1, 3), (1,3\ \frac{1}{2})\) as they line on the same vertical line.

Main answer:Long multiplication is a method of multiplying two difficult-to-multiply numbers.

supporting answer:

what is multiple long?

Finding the product is not always this simple. In such cases, the long method of multiplication is used.

body of the answer:

let us understand long multiplication by taking an example

     6.Add the two partial products

final answer: by following above steps we can perform long multiplication

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Long multiplication is a method of multiplying two difficult-to-multiply numbers.

What is multiple long?

Finding the product is not always this simple. In such cases, the long method of multiplication is used.

Let us understand long multiplication by taking an example

1. Write the two numbers one beneath the other in the order of their digits. On top, write the larger number, and on the left, a multiplication sign.

2. Multiply the top number's one digit by the bottom number's one digit.

3. Put a 0 below the one's digit,

4. Multiply the top number's ones digit by the bottom number's tens digit.

5. Multiply the top number's tens digit by the bottom number's tens digit.

6. Add the two partial products

By following the above steps we can perform long multiplication

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