With a tail wind, a small aircraft can fly 1200
miles in 5 hours. Against this same wind, the
plane can fly the same distance in 6 hours.
Find the average wind speed and the average
airspeed of the plane.

Answer:

y=2

Step-by-step explanation:

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

6+y-y = 4+2y-2

6 = 2y+2

4 = 2y

2 = y

check:

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

12-2 = 4+6

Step-by-step explanation:

solution given.

relationship between perpendicular and base is given by tan angle

tan ø=perpendicular/base

ø=tan-¹(4/13)=17.10272897=17° is your answer

Answer:

Closer to 1\2

Step-by-step explanation:

half of 18 is 9 and if you add 1 to 8 you get 9 so 8\18 is closer to 1\2

Hope it helps!

Answer:

1/3

Step-by-step explanation:

P(rolling a number less than 5 by using a 6 sided die) = 4/6

Complement = 1 - 4/6

Complement = 2/6 = 1/3

Answer:

I believe it would be 2/3

Answer:

Yamato's here!

Step-by-step explanation:

−4−22−4=4(x−1)

Step 1: Simplify both sides of the equation.

−4−22−4=4(x−1)

−4+−22+−4=(4)(x)+(4)(−1)(Distribute)

−4+−22+−4=4x+−4

(−4+−22+−4)=4x−4(Combine Like Terms)

−30=4x−4

−30=4x−4

Step 2: Flip the equation.

4x−4=−30

Step 3: Add 4 to both sides.

4x−4+4=−30+4

4x=−26

Step 4: Divide both sides by 4.

4x 4 = −26 /4

x= −13 /2

Answer:  x= −13/2

Hope this helps!

(^ - ^ ")/ XoXo, Yamato-

Answer:

anser is -13/2 havea good day

There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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Answer: 40

Step-by-step explanation: 40 divided by 5 gives you 8, and 8*2 is 16, which is 6 more than 10

Answer is 40

Step by step
a number (we will call it n)

2/5 of the number (2/5n)

Is (=)

6 more than 10 (10 + 6)

Put this into equation form and solve

2/5n = 10 + 6

2/5n = 16
divide both sides by 2/5 to solve for n

When we divide a fraction we flip the divisor and multiply

2/5 * 5/2 n = 16 * 5/2

Multiply across

N = 80/2

N = 40

Check your work, substitute 40 for n

2/5 n = 16(2/5) (40) = 16

80/5 = 16

16 = 16

problem solved

Answer:

The area under a curve between two points can be found by doing a definite integral between the two points. To find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. Areas under the x-axis will come out negative and areas above the x-axis will be positive.

Step-by-step explanation:

Answer:

\((x,y) = \left(5,\dfrac{27}2 \right), \left(0,-9), \left(9, -\dfrac 92 \right)\)

Step-by-step explanation:

Answer:

Um.... Wouldn't angle 1 just be 180-17 which is 163. Angle 3 would be equal to angle 1 so also 163. Angle 4 and angle 2 are equal to 17.

Step-by-step explanation:

Answer:

angle1 = 163°

angle2 = given in diagram

angle 3 = alternating angle 1, so 163°

angle 4 = alternating angle 2, so 17°

Step-by-step explanation:

noticing that the two lines intercept each other at the centre, making angles going around that interception point add up to 360° (you can use this information to check the answers).

an angle on a straight line is always 180°, so given that angle2 is 17°, you can already do 180 - 17 to get an easy answer to angle 1 and 3.

Answer:

Below

Step-by-step explanation:

There are many ways to write an equation using 1/4 and 1000, depending on the context and what you are trying to express. Here are a few examples:

To find out what 1/4 of 1000 is, you can use the equation:

1/4 * 1000 = 250

This equation multiplies 1/4 (or 0.25) by 1000 to get the result of 250.

If you want to express a ratio between 1/4 and 1000, you can use the equation:

(1/4) : 1000 = x : 1

This equation sets up a proportion where x is the unknown value that represents the ratio between 1/4 and 1000. By cross-multiplying and solving for x, you can find the answer. For example:

(1/4) : 1000 = x : 1

1000x = 1/4

x = (1/4) / 1000

x = 0.00025

So the ratio of 1/4 to 1000 is 0.00025 to 1.

Another example of an equation using 1/4 and 1000 could be:

1/4 + 1000 = x

This equation adds 1/4 to 1000 to find the value of x. The result would be:

1/4 + 1000 = 1000.25

So x is equal to 1000.25.

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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hope this helps :)

Answer: six-hundred and nineteen thousand four-hundred and ninety three

Step-by-step explanation:

The scientific notation of the given number is 1.24×10⁻⁶.

The given number is 0.00000124.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

Here, 0.00000124=1.24×10⁻⁶.

Therefore, the Scientific notation of the given number is 1.24×10⁻⁶.

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The length of the longest leg in the right triangle is 5 units

Let x be the length of the shortest leg. Then the other leg has length x + 1, and the hypotenuse has length x + 2.

By the Pythagorean Theorem, we have:

x^2 + (x + 1)^2 = (x + 2)^2

Set x = 3

So, we have

3^2 + (3 + 1)^2 = (3 + 2)^2

Evaluate

25 = 25

The above equation is trie

So, we have

Longest = x + 2

Longest = 3 + 2

Evaluate

Longest = 5

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The velocity of the ball in ft/sec, when t = 1 second is equal to -12 ft/sec.

Given the following data:

To calculate the velocity of the ball in ft/sec, when t = 1 second:

Mathematically, the velocity of an object or physical body is equal to the differentiation of it's position function.

Velocity = s'(t)

Velocity = \(s(t) = -16t^2 + 20t + 100\)

\(Velocity = -32t + 20\)

Substituting the value of time (t), we have:

\(Velocity = -32(1) +20\\\\Velocity =-32+20\)

Velocity = -12 ft/sec

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Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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Answer: the picture

Step-by-step explanation:

Answer:

not sure

Step-by-step explanation:

Answer:

100 + 50x = 600

Step-by-step explanation:

Answer:

SPEA should have install the new power generator.

Step-by-step explanation:

The information provided is as follows:

Consider the decision tree attached below.

The loss that will be incurred after the generator is installed is, $80,000.

Compute the loss that will be incurred if the generator is not installed as follows:

\(E(\text{Loss})=P(HL|P)P(P)\times \$7000000+P(SL|P)P(P)\times \$1000000\)

             \(=(0.07\times 0.12\times \$7000000)+(0.93\times 0.12\times \$1000000)\\=58800+111600\\=170400\)

The loss that will be incurred if the generator is not installed is $170,400.

The loss from not installing the generator is more than from installing it.

Thus, SPEA should have install the new power generator.

Answer:

3.85 because you have to divide 46.20 and 12  

Step-by-step explanation:

Answer:

7 square root 9^4

Step-by-step explanation:

The case is Dependent case.

In mathematical modelling, statistical modelling, and experimental sciences, there are dependent and independent variables. The assumption or demand that dependent variables must depend on the values of independent variables is the basis for studying dependent variables.

Given:

A box of granola bars contains an assortment of flavors.

You randomly choose a granola bar and eat it.

Then you randomly choose another bar.

So, in the above case we have two flavors bars.

If we choose one then it definitely depends which flavor we are going to get.

As, the choice is random then the events here are Dependent of each other.

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The required simplified value of the f⁻¹(f(x)) is given as x.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Property of function states that function of function would be x, if the last function is an inverse function of its substituting function or vice versa. So,

f⁻¹(f(x)) = f(f⁻¹(x)) = x

Thus, the required simplified value of the f⁻¹(f(x)) is given as x.

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The number that has a 4 in the hundred places.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

A 4 with a value ten times less than the 4 in the number 123,469.

First, the value of the 4 in the number 123,469 can be found by separating each digit as:

123,469 = 100,000 + 20,000 + 3,000 + 400 + 60 + 9

Then the value of the 4 is 400.

Now we want a number that has a 4 with a value then times less than 400. Then we have

400/10 = 40

Then we want a number that has a 4 in the hundred places.

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The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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