t/f the mean and standard deviation are more accurate measures of center and spread when the data is skewed

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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We are given the following expressions

Let us add the above expressions.

We need to re-group the like terms together as shown below

Now simplify the expression

Therefore, the simplified expression is

Answer:

i dont know  if this the answer for the first on x=1.45454545455 and the other on is 3s

Step-by-step explanation:

The speed of airplane in miles per hour (mph) is 380.2968 .

What is speed?

Speed is the time rate at which an object is moving along a path. The SI unit of speed is meter per second ( m/s ). Miles per hour ( mph ) is a British imperial and United States customary unit of speed expressing the number of miles travelled in one hour.

Given that

Speed of a certain airplane = 170 m/s or m\(s^{-1}\)

We know that

In 1 meter = 0.0006214 miles

In 1 sec = \(\frac{1}{3600}\) hour

but 1 \(sec^{-1}\) = 3600 hour

Speed of this airplane in miles per hour = 170 × 0.0006214 ×  3600 mph

                                                                  = 0.105638 × 3600 mph

                                                                  = 380.2968 mph

Hence, the speed of airplane in miles per hour (mph) is 380.2968 .

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Answer:

v = Δs/Δt

Step-by-step explanation:

Velocity is equal to the displacement/distance (delta symbol s) over the change of time (delta symbol t).

Answer: 1/2

First you do 4/4 times 4/4. Which is equal to 1. Then, you multiply by 2/4 to get 1/2.

Answer:

4 in(a)

Step-by-step explanation:

height-?

volume-314

radius-5

pie-22÷7 or 3.14

volume= πrsquared h

314=3.14×5×5×h

314= 78.5h

314÷78.5

= 4 in

The smaller number is 6 .

The larger number is 22

Let's let x be the smaller number and y be the larger number.

From the problem, we know that one number is eight less than five times the other, so we can write:

y = 5x - 8

We also know that the sum of the two numbers is 28, so we can write:

x + y = 28

Now we have two equations in two variables. We can solve for one of the variables in terms of the other, and substitute that expression into the other equation to eliminate one variable.

Let's solve the first equation for x

x = (y + 8)/5

Now we can substitute this expression for x into the second equation:

(y + 8)/5 + y = 28

Multiplying both sides by 5 to eliminate the fraction, we get:

y + 8 + 5y = 140

Combining like terms, we get:

6y + 8 = 140

Subtracting 8 from both sides, we get:

6y = 132

Dividing both sides by 6, we get:

y = 22

Now we can use the equation y = 5x - 8 to solve for x:

22 = 5x - 8

Adding 8 to both sides, we get:

30 = 5x

Dividing both sides by 5, we get:

x = 6

Therefore, the smaller number is 6 and the larger number is 22.

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The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer:

5 + 8 × 4

Assuming "five and eight" means 5 + 8

Answer:84

Step-by-step explanation:

Answer:

84 hamburgers were sold

Answer:

obtuse angle,acute angle,right angle,straight angle hope it helps

Answer:

The answer is the 3rd one, not equivalent. 8x+4y=4(2x+y)

Answer:

\( x = 8\sqrt{2} \)

Step-by-step explanation:

Leg = x

Hypotenuse = 16

\( x\sqrt{2} = 16 \)

\( x = \dfrac{16}{\sqrt{2}} \)

\( x = \dfrac{16}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}} \)

\( x = \dfrac{16\sqrt{2}}{2} \)

\( x = 8\sqrt{2} \)

Answer:

r = 97.6

Step-by-step explanation:

3 - r/8 = -9.2

24 - r = - 73.6

- r = - 73.6 - 24

- r = - 97.6

r = 97.6

The probability of a prime number or a number greater than 3 coming up is given as follows:

5/6.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

When a dice is thrown, there are six possible outcomes, ranging from 1 to 6, and the desired outcomes are given as follows:

Hence the probability is given as follows:

5/6.

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The fraction of the original passengers remaining on the bus is 11/21.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A crowded bus makes several stops along a city street, with no passengers boarding the bus at any stop.

.At the 1st stop 1/3 of the passengers exit.

At the 2nd stop, 3/7 of the remaining passengers exit the bus.

Therefore, The fraction of the original passengers who remain on the bus is,

= [(1 - (1×1/3) - (1)×(1/3)×(3/7)].

= [ 1 - (1/3) - (3/21)].

= [ (2/3) - (3/21)].

= [(14 - 3)/21].

= 11/21.

So, 11/21 remains on the bus.

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Answer:

Step-by-step explanation:

diameter  = 12 cm

r = 12/2 = 6 cm

\(Area \ of \ semicircle = \dfrac{1}{2}\pi r^{2}\\\\\\=\dfrac{1}{2}* 3.14*6*6\\\\\\= 56.52 \ cm^{2}\)

We are given with a rectangle whose length is 27 miles , and breadth is (3y + 1) miles and we are asked to find it's area . As , we know that , the area of a rectangle with Length and Breadth , L and B is given by Area = L × B respectively . Now , using this same formula in our question we have ;

\({:\implies \quad \sf Area=27\times (3y+1)}\)

\({:\implies \quad \sf Area=27\times 3y + 27\times 1}\)

\({:\implies \quad \bf \therefore \quad \underline{\underline{Area=81y+27\:\: sq\:\: mi.}}}\)

Applying the sine rule the value of side w is calculated to be 6.2

The size of w is calculated using the sine rule which states that the ratio of a side and the opposite angles are equal

the formula is

Sin A / a = Sin B / b = Sin C / c

applying the formula for the problem

Sine W / w = Sine X / x

plugging in the values

Sine 38 / w = Sine 84 / 10

cross multiplying

w = 10 x Sin 38 / Sine 84

x = 6.185

x =  6.2 to the nearest tenth

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Answers:

3x + 40 =64

4x - 6 =26

Step-by-step explanation:

So we are dealing with 2 complementary angles with both add up to 90 degrees. We can write an equation that shows this:

(3x+40) + (4x-6) = 90

Combine like terms

7x + 34 =90

Isolate x

7x = 56

x = 8

Now that we found x, all we have to do is substitute it in the equations:

3x + 40 = ?

3(8) +40 = ?

24+40 = ?

64 = ?

4x - 6 = ?

4(8) - 6 = ?

32 - 6 = ?

26 = ?

Answer:

3x+40= 66

4x-6= 26

Step-by-step explanation:

3x+40+4x-6=90˚ (because the square on the angle represents a 90˚)

Add 4x and 3x

Which is 7x

40 minus 6 is 34

The equation now looks like this:

7x+34=90˚

Subtract 34 on both sides:

7x=56

Divide 7 on both sides:

x=8

For 3x+40

Substitute x with 8

the equation now looks like this:

24+40 Which is 66

For 4x-6

4 times 8 is 32

32 minus 6 which is 26

Hope this helps!

Answer:

???

Notes:

Hi, sorry, but I can't really do this if I don't know what 15 shirts cost, or if there isn't an equation of some sort. (Sorry again...)

Answer:

length=28 cm

the area = 196 cm²

Step-by-step explanation:

length = 4 × width

2×(4w+w) = 70

2×5w=70

10w=70

w= 7 cm

length = 4×7 = 28 cm

the area = 28 ×7 = 196 cm²

Answer:

54/3=18

Step-by-step explanation:

18/3=6

6/1=6

54/9=6

Answer:

hi

Step-by-step explanation:

1. Circle the two boats you picked for your trip.

the yacht and the tall ship (aka the pirate ship)

2. Make sense of the problem.

what do you know?

The tall ship makes the trip in 10 hours. The yacht makes the trip in 2.5 hours. The tall ship is 30 knots slower than the yacht.

what do you want to find out?

How fast is each boat traveling in knots (nautical miles per hour)?

what kind of answer do you expect?

probably just some numbers like 10 miles per hour or 40 miles per hour

Writing some expressions

3. Write an expression for the distance going to the island. Let x be the speed of the boat you are taking to the island. Distance is equal to speed times time. (2 points)

the expression would be D = 10(x-30), d is the distance. it could also be simplified to 10x - 300

4. Write an expression for the speed of the boat coming back from the island in terms of the other boat's speed. Let x be the speed of the boat you are taking to the island. (2 points)

so the yacht's speed would be S = x knots, s is for speed.

5. Write an expression for the distance returning from the island. Use the expression for speed you found in question 4. Remember that distance is equal to speed times time. (2 points)

the distance returning from the island would be D = 2.5x.

6. Each ship travels the same distance. Set the distances equal to each other to get the equation for the speed of the ship you are taking to the island. (1 point)

10x - 300 = 2.5x

7. Solve the equation from question 6 for x. What does this tell you? (5 points: 1 point for showing your work, 3 points for solving for x, 1 point for explaining the answer)

  10x - 300 = 2.5x  

10x - 300 + 300 = 2.5x + 300

  10x -2.5x = 300

   7.5x = 300

        x = 40

x is the speed of the yacht. (40 nautical miles per hour)

8. How fast does the second boat travel? Show your work. (2 points: 1 point for showing your work, 1 point for the answer)

the yacht travels at 40 nautical miles per hour and the tall ship travels at 100 (10x - 300) nautical miles per hour.

9. When you get to the island, you decide to take a kayak tour to a nearby reef. A kayak is a small boat you row with a paddle.

Find the speed for the kayak. Use one of these facts to help.

The steamboat's speed is 4 less than 8 times the speed of the kayak.

The tall ship's speed is 1 more than 3 times the speed of the kayak.

The yacht's speed is 5 less than 15 times the speed of the kayak.

Write and solve an equation for the speed of the kayak. Show your work. (5 points: 2 points for writing a correct equation, 3 points for the solution)

the equation for the speed of the kayak is 40 = 15x - 5, which in this case, x is the speed of the kayak

 40 = 15x - 5

  40 + 5 = 15x -5 + 5

 45 = 15x

   x = 3

therefore, the speed of the kayak is 3 nautical miles per hour.

10. The length of your trip to the island is 40 nautical miles less than 20 times the distance to the reef.

It's 2:00 p.m. now, and your boat leaves the island at 7:30 p.m. Will you be able to kayak to the reef and back by then?

If so, how long will you have to spend at the reef?

If not, how late will you be for the return trip?

Explain how you plan to solve this problem. Then solve the problem, showing all work. (5 points: 2 points for the explanation of the plan, 1 point for deciding if you will make it back to the island on time, and 2 points for determining either how long you can spend at the reef or how late you'll be)

the distance to the island is 100 nautical miles, so the expression would be 100 = 20x -40, with x being the distance to the reef.

we can solve for x by doing:

100 = 20x -40

100 + 40 = 20x - 40 + 40

140 = 20x

140 / 20 = x

    x = 7

so the distance from my starting point to the reef will be 7 nautical miles, and the distance from the island to the reef would be 93 nautical miles.in that case, I would be like a day and a half late, but if you are trying to say that the ship is waiting for me at the starting point of my "adventure", then I would not be late if I kayak from my starting point to the reef, in fact, I could stay at the reef for like 50 min, because:

7 / 3 = 2 1/3 hours.

2 1/3 x 2 = 4 2/3 hours or 280 min. (to the reef and back)

7:30 p.m. - 2:00 p.m. = 5 1/2 hours or 330 min. (how much time I have till the ship leaves)

330 - 280 = 50 min. (how many min I can spend at the reef)

This is for the people that want to find out how to find the distance to the island.

jamescodwell answered all the questions  correctly btw.

Step-by-step explanation:

Distance travelled divided by trip time = speed

trip time multiplied by speed = distance travelled

So the steamboat makes the trip in 5 hours travelling at a speed of 20 knots.

5 * 20 = 100 The trip to the island is 100 nautical miles.

Answer: 363+368=731

Step-by-step explanation:

The meaning of the derivative f'(8) is the rate of change of the quantity of coffee sold with respect to the price per pound when the price is $8 per pound.

It represents how the quantity of coffee sold changes with respect to changes in the price per pound, when the price per pound is $8.

In mathematics, the derivative of a function is a measure of how the value of the function changes with respect to changes in one of its variables. In other words, the derivative gives the rate of change of a function with respect to its independent variable.

The derivative can be thought of as the slope of the tangent line to the function at a particular point. It can be calculated using limits, differential calculus, or other methods. The derivative is represented by the symbol "d/dx" for a function of a single variable x, where d/dx represents the rate of change of the function with respect to x.

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