If the sides of a right triangle are 6 feet and 8 feet, what is the length of the hypotenuse? *

The slope means that the rate of change of height of the unmanned aerial vehicle after it begins its descent from cruising altitude is -0.2 ft/minutes.

The y-intercept means that the height before the descent was; 62 ft

The slope is the change in y-values divided by the corresponding change in x -values. Meanwhile, the y-intercept is the point at which x = 0 or where there graph crosses the y-axis.

In this case, the formula for the slope is;

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

Slope = (60 - 62)/(10 - 0)

Slope = -2/10

Slope = -0.2

From the table, the y-intercept is at y = 62

Thus, the slope means that the rate of change of height of the unmanned aerial vehicle after it begins its descent from cruising altitude is -0.2 ft/minutes

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Answer:

110

Step-by-step explanation:

you place 30 in the place of X, and it becomes 4×30-10. in PEMDAS, multiplication goes first and 4×30=120. 120-10=110

Answer: moderate, C, B

Step-by-step explanation:

A)  A shows a moderate negative correlation.  It is moderate because the scattered points are sort of close to the line so it has moderate/medium correlation.  It is also negative because it has a negative slope

B) C shows the strongest correlation because the points around the line are tight and close.

C)  B should not have been drawn.  The  correlation is very weak.  You do know where the line should be because the points are all over the place.

Answer:

  4 cm

Step-by-step explanation:

You want the length of the smaller of two similar pieces of cardboard when the larger has an area of 150 cm² and a length of 10 cm, while the smaller has an area of 24 cm².

The scale factor for lengths is the square root of the scale factor for areas. It will be ...

  √(24/150) = 0.4 . . . . . . = smaller / larger

The smaller cardboard has a length of ...

  0.4 × 10 cm = 4 cm

__

Additional comment

Sometimes folks like to write this as a proportion:

  \(\dfrac{\text{smaller length}}{\text{larger length}}=\sqrt{\dfrac{\text{smaller area}}{\text{larger area}}}\)

Solving this for "smaller length" gives the expressions we used above:

  smaller length = (larger length) × √(smaller area/larger area)

Answer:

The consumer surplus when the sales level is 250 is approximately $2,016,111.11.

Step-by-step explanation:

To find the length of the cardioid r = 1 + sin(θ) over the interval [0, 3], we can use the arc length formula for polar curves:

L = ∫[a to b] √(r^2 + (dr/dθ)^2) dθ

In this case, a = 0 and b = 3, so we have:

L = ∫[0 to 3] √((1 + sin(θ))^2 + (d(1 + sin(θ))/dθ)^2) dθ

Simplifying:

L = ∫[0 to 3] √(1 + 2sin(θ) + sin^2(θ) + cos^2(θ)) dθ

L = ∫[0 to 3] √(2 + 2sin(θ)) dθ

Now, let's evaluate this integral:

L = ∫[0 to 3] √2√(1 + sin(θ)) dθ

Since √2 is a constant, we can pull it out of the integral:

L = √2 ∫[0 to 3] √(1 + sin(θ)) dθ

Unfortunately, there is no simple closed-form solution for this integral. However, you can approximate the value of L using numerical integration methods or calculator software.

Regarding the second part of your question, to find the consumer surplus when the sales level is 250 for the demand function P = 2000 - 0.2x - 0.01x^2, we need to calculate the area between the demand curve and the price axis up to the sales level of 250.

Consumer surplus is given by the integral of the demand function from 0 to the sales level, subtracted from the maximum possible consumer expenditure. In this case, the maximum possible consumer expenditure is given by P = 2000.

The consumer surplus is:

CS = ∫[0 to 250] (2000 - (0.2x - 0.01x^2)) dx

Simplifying:

CS = ∫[0 to 250] (2000 - 0.2x + 0.01x^2) dx

CS = [2000x - 0.1x^2 + 0.01x^3/3] evaluated from 0 to 250

CS = (2000(250) - 0.1(250)^2 + 0.01(250)^3/3) - (0 + 0 + 0)

CS = (500000 - 62500 + 5208333.33/3)

CS = 500000 - 62500 + 1736111.11

CS ≈ 2016111.11

Therefore, the consumer surplus when the sales level is 250 is approximately $2,016,111.11.

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The 10.547 feet up the wall will the top of the ladder be if the 11-foot ladder is placed against the wall. The ladder is on ground level at an angle of 73.5° to the horizontal.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

Length of the ladder = 11 foot

The angle between ladder and horizontal = 73.5 degree

The height of the wall, the top of the ladder be(h):

From the sin ratio:

sin73.5 =  h/11

h = 11sin73.5 = 10.547 feet

Thus, the 10.547 feet up the wall will the top of the ladder be if the 11-foot ladder is placed against the wall. The ladder is on ground level at an angle of 73.5° to the horizontal.

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All polar coordinates of point P where P = ordered pair 7 comma pi divided by 3 is (7, π/3 + 2nπ) or (-7, π/3 + (2n + 1)π)

In polar coordinates, the radius is always positive, so we take the positive value of 7. The angle can be any multiple of 2π added to π/3, giving us π/3 + 2nπ, where n is an integer. Additionally, since we have the option of moving in the negative direction, we can also add (2n + 1)π to the angle, resulting in π/3 + (2n + 1)π. Therefore, the correct answer is (7, π/3 + 2nπ) or (-7, π/3 + (2n + 1)π).

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Step-by-step explanation:

|x|-2=7 -------equation 1

/x/ = 5+2

|x| = 7

x = +- 7

check:

put x =-7 in equation one

|-7|-2 = 5

7-2=5

5=5

hence correct

not put x= 7 in eq 1

|7| - 2 = 5

7-2 = 5

5= 5

just remember that when we take a variables absolute value so we must keep plus minus sign on other side whereas if we take absolute value of constant then its always positive.

Answer:

i believe the answer is A.

Step-by-step explanation: Because the angle PQS is not a 90 degree angle it should equal 180 degrees, it is now lowered down to the answers A. and B. Answer B. has 2x and answer A. has just x. if it were to be 2x then the x would  have to represent 30 degrees but the point plotted x does not equal 30 degrees therefore leaving the last answer as A. x-60=180

Answer:

B.

Step-by-step explanation:

First find the other two angles in the triangle using supplementary angles.

They are 90° and 55°

Now just subtract them from 180

180 - 90 - 55 = 35°

Answer: y=18x+150

You would make sure x was for x since that's the amount she gets paid per hour, and you would add 150 to it because that's her sign on bonus, the total would be represented by y.

The probability that the first 5 locations are in water and the last 2 locations are on land is 0.0010.

The probability of selecting a water location is 71%, which means the probability of selecting a land location is 29%. To find the probability of a specific sequence of locations, we multiply the probabilities of each individual event.

For the first 5 locations to be in water, the probability is (0.71)^5 since each location is independent. Similarly, the probability of the last 2 locations being on land is (0.29)^2.

To find the probability of both events occurring, we multiply these probabilities together: (0.71)^5 * (0.29)^2 = 0.0010.

Therefore, the probability that the first 5 locations are in water and the last 2 locations are on land is 0.0010.

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Answer:

Step-by-step explanation:

$15 × 0.75 × 1.04 = $11.70

$25 × 0.75 × 1.04 = $19.50

$37 × 0.75 × 1.04 = $28.86

$65 × 0.75 × 1.04 = $50.70

Answer:

Keep going! If needed, round your answer to the nearest cent.

per notebook

per pound

5 notebooks for $7.37

14 pounds of broccoli for $2.24

$12.48 for 16 quarts of potting soil

6-pack of pens for $9.69

per quart

per pen

Answer:

slope: 4

y-intercept: 2

Step-by-step explanation:

We are given an equation, y = 4x + 2, and we are asked to find the slope and y-intercept of the line. Looking carefully, we can see that the equation is given to us in slope-intercept form.

Slope-intercept form is:

y = mx + b

where m is the slope and b is the by-intercept.

Knowing this, we can find that 4 is the slope of the line and 2 is the y-intercept.

I hope you find my answer and explanation to be helpful. Happy studying.

Answer: Mila is climbing 28 feet per hour faster than Malik.

Step-by-step explanation:

Mila is climbing 721 feet per hour.

hope this helps :)

Since the relationship is proportional, the line will pass through the origin (0, 0). This means that if there is a bag with zero weight, it would have zero cost.

To graph the proportional relationship between the weight and total cost of the bags of lemons, follow these steps:

1. Identify the independent variable and the dependent variable. In this case, the weight of the bag (in pounds) is the independent variable, and the total cost of the bag (in dollars) is the dependent variable.

2. Create a coordinate plane. Label the x-axis as "Weight (pounds)" and the y-axis as "Total Cost (dollars)".

3. Plot the data points. For the first bag, with a weight of 2.4 pounds and a cost of $5.28, plot a point at (2.4, 5.28) on the coordinate plane. For the second bag, with a weight of 2.7 pounds and a cost of $5.94, plot a point at (2.7, 5.94) on the coordinate plane.

4. Draw a straight line passing through the two plotted points. This line represents the proportional relationship between the weight and total cost of the bags of lemons.

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Answer:

n=7

Step-by-step explanation:

it told me I couldn't send this unless it was 20 words so that's why I'm typing this lol but the answer is 7

1.

a) metres to centimetres :

multiply length by 100

b) metres to millimetres:

multiply length by 1000

c) kilograms to grams:

multiply the mass value by 1000

d) litres to millilitres :

multiply volume by 1000

2.

a) 3 m = 3× 100 = 300 cm

b) 28 cm = 28 × 10 = 280 mm

c) 2.4 km = 2.4 × 1000

= 24 × 10^-1 × 10^3

= 24 × 10^2 =2400 m

d) 485 mm =485 / 10

= 485 / 10 ^1

= 485 × 10 ^-1

= 48.5 cm

e) 35 cm = 35 / 100

= 35 /10^2

= 35 × 10 ^ -2

= 0.35 m

f) 2.4 m = 2.4 / 1000

= 24 × 10 ^-1 / 10^3

= 24 × 10^-1 × 10 ^-3

= 24 × 10 ^ -4

= 0.0024 km

g) 2495 mm = 2495 /1000

= 2495 /10^ 3

= 2495 × 10 ^-3

=2.495 m

Okay, so it sounds like you just need a die to do this assignment. If you need a website, you can use this: https://freeonlinedice.com/#dice

There should already be one die here. Just click "roll" and record the value at the top of the screen labeled "total." Do this 30 times and write down the values each time.

I am sorry for not giving you the answer right away, I would but my school blocked the website of the link I put above.

Answer:

40:3

Step-by-step explanation:

1.6kg:120g

1600g:120g

1600:120

160:12

80:6

40:3

Answer:

1. 35 km

2. 1 cm to 5m

3. 6 cm

4. \(42^\circ\)

5. 16.73 m

Step-by-step explanation:

Solution 1.

Reading of map scale = 1cm:5km

i.e. 1 cm is equivalent to 5 km

Measurement of map  = 7 cm

Actual distance = Measurement of map \(\times 5\)

Actual distance = 7 \(\times 5\) = 35 km

-------------------

Solution 2.

Length of dining hall = 35 m

Measurement of map = 7 cm

Scale = Measurement of map : Length of dining hall (i.e. ratio)

Scale = 7 cm :35 m = 1 cm : 5 m

-------------------

Solution 3.

Length of building = 30 m

Scale = 1 cm to 5m

5 m is equivalent to 1 cm on scale

1 m is equivalent to \(\frac{1}{5}\) cm on scale

30m is equivalent to \(\frac{1}{5} \times 30\) = 6 cm on scale

-------------------

Solution 4.

Angle of elevation of A from B = \(42^\circ\)

Angle of depression of B from A = ?

Please refer to the image attached, we can clearly observe that both the angles (i.e. angle of elevation from A to B and angle of depression from B to A )will be equal.

Angle of depression of B from A = \(42^\circ\)

-------------------

Solution 5.

Given that:

String length, or hypotenuse of triangle BC= 25 m

Angle of string with horizontal, \(\angle B = 42^\circ\)

Please refer to the attached image for the clear understanding of the situation.

To find:

Height, AC = ?

We can use trigonometric identity:

\(sin\theta = \dfrac{Perpendicular}{Hypotenuse}\)

OR

\(sinB = \dfrac{AC}{BC}\\\Rightarrow sin42^\circ = \dfrac{AC}{25}\\\Rightarrow AC = 25 \times 0.67\\\Rightarrow AC = 16.73 m\)

============

So, the answers are:

1. 35 km

2. 1 cm to 5m

3. 6 cm

4. \(42^\circ\)

5. 16.73 m

An appropriate theorem to show that the given set, W, is a vector space. A specific example can be

\(\left[\begin{array}{ccc}p\\q\\r\end{array}\right]\) , -p- -3q = s  and 3p = -2s - 3r

Sets represent values ​​that are not solutions. B. The set of all solutions of a system of homogeneous equations OC.

The set of solutions of a homogeneous equation. Thus the set W = Null A. The null space of n homogeneous linear equations in the mx n matrix A is a subspace of Rn. Equivalently, the set of all solutions of the unknown system Ax = 0 is a subspace of R.A.

The proof is complete because W is a subspace of R2. The given set W must be a vector space, since the subspaces are themselves vector spaces. B. The proof is complete because W is a subspace of R. The given set W must be a vector space, since the subspaces are themselves vector spaces.

The proof is complete because W is a subspace of R4. The given set W must be a vector space, since the subspaces are themselves vector spaces. outside diameter. The proof is complete because W is a subspace of R3. The given set W must be a vector space, since the subspaces are themselves vector spaces.

Let W be the set of all vectors of the right form, where a and b denote all real numbers. Give an example or explain why W is not a vector space. 8a + 3b -4 8a-7b. Select the correct option below and, if necessary, fill in the answer boxes to complete your selection OA. The set pressure is

S = {(comma separated vectors as required OB. W is not a vector space because zero vectors in W and scalar sums and multiples of most vectors are not in W because their second (intermediate) value is not equal to -4. OC. W is not a vector space because not all vectors U, V and win W have the properties

u +v =y+ u and (u + v)+w=u + (v +W).

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Answer:

y = 5/4x - 4

Step-by-step explanation:

First, find the slope by doing change in y/change in x

You have the points (4, 1) and (0, -4), so the slope would be:

-4 - 1 / 0 - 4 = -5 / -4 = 5/4

Then, find the y-intercept

It gives you that the y-intercept is (0, -4).

Now put the equation in the form y = mx + b where m is the slope and b is the y-intercept.

You have that m = 5/4 and b = -4, so it would be y = 5/4x - 4.

When selecting a random sample of people to survey, Julio should consider a few important elements. Firstly, he should ensure that his sample is representative of the population he is trying to study. This means that he should try to include a diverse range of people from different ages, genders, socioeconomic backgrounds, and so on.

Additionally, he should consider the size of his sample, as larger samples generally provide more accurate results. Finally, he should strive for a random sample, where each person in the population has an equal chance of being selected, to avoid bias and ensure that his results are generalizable to the larger population. In summary, when selecting a random sample for his survey, Julio should consider factors such as representativeness, sample size, and randomness to ensure accurate and reliable results.


1. Representativeness: Ensure the sample accurately represents the population he's studying, covering various demographics such as age, gender, and socioeconomic status.

2. Sample Size: Choose an appropriate sample size (e.g., 100 people) to ensure the survey results are statistically significant and minimize sampling error.

3. Randomization: Use a random selection method, like a random number generator or drawing names from a hat, to ensure each individual has an equal chance of being chosen.

4. Avoid Bias: Make sure the selection process is free from personal or external influence, so the sample remains truly random and unbiased.

By considering these elements, Julio can ensure his random sample provides accurate and reliable data for his newspaper article.

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Answer: Stella has a reasonable Answer

Step-by-step explanation:

When you add up all of the Costs, you get an answer of $20.80

You Divide $20.80 by 3

And you get your answer of 6.93333

Which estimates around 7 dollars making Stella Right!

Hope this helps :)

Answer:

15.4269444444

Step-by-step explanation:

The proof that the Quadrilateral WXYZ is a rectangle is shown below

To prove that Quadrilateral WXYZ is a rectangle, we need to show that it has four right angles.

First, we can find the slopes of each pair of opposite sides to determine if they are perpendicular.

The slope of WX is:

m(WX) = (y2 - y1)/(x2 - x1) = (-2 - 1)/(2 - (-1)) = -1

The slope of YZ is:

m(YZ) = (y2 - y1)/(x2 - x1) = (6 - 3)/(4 - 7) = -1

Since the slopes of WX and YZ are equal , we know that they are opposite sides.

Now we can use the distance formula to check if the sides of the quadrilateral are congruent. The length of WX is:

√((2 - (-1))^2 + (-2 - 1)^2) = √18

The length of YZ is:

√((7 - 4)^2 + (3 - 6)^2) = √18

The length of WY is:

√((7 - (-1))^2 + (3 - 1)^2) = √68

The length of XZ is:

√((4 - 2)^2 + (6 - (-2))^2) = √68

We can see that opposite sides WX and YZ have the same length, as do opposite sides WY and XZ.

So, the quadrilateral is a rectangle

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The algebraic expression for the trigonometric expression sin (tan⁻¹ (x)) is given by x/(√(1 + x²)).

Given the trigonometric expression is,

sin (tan⁻¹ (x))

Let y = tan⁻¹ (x)

tan y = x

tan² y = x²

sec² y - 1 = x²

sec² y = 1 + x²

cos² y = 1/(1 + x²)

1 - sin²y = 1/(1 + x²)

sin² y = 1 - 1/(1 + x²) = (1 + x² - 1)/(1 + x²) = x²/(1 + x²).

sin y = x/(√(1 + x²))

y = sin⁻¹ [x/(√(1 + x²))]

So, now the trigonometric expression becomes

sin (tan⁻¹ (x)) = sin y = sin {sin⁻¹ [x/(√(1 + x²))]} = x/(√(1 + x²)).

Hence, the algebraic expression for the trigonometric expression sin (tan⁻¹ (x)) is given by x/(√(1 + x²)).

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