Suppose that the radius of the base of a cone is R. Suppose, moreover, that the volume
of the cone is the same as the volume of the sphere with radius R (same as the base radius of
the cone). How many times is the height of the cone larger than R?

163. The distance between A(-5, 6) and B(5, -5) is: AB ≈ 14.9 units

164. Applying the Pythagorean theorem, we have: Diagonal ≈ 21.2 ft.

165. Marissa's final answer is wrong. It should be, c = √676 = 26 units.

166. Missing side = 29 ft.

The Pythagorean theorem states that c² = a² + b², given that a and b are shorter legs and c is the hypotenuse or longest leg of the right triangle.

163. The distance between A(-5, 6) and B(5, -5):

AB = √[(5−(−5))² + (−5−6)²]

AB = √221

AB ≈ 14.9 units

164. Apply the Pythagorean theorem to find the diagonal:

Diagonal = √(15² + 15²) ≈ 21.2 ft.

165. The answer Marissa got is wrong. The final answer which is the square root of 676 is:

c = √676 = 26 units.

166. Missing side = √(20² + 21²) = 29 ft.

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Answer:

+ 0.5 then 1.5 n

Step-by-step explanation:

If a value of 80.2° is added to the data, the range stays at 48º.

The mean of the data-set would change the most, and it would assume a value of 84º.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations. The range of a data-set is given by the difference between the highest value of the data-set by the smallest value of the data-set.

here, we have,

The highest and smallest high temperatures for the city are given as follows:

Smallest: 57º.

Highest: 105º.

Hence the range is obtained as follows:

105 - 57 = 48º.

80.2º would be neither the highest nor the smallest value in the data-set, which would then remain constant.

As it involves all values, it would be changed the most by changing the value of 58º to 101º, and would then assume a value of 84º.

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Answer:

a) 8 b)9 c)1 d) 3

Step-by-step explanation:

The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.

Let's solve the system of linear equations correctly.

The given system of linear equations is:

x = y + 3z = 6

x - 2y = 5

2x - 2y + 5z = 9

To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:

From equation 1, we have:

x = y + 3z

Substituting this value of x in equation 2:

(y + 3z) - 2y = 5

y + 3z - 2y = 5

-z + 3z = 5 - y

2z = 5 - y

Now, let's substitute the value of x in equation 3:

2(y + 3z) - 2y + 5z = 9

2y + 6z - 2y + 5z = 9

11z = 9

Simplifying the equation, we find:

z = 9/11

Now, substituting this value of z back into the equation 2z = 5 - y, we get:

2(9/11) = 5 - y

18/11 = 5 - y

18/11 - 5 = -y

18/11 - 55/11 = -y

-37/11 = -y

y = 37/11

Finally, we can substitute the values of y and z into equation 1 to find the value of x:

x = y + 3z

x = 37/11 + 3(9/11)

x = 37/11 + 27/11

x = 64/11

Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).

The system has exactly one solution.

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The value of x in the pentagon JKLMN is 7.2.

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

The pentagons ABCDE and JKLMN are similar.

when two figures have the same shape but their sizes are different, then such figures are called similar figures.

We need to find the value of x.

1/1.8=4/x

Apply cross multiplication

x=4×1.8

x=7.2

Hence, the value of x in the pentagon JKLMN is 7.2.

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PART A: Linda has $4.41 more than Enrique after one year.

PART B: Enrique has $12.10 more than Linda after the second year.

PART A: After one year, we can calculate the amount of money each person has in their respective accounts.

For Linda's account:

Principal amount = $610

Interest rate = 1.2%

\(Interest $ earned = Principal $ amount \times (Interest rate/100) = $610 \times (1.2/100) = $7.32\)

\(Total $ amount after one year = Principal amount + Interest earned = $610 + $7.32 = $617.32\)

For Enrique's account:

Principal amount = $590

Interest rate = 3.9%

\(Interest $ earned = Principal amount \times (Interest rate/100) = $590 \times (3.9/100) = $22.91\)

Total amount after one year = Principal amount + Interest earned = $590 + $22.91 = $612.91

Comparing the two amounts, after one year Linda has more money.

The difference in the amount is:

$617.32 - $612.91 = $4.41

Therefore, Linda has $4.41 more than Enrique after one year.

PART B: After a second year, we need to calculate the amounts again.

For Linda's account:

Principal amount = $617.32

Interest rate = 1.2%

\(Interest earned = Principal amount \times (Interest rate/100) = $617.32 \times (1.2/100) = $7.41\)

Total amount after the second year = Principal amount + Interest earned = $617.32 + $7.41 = $624.73

For Enrique's account:

Principal amount = $612.91

Interest rate = 3.9%

\(Interest earned = Principal amount \times (Interest rate/100) = $612.91 \times (3.9/100) = $23.92\)

Total amount after the second year = Principal amount + Interest earned = $612.91 + $23.92 = $636.83

Comparing the two amounts, after the second year Enrique has more money.

The difference in the amount is:

$636.83 - $624.73 = $12.10

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Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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Answer:  (if that's the question?)

SARAH:: 2 rocks

CAMILLA:: 6 rocks

ZACHARY:: 24 rocks

Step-by-step explanation:

If Sarah has 2 rocks and Camilla has 3 times as many, then Camilla has 6 rocks because 2*3= 6

And if Camilla has 6 rocks while Zachary has four times as many as Camilla, then Zachary has 24 rocks because 6*4= 24

(hope this helps :)

It sounds like you're asked to find c such that f(x), defined by

\(f(x)=\begin{cases}cx^2+8x&\text{for }x<5\\x^3-cx&\text{for }x>5\end{cases}\)

is continuous at x = 5.

With the strict inequalities given in the definition, this is not possible. So you probably meant to use ≤ or ≥ in one of the pieces of the definition.

In order for f(x) to be continuous at x = 5, the limit from either side as x approaches 5 must be the same.

We have

\(\displaystyle\lim_{x\to5^-}f(x)=\lim_{x\to5}(cx^2+8x)=25c+40\)

and

\(\displaystyle\lim_{x\to5^+}f(x)=\lim_{x\to5}(x^3-cx)=125-5c\)

Then

\(25c+40=125-5c\implies30c=85\implies c=\dfrac{85}{30}=\boxed{\dfrac{17}6}\)

Answer:

y = 5

Step-by-step explanation:

\(14y-7y=35\\7y=35\\y=5\)

14 minus 7 is 7

7Y is equal to 35

divide both sides by 7 is equal to 5

Answer:

x = 139

Step-by-step explanation:

Isosceles triangle.

Let the equal angles = y

y + y + 98 = 180   {Sum of all the angles of triangles}

  2y + 98 = 180

          2y = 180 - 98

          2y = 82

           y = 82/2

          y = 41

x = 41 + 98     { exterior angles equals the sum of interior opposite angles}

x = 139

Answer - 12%

6/50 = 12/100

Answer:

x = 29.44

y = 34

Step-by-step explanation:

For this problem, we will simply use trigonometry to find the values of y and x for the given triangle.

The two trigonometric functions we will use are tangent and sine.

The general form for tangent is:

tan (Θ) = opposite / adjacent

The general form for sine is:

sin (Θ) = opposite / hypotenuse

For our given triangle, let's solve for x.

tan (30) = 17 / x

x * tan(30) = (17 / x) * x

x tan(30) = 17

x tan(30) * ( 1 / tan(30) ) = 17 * ( 1 / tan(30) )

x = 17 / tan(30)

x = 29.44

Now, let's solve for y.

sin (30) = 17 / y

y * sin(30) = (17 / y ) * y

y sin (30) = 17

y sin (30) * ( 1 / sin(30) ) = 17 * ( 1 / sin(30) )

y = 17 / sin(30)

y = 34

Hence, the values of x and y in our triangle are as follows:

x = 29.44

y = 34

Cheers.

Answer: 28.25%

Step-by-step explanation:

113/400=0.2825=28.25%

Any line with a slope different than 3 will intercept the given line only once.

The answer will be any line that is not parallel (nor the same) to the given line.

Remember two lines are parallel if the lines have the same slope and different y-intercept

In this case, the given linear equation is:

6x - 2y = 10

y = 3x - 5

So the slope is 3 and the y-intercept is -5.

Then, any line with a slope different than 3 will intercept this line only once.

An example can be:

y = 314*x

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Answer:

Answer is the first one :)

Step-by-step explanation:

√(-7-5)² + (-7-9)²

answer is 20

hope this helps

Answer:

A.

Step-by-step explanation:

In the attached file

Answer:

The answer would be 9 - x because you can see the word fewer is in the problem and that means it's subtraction, and since we don't know what the number is they're subtracting by, we'd put x

Step-by-step explanation:

Survey was wrong: holiday, systematic sample, 6 similar flights. To improve: questionnaire, various times/locations, entrance, different days.

The problems with the survey conducted by the airline are:

1) Conducting the survey on a holiday weekend is not representative of the entire population of air travelers;

2) The survey uses systematic sampling which may not accurately reflect the entire population;

3) The survey was only conducted on 6 similar flights and does not represent the entire population of air travelers.

To improve the survey, the following steps can be taken:

1) Ask travelers to fill out a questionnaire;

2) Conduct the survey at the entrance to the airport;

3) Conduct the survey during different times of the year;

4) Use various days of the week to conduct the survey;

5) Conduct the survey using flights to and from various locations.

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Answer:

-b-6

Step-by-step explanation:

4(1-2b)+7b-10 multiply inside the parenthesis with 4

4 - 8b + 7b - 10 now add like terms

-b - 6

Answer:

-b-6

Step-by-step explanation:

\(4(1-2b)+7b-10\\\)

Expand

\(4\left(1-2b\right):\quad 4-8b\)

\(=4-8b+7b-10\)

Simplify

\(\mathrm{Simplify}\:4-8b+7b-10:\\\\\quad -b-6\)

Answer:

Step-by-step explanation:

Volume = Bh

Turn the shape so the trapezoid is on the bottom/base

h=18   for overall shape

B = area of base, trapezoid

B = 1/2 (b₁ + b₂) h  

b₁ = 11

b₂ = 25

h = 24   for trapezoid

B = 1/2 (11 + 25)(24)

B = 432

V = Bh

V = (432)(18)

V= 7776 in³

Answer:

8.   10

11.   10

Step-by-step explanation:

put 5 instead of b

8.  (15 - b)

    = (15-5)

   = (10)

11. b +b

  = 5 +5

  = 10

A. $4500

To find the maximum possible income, we need to find the maximum value of R with the given formula. In this case, you can find the maximum value of R by setting the derivative of R with respect to d to 0 and solving for d.

The derivative of R after d is

R' = -50(d - 3.5)

Setting this to 0 and solving for d yields:

0 = -50 (days - 3.5)

d = 3.5

Substituting this value of d into the original R formula yields:

R = -50 (3.5 - 3.5) + 4500

= 4500

So the maximum possible income is 4500 USD this is the correct answer among the four choices

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Looks like f(x, y) = cot⁻¹(xy), as in the inverse cotangent.

If you're like me and you don't remember the derivative of the inverse trig functions, we can derive it as follows. Let y = cot⁻¹(x), so that for appropriate x we can write cot(y) = x. By the chain rule, differentiating both sides gives

-csc²(y) y' = 1

y' = -sin²(y) = -sin²(cot⁻¹(x)) = - 1 / (x² + 1)

Next, recall that the derivative of a function f(x, y) at a point (a, b) in the direction of a vector v is given by

∇ f(a, b) • v

Compute the gradient ∇ f(x, y) :

∇ f(x, y) = - y / ((xy)² + 1) i - x / ((xy)² + 1) j

At the point P, we have

∇ f(x, y) = - 8/17 i - 8/17 j

So, the derivative of f at P along v = - 4 i + 5 j is

(- 8/17 i - 8/17 j) • (- 4 i + 5 j) = - 8/17

Answer:

Julio's gross income before the tax deductions is $ 405.

Step-by-step explanation:

Given that Julio has a net pay of $ 537.00 each paycheck, and he pays $ 142.00 in pre-tax deductions and taxes each paycheck, to determine what is Julio's gross income before the tax deductions the following calculation must be performed:

547 - 142 = X

405 = X

Therefore, Julio's gross income before the tax deductions is $ 405.