If y varies directly as x, which equation represents when x = 36 and y = 12?

Answer:

As x → ∞, f(x) → ∞

As x → -∞, f(x) → 3

Step-by-step explanation:

This question is asking for the end behavior of the graph. In this case, as x increases f(x) also increases; therefore, they both approach positive infinity at the same time. Additionally, the horizontal asymptote of the graph is 3. This means that as x approaches -∞, f(x) will approach the asymptote, 3.

15.05x6= 90.3

171.00-90.3=80.7

Given:

The length of the ladder  = 12 ft

The angle of ladder with ground = 60 degrees

To find:

How far up the building the ladder will reach.

Solution:

Using the given information draw a figure as shown below.

We need to find the vertical distance between the top of ladder and the ground.

Let x be the required distance.

In a right angle triangle,

[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

In the below triangle ABC,

[tex]\sin A=\dfrac{BC}{AC}[/tex]

[tex]\sin 60^\circ=\dfrac{x}{12}[/tex]

[tex]\dfrac{\sqrt{3}}{2}=\dfrac{x}{12}[/tex]

Multiply both sides by 12.

[tex]\dfrac{\sqrt{3}}{2}\times 12=x[/tex]

[tex]6\sqrt{3}=x[/tex]

Therefore, the ladder will reach [tex]6\sqrt{3}[/tex] ft far up the building.

Answer:

33 plants

Step-by-step explanation:

6 x 550 = 3300

3300/100 = 33

Answer:

268 m²

Step-by-step explanation:

8x26=208

3x10x2=60

208+60=268

Answer:

101

Step-by-step explanation:

180-79

Answer:

option 1

Step-by-step explanation:

[tex]volume \ of \ cone = \frac{1}{3} \pi r^2 h \\r = 4\\h = 8\\so, volume = \frac{1}{3} \pi (4^2)( 8)[/tex]

Answer:

16m 24m and 24m

Step-by-step explanation:

Given the fact that it's a rectangle, and 1 side is 16m, we know that 1 of the other sides will be 16m. After that and some simple subtraction, we get the other 2 sides are 24m.

Answer:

Step-by-step explanation:

11.5 is greater than -12.5

Answer: -12.5 is greater

-

Step-by-step explanation:

Answer: 25 total apples

Step-by-step explanation:

so you would set up an equation where 20 = 0.80x

20 is 80 percent of the total (x)

so then solve for x, which would be 20 divided by 0.8

That's 25

Given:

Consider the rule of a sequence is:

[tex]T_n=\dfrac{n^2-n}{2}[/tex]

To find:

The 6th term generated by the given rule.

Solution:

We have,

[tex]T_n=\dfrac{n^2-n}{2}[/tex]

Substituting [tex]n=6[/tex] in the above rule, we get

[tex]T_6=\dfrac{6^2-6}{2}[/tex]

[tex]T_6=\dfrac{36-6}{2}[/tex]

[tex]T_6=\dfrac{30}{2}[/tex]

[tex]T_6=15[/tex]

Therefore, the 6th term generated by the given rule is 15.

Answer:

(4.5, 0.3125)

Step-by-step explanation:

given that

The mean is 4.5 inches

the standard deviation is 1.25 inches

and, the sample of 16 rabbits is selected

we need to find out the approximate distribution

so,

= (4.5, 1.25 ÷√16)

= (4.5, 0.3125)

hence, the same is to be considered

Answer:

Step-by-step explanation:

When interest compounds once per year, the formula for this is

[tex]A(t)=P(1+r)^t[/tex] where P is the initial investment, r is the interest rate at which it grows, and t is the time in years. Therefore, our model is

[tex]A(t)=6500(1+.03)^t[/tex] or simplified a bit:

[tex]A(t)=6500(1.03)^t[/tex]

Answer:

x  =  28 m

y  =  14  m

A(max)  =  392 m²

Step-by-step explanation:

Rectangular garden    A (r ) =  x * y

Let´s call x the side of the rectangle to be constructed with a rock wall, then only one x side of the rectangle will be fencing with wire.

the perimeter of the rectangle is  p  =  2*x  +  2*y    ( but in this particular case only one side x will be fencing with wire

56   =   x    +  2*y      56   -  2*y  =  x

A(r)   =  ( 56  -  2*y ) * y

A(y ) =  56*y  -  2*y²

Tacking derivatives on both sides of the equation we get:

A´(y )  =  56  - 4 * y        A´(y) = 0     56  -  4*y  =  0    4*y  =  56

y =  14 m

and x  =  56  - 2*y    =  56 - 28  = 28 m

Then dimensions of the garden:

x  =  28 m

y  =  14  m

A(max)  =  392 m²

How do we know that the area we found is a local maximum??

We find the second derivative

A´´(y)  = - 4     A´´(y)  <  0   then the function A(y) has a local maximum at y = 14 m

Answer:

x = -4,      y = 8

Step-by-step explanation:

y = 2x + 16 -----(1)

2x - 7y = - 64 -------(2)

Substitute (1) in (2)

2x - 7(2x + 16) = - 64

2x - 14x - 112 = - 64

-12x = -64 + 112

-12x = 48

x = -4

Substitute x = -4 in (1)

y = 2(-4) + 16

y = -8 + 16

y  =8

Answer:

It is -4,8.

Step-by-step explanation:

y=2x +16

{

-7y=-2x-64

-6y=-48

y=8 then using substitution you will get x=-4

Answer:

B) 204

Step-by-step explanation:

Rectangle 12 * 12 = 144

+

(2) Triangle A=h (b/2) = 12*(5/2) = 30 each

Answer:

make x=0 then y=-3-7(0)= (0 -3)

Answer:

y=-3

Step-by-step explanation:

see steps below:)

Answer:

a. Flipping a coin

b. heads ⇒ boy   tails ⇒ girl

c. Flip 4 coins (1 for each child) ten times

Step-by-step explanation:

Answer:

H0 : p = 0.5

H1 : p > 0.5

Step-by-step explanation:

The the claim to test and determine if a signifant evidence for is if more than half of viewers want a return to original day time program. Since, this is

Since, p is the proportion who prefer the regular day time program;

The hypothesis to test is :

If p > 0.5 `; this represents the alternative hypothesis which we want to check if it we have significant evidence to adopt the claim.

The Null value on the other hand will take the a proportion equal to the p: and it is the initial truth until the alternative has a strong evidence to reject the null.

The null ;

H0 : μ = 0.5

Answer:

4 or....

Step-by-step explanation:

I think its 4. maybe not

9514 1404 393

Answer:

  ∛(2500π)√37 m² ≈ 120.911 m²

Step-by-step explanation:

If the height is 3 times the diameter, it is 6 times the radius. Then the volume is ...

  V = 1/3πr²h

  V = 1/3πr²(6r) = 2πr³

For a volume of 100 m³, the radius is ...

  100 m³ = 2πr³

  r = ∛(50/π) m

The lateral area of the cone is computed from the slant height. For this cone, the slant height is found using the Pythagorean theorem:

  s² = r² +(6r)² = 37r²

  s = r√37

Then the lateral area is ...

  LA = πrs

  LA = π(∛(50/π) m)(∛(50/π) m)√37

  LA = ∛(2500π)√37 m² ≈ 120.911 m²

The lateral area of the economical cone with a volume of 100 m³ is 120.911 m².

The lateral area of the cone is the curved area of the cone, therefore, the total area of the cone is without the base area.

As we know that the volume of the cone is given by the formula,

[tex]V = \dfrac{1}{3}\pi r^2h[/tex]

Now, for the right circular cone to be economical, the height must be 3 times the diameter or it should be 6 times the radius. Therefore, the economical volume can be written as,

 [tex]V = \dfrac{1}{3}\pi r^2h\\\\V = \dfrac{1}{3}\pi r^2(6r)[/tex]

Now, if cancel out the 3 in the remainder with the six in the numerator, the volume of the cone can be written as,

[tex]V = 2\pi r^3[/tex]

Further, we need to calculate the lateral area of the cone, whose volume is 100 m³. Now, in order to get the radius of the economic cone with the volume of 100 m³, substitute it with 2πr³,

[tex]V = 2\pi r^3\\\\100 = 2\pi r^3\\\\r = 2.5154\rm\ m[/tex]

We know that in order to calculate the lateral area of the cone we need to calculate the slant height. Thus, according to the Pythagorean theorem, the slant height can be written as

[tex]s^2 = r^2 +(6r)^2\\\\ s^2 = 37r^2\\\\ s = r\sqrt{37}[/tex]

Now, the lateral area of the economical cone with the volume of 100 m³ can be written as,

[tex]LA = \pi rs\\\\LA = \pi \times r \times r\sqrt{37}\\\\LA = \pi \times r^2 \times \sqrt{37}\\\\LA = \pi \times (2.5154)^2 \times \sqrt{37}\\\\LA = 120.911\rm\ m^2[/tex]

Hence, the lateral area of the economical cone with a volume of 100 m³ is 120.911 m².

Learn more about the Lateral Area of the Cone:

https://brainly.com/question/12267785

Answer:

[tex]x=19.67[/tex]cm

Step-by-step explanation:

Por Pitágoras,

[tex]x^{2} = 26^{2} - 17^{2} \\\\x^{2} = 676 - 289\\\\x^{2} =387\\\\x=\sqrt{387} \\\\x=19.67[/tex]

Answer:

(1,4)

Step-by-step explanation:

(1,-4) is over 1 and down negative 4 so reflected over the x-axis(the horizontal one) it would be four up so the answer is (1,4)

Answer: (1,4)

Step-by-step explanation:

The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same. For example, when point P with coordinates (1,-4) is reflecting across the X axis and mapped onto point P', the coordinates of P' are (1,4)

Answer:

252

Step-by-step explanation:

To answer the equation, you first need to note that it asks for surface area.

To find surface area, you use an input formula, known as SA=2lw+2lh+2hw. 'H' stands for height, 'L' stands for length, and 'W' stands for width.

Since the current height is 12, the current length is 6, and the width is 3, you need to plug them into the equation.

SA=2(6)(3)+2(6)(12)+2(12)(3)

SA=252

Quick tip! It's tempting to just multiply them all at once, but using the power of distribution is vital to solving these equations.

Answer:

The margin of error is of 0.01.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.7}{2} = 0.15[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.15 = 0.85[/tex], so Z = 1.037.

The margin of error is of:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Standard deviation was 0.21.

This means that [tex]\sigma = 0.21[/tex]

Sample of 450:

This means that [tex]n = 450[/tex]

What is the margin of error, assuming a 70% confidence level, to the nearest hundredth?

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]M = 1.037\frac{0.21}{\sqrt{450}}[/tex]

[tex]M = 0.01[/tex]

The margin of error is of 0.01.

Answer:

The age of Sydney's is 46 and the age of Devaughn is 61

Step-by-step explanation:

Here;

Devaughn: 15yrs older that S..= 15+7= 22yrs old

sum of their age= 107

Now;

Sydney age= 107 - 100

7yrs old,,

Answer:

Come out even

Step-by-step explanation:

The total numbers of faces in rolling two dice = 6 X 6 = 36

The sum of appears in the following cases: {6, 1}, {1, 6}, {2, 5}, {5, 2}, (3, 4}, {4, 3}. Making a total of 6 cases

Probability of obtaining a sum of 7 = possible number of cases where the sum of 7 appears ÷ total number of outcome

= 6/36 = 1/6

Probability of not obtaining a sum of 7 = 1 - Probability of obtaining a sum of 7

= 1 - 1/6

= 5/6

Expected Value: (1/6)10 + (5/6)(-2) = (10-10)/6 = 0

So the answer is come out even

Answer:

DE

Step-by-step explanation:

You can tell by the markings. Since there are two vertical markings it concludes that those sides are the same length.