as part of a science experiment, Carson designs and creates a cushioned egg carrier. he puts an egg inside it and then drops it from a window to see whether his design can safely cushion the egg and keep it from breaking. the egg's height in feet x seconds after being dropped is given by 27 - 16x^2. after how many seconds will the egg hit the ground?

The area of the green region of the circle is 96.4 ft².

Area is the region bounded by a plane shape.

To calculate the area of the green region of the circle, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

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The area of the green region in the circle given is expressed as approximately: a. 96.5 square feet.

The sector of a circle is calculated as:

A = ∅/360 * πr², where r is the radius and ∅ is the reference or central angle of the sector.

Given the following:

Central or reference angle (∅) = 180 - 27 = 153 degrees

Radius (r) = 17/2 = 8.5 feet

Plug in the values:

Area of the green region = 153/360 * π * 8.5²

Area of the green region ≈ 96.5 square feet.

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Answer:

option b I guess

Step-by-step explanation:

D=c/s³ would be the answer

The solution set of f(x) > 0 is x ∈ (-2, 8).

To find the solution set of f(x) > 0, we need to first determine the critical values of x where f(x) changes sign.

Let's start by finding the domain of the function:

x² - 6x - 16 ≠ 0

We can solve for x by using the quadratic formula:

x = [6 ± √(6² + 4(16))]/2 = [6 ± √52]/2 = 3 ± √13

So the domain of f(x) is (-∞, 3 - √13) U (3 + √13, ∞).

Now let's factor the numerator and denominator of f(x):

f(x) = (x + 10)/[(x - 8)(x + 2)]

The critical points occur where the numerator or denominator of f(x) changes sign.

The numerator changes sign at x = -10, and the denominator changes sign at x = -2 and x = 8.

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Correct option is A. To form the image, the pre-image moved, five units right and three units up.

Its image refers to a point's, a line's, a line segment's, or a figure's new location following a transformation.

The image of Q's coordinates are (x1+ ar, y1+ br, z1+ cr). The midpoint R of PQ's coordinates are discovered. By changing the coordinates of R in the planar equation, the value of r is determined. The r-value is then entered into the Q coordinates.

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Complete Question -

To form the image, the pre-image moved

O five units right and three units up.

O two units right and three units up.

O five units left and three units down.

O two units left and three units down.

The image is attached below -

Answer:

a

Step-by-step explanation:

i rjrjejjejejejebruex so yeah thats it

Answer:12 2/24

If this helped please leave a brainliest it would really help out!

t (23) ≤ 97 - 23

The minus 23 at the back represents the feet she already descended before what the question wants us to calculate

≤ is used instead of < because it states more than, not "equal or more than" (meaning 97 sharp is fine)

Answer:

5

Step-by-step explanation:

This is Pythagorean triple 3-4-5 or you can verify by plugging into Pythagorean Theorem:

\(3^2 + 4^2 = c^2\)

c = 5

To determine the area of the remaining piece of cardboard expressed in terms of x when a square of side length x inches is cut out from a rectangular piece of cardboard having a length of 6x+2 inches and a width of 2x-4 inches, use the following steps.

Draw and label a diagram of the problem. The rectangle should be labeled as 6x+2 inches by 2x-4 inches, and the square cut out should be labeled as x inches by x inches. This is how the diagram looks like: Determine the area of the rectangle, Arect.

The area of the rectangle is given by the product of its length and width. Thus, Arect = (6x + 2)(2x - 4) Determine the area of the square, Asq. The area of the square is given by the square of its side length. Thus, Asq = x²Step 4: Determine the area of the remaining cardboard after the square is cut out, Ar.

This is the difference between the area of the rectangle and the area of the square. Thus, Ar = Arect - Asq= (6x + 2)(2x - 4) - x²= 12x² - 20x - 16

Simplify the expression. The final answer is given in terms of x. Thus, Ar = 12x² - 20x - 16.The area of the remaining piece of cardboard is expressed in terms of x as 12x² - 20x - 16.

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The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

\(-x^2 + 7 = 2x + 4\)

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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C. The point estimate of the difference between the two population means is 2.

D. The 90% confidence interval estimate of the difference between the two population means is (1.748, 0.867)

Given that:

Sample 1 mean (x1) = 9

Sample 2 mean (x2) = 7

Sample 1 standard deviation (σ1^2) = 2.28

Sample 2 standard deviation (σ2^2) = 1.79

C. To find point estimate of the difference between the two population   means.

sample mean(x1) - sample mean(x 2)

 = 9 - 7

= 2

Therefore, point estimate = 2

D. To find 90% confidence interval estimate of the difference between the two population means

90% confidence for 't'

df = (n1 + n2) - 2

   = 12-2

   = 10

90%  confidence with df = 10 is t

t = 1.812

point estimate + 1 - t * \(\sqrt{\frac{s^2_{1} }{n_{1} } + \frac{s^2_{2} }{n_{2} } }\)

2 + 1 - 1.812*\(\sqrt{\frac{2.28^2}{6} + \frac{1.79^2}{6} }\)

3 - 1.812 *\(\sqrt{0.866 + 0.534}\)

1.188 * 0.9305 + 0.7307

(1.748, 0.867)

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According to the graph, the value of the constant in the equation below is 80 and is denoted as option D.

What is a Graph?

This is defined as a pictorial representation of data or variables in an organized manner.

From the equation:  Height = constant/width

We can pick any point(4,20) on the graph.

20 = c/ 4

c = 20 × 4 = 80

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Answer:

(7 + 3) + 2 equals 10 + 2 which equals 12

7 + (3 + 2) equals 7 + 5 which equals 12

Step-by-step explanation:

Answer:

x= 8,5

x=0

X= 2

x= -2

Step-by-step explanation:

Answer:

25.2

Step-by-step explanation:

168 x .15 = 25.2

\(\large\text{Hey there!}\)

\(\rm{15\%\ of\ 168}\\\\\rm{= 15\% \times 168} \\\\\rm{= \dfrac{15}{100}\times 168}\\\\\rm{= \dfrac{15}{100}\times \dfrac{168}{1}}\\\\\rm{=\dfrac{15\times168}{100\times1}}\\\\\rm{= \dfrac{2,520}{100}}\\\\\rm{= 25.2}\)

\(\huge\text{Therefore, your answer should be: }\)

\(\huge\boxed{\frak{25.2}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The area of the figure in this problem is given as follows:

A. 30 in².

The area of a triangle is given by half the multiplication of the base length by the height of the triangle.

Applying the Pythagorean Theorem, we can obtain the missing side length, as follows:

4² + x² = 6²

x² = 36 - 16

x² = 20

x = square root of 20

x = 4.47.

For a right triangle, one side is considered the height of the other, hence the sides are:

Hence the area of the triangle is then obtained as follows:

Area = 0.5 x 4 x 12.47

Area = 25 in².

Which is closest to 30 in².

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Answer:

44.85

Step-by-step explanation:

There are two ways to do it, you can either multiply 0.3 by 34.5 and then add it to 34.5 to get 44.85, or you can add the 30% to 100% and get 1.3 which you multiply by 34.5 and that gets you 44.85

Answer:

Suri= 40.7   Baseball=C   19=19.417   20=11.167   Tens=6  Thousanths=9  Hundreths=7  Tenths=5     Write in standard form=82.007    4.567   72.85

Write in expanded form= 20+4+0.1+0.07   30+6+0.9    1+0.8+0.02+0.004

Step-by-step explanation:

i gotchu

Answer:

3

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

A) 4

Step-by-step explanation:

4 + 5 = 9

9 is NOT greater than 10.

Answer:

12

Step-by-step explanation:

1.2*10 = 1.2

Answer:

12

Step-by-step explanation:

the "normal form" to write numbers : just the digits and a decimal point when needed.

so, 1.2 × 10 = 12

12 is the normal, standard decimal notation.

in some cases it can be also 12.0 or 12.00 (especially with money).

the other form is the scientific notation, where a number is written with its leading digits and the power of 10 as the total value "weight". like in this example 1.2 × 10¹

Answer:

7.33333333333 I think. Hope this helped.

Answer:

\(y = -2(x + 5)^2 - 5\)

or
\(y = -2x^2 -20x - 55\)

Step-by-step explanation:

The vertex (maximum) of this quadratic equation is (-5, -5)

This graph and related function represents a parabola with vertex = (-5, -5)

The vertex form equation of a parabola is
y =a(x - h)² + k

where (h, k) is the vertex

Plugging in h = -5, h = -5:

y = a(x - (-5))² + (-5)

y = a(x + 5)² - 5

All that remains is to find the value for the coefficient, a

We note that the graph passes through the point (-7, -13) which corresponds to x = - 7 and y = - 13

Plug in these values for x and y into the equation and solve for a
-13 = a(-7 + 5)² - 5

-13 = a(-2)² -5

- 13 = 4a -5

Switch sides

4a - 5 = -13

Add 5 to both sides:
4a - 5 + 5 = -13 + 5

=> 4a = -8

=> a = -2

The equation is

\(y = -2(x + 5)^2 - 5\)

(x + 5)² = x² + 10x + 25

-2 (x+5)² = -2 (x² + 10x + 25) = -2x² -20x - 50

-2 (x+5)²  - 5 = -2x² -20x - 50 - 5 = -2x² -20x - 55

Answer:

x=3.536, y=7.356

Step-by-step explanation:

The point of intersection can be found out be equating the equations x^2+(y-4)^2=25 and y=x+4. Solving it we will get x=3.536, y=7.356

Answer:

Well on my end i got 47.12, with pi included

Step-by-step explanation:

The surface area of the cylinder with the diameter 2cm and height 15cm  is \(100.48 \; cm^2\)

Calculation to find Surface area of cylinder:

Given the diameter of the cylinder is 2cm and height  15cm

Formula :

The surface area of the cylinder =\(2\pi r^2+2\pi rh\)

where 'r' is the radius and 'h' is the height of the cylinder

Diameter = 2cm

\(radius =\frac{diameter }{2} =\frac{2}{2} =1\)

radius = 1cm and height is 15 cm

the value of pi is 3.14

Substiute all the values

\(SA = 2\pi r^2+2\pi rh\\SA=2(3.14)(1)^2+2(3.14)(1)(15)\\SA=6.28+94.2\\SA=100.48 cm^2\)

The surface area of the cylinder with the diameter 2cm and height 15cm  is \(100.48 \; cm^2\)

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69 ÷ 7 = 9 r6

hope it helps.

When there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents. The number of flags will be 40.

From the information, there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents.

It should be noted that this simply means that we should find the highest multiple for 2, 4, and 5 between 20 and 50. This is 40.

Therefore, the number of flags is 40.

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Answer:

P u s s y + p e n I s = babyyyyyyyyyy