Can somebody plz help me 15-[7+(-6)+1]^3

Answer: A 5,3

Step-by-step explanation:

I just took the test

The coordinates of the image of vertex D after a reflection across the x-axis is (5.3).

The correct option is (A).

A reflection of a point, a line, or a figure in the X axis involved reflecting the image over the x axis to create a mirror image. In this case, the x axis would be called the axis of reflection.

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 (5,4) is reflecting across the X axis and mapped onto point P’, the coordinates of P’ are (5,-4). Notice that the x-coordinate for both points did not change, but the value of the y-coordinate changed from 4 to -4.

The given coordinates of D is (5, -3).

Now, to get the reflection over x- axis we have negate the value of y- coordinate and no changes in x- coordinate.

Hence, the coordinate of vertex D is (5, 3).

Learn more about reflection here:

https://brainly.com/question/3480959

#SPJ2

Answer:

β = (-0.19 dB).

Step-by-step explanation:

The formula which is used to calculate the decibel level of a sound is given by :

[tex]\beta=10\log (\dfrac{I}{I_o})[/tex]

I is intensity of the sound of a ticking clock

[tex]I_o=10^{-12}\[/tex] watts per square meter

Since, [tex]1\ \text{inch}^2=\dfrac{1}{1550}\ \text{m}^2[/tex]

The intensity of a monster truck is converted into per square meter as follows:  

[tex]10^{-9}\ {W/in^2}= \dfrac{10^{-9}}{1550}\ W/m^2\\\\10^{-9}\ {W/in^2}=6.45\times 10^{-13}\ W/m^2[/tex]

So, Decibal level is :

[tex]\beta=10\log (\dfrac{6.45\times 10^{-13}}{10^{-12}})\\\\\beta =-0.19\ dB[/tex]

So, the decibel level of the sound of a ticking clock is (-0.19 dB).

Answer:

30dB

Step-by-step explanation:

Answer:

[tex]b = 74\ cm[/tex]

Step-by-step explanation:

The volume of a prism is given by the following equation:

[tex]Volume = base\ area * height[/tex]

In our case, the base is a triangle, so the area is given by:

[tex]base\ area = base * height_{\Delta}/2[/tex]

The base of the triangle is 43 cm, the height of the triangle is b, the height of the prism is 24 and the volume of the prism is 38,184, so we have:

[tex]base\ area = 43 * b/2 = 21.5b[/tex]

[tex]38184 = 21.5b * 24[/tex]

[tex]b = 38184/(24*21.5)[/tex]

[tex]b = 74\ cm[/tex]

Answer:

8π cm^2

Step-by-step explanation:

We proceed as follows;

To answer this question, what we need firstly is the name of the cross section that results from slicing a sphere into half.

The cross section that results is called a hemisphere, which is half the size of the sphere.

But before we can calculate the area of the new cross section, we will need the radius of the original shape.

This is obtainable from the volume of the shape.

Mathematically;

Volume of a sphere = 4/3 * π * r^3

32/3 * π = 4/3 * π * r^3

We can take off π/3 from both sides so we are left with;

32 = 4r^3

Divide through by 4

r^3 = 8

r is the cube root of 8 = 2 cm

Now we find the area of the hemisphere

Mathematically, the area of a hemisphere is 2 * π * r^2

using the value of r = 2 cm given above, we have Hemisphere area = 2 * π * 2^2 =8 π cm^2

Answer:

median

Step-by-step explanation:

(median is used to measure the middle)

you just line up all the numbers from least to greatest, then pick the middle number, IF there are NO numbers in the middle, you add the the 2 middle numbers up, then divided by 2

Answer:

Median, because there is 1 outlier that affects the center

Step-by-step explanation:

"The median is the middle number of the data set. It is exactly like it sounds. To figure out the median you put all the numbers in order (highest to lowest or lowest to highest) and then pick the middle number. If there is an odd number of data points, then you will have just one middle number."

Answer: 50 degrees

Step-by-step explanation:

180-85=95

180-145=35

interior angle sum for a triangle is 180 degrees, so 180=95+35+a

m of angle A is 50 degrees

Answer:

Option D is the correct option.

Step-by-step explanation:

Given,

A ( 4, 5 ) , B ( 2 , 2 ) , C ( 4 , 2 )

Let,

A ( 4 , 5 ) → ( x1 , y1 )

B ( 2 , 2 ) → ( x2 , y2 )

Now, finding the length of AB

Use the distance formula to find the length of AB

[tex] = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]

plug the values

[tex] = \sqrt{ {(2 - 4)}^{2} + {(2 - 5)}^{2} } [/tex]

Calculate the difference

[tex] = \sqrt{ {( - 2)}^{2} + {( - 3)}^{2} } [/tex]

Evaluate the power

[tex] = \sqrt{4 + 9} [/tex]

Add the numbers

[tex] = \sqrt{13} [/tex]

Hope this helps..

Best regards!!

Answer:

Area of the triangle WXY = 111.8 mm²

Step-by-step explanation:

By applying Sine rule in the given triangle WXY,

[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinX}}{\text{WY}}=\frac{\text{SinY}}{\text{WX}}[/tex]

Since m∠W + m∠X + m∠Y = 180°

m∠W + 26° + 130° = 180°

m∠W = 180° - 156°

m∠W = 24°

[tex]\frac{\text{Sin24}}{\text{XY}}=\frac{\text{Sin130}}{31}=\frac{\text{Sin26}}{\text{WX}}[/tex]

[tex]\frac{\text{Sin24}}{\text{XY}}=\frac{\text{Sin130}}{31}[/tex]

XY = [tex]\frac{31\times (\text{Sin24})}{\text{Sin130}}[/tex]

XY = 16.4597

     ≈ 16.4597 mm

Area of the triangle = [tex]\frac{1}{2}(\text{XY})(\text{WY})\text{SinY}[/tex]

                                 = [tex]\frac{1}{2}(16.4597)(31)\text{Sin26}[/tex]

                                 = 111.83 mm²

                                 ≈ 111.8 mm²

Therefore, area of the triangle WXY = 111.8 mm²

Answer: 82%

Step-by-step explanation:

- - - - - - - - college - - not college - - - - total

Travel - - - - 43 - - - - - - - 10 - - - - - - - - 53

Not travel - 24 - - - - - - - 5 - - - - - - - - - 29

Total - - - - 67 - - - - - - - 15 - - - - - - - - - 82

Marginal relative frequency of students who plan to attend college:

(Number of students who plan to attend the college / Total number of the students)

Number of students who plan to attend college = 67

total number of students = 82

Marginal relative frequency = 67/82

= 0.8170731

= (0.8170731) * 100%

= 81.7% = 82%

Answer:

a: 14/50

b: 15/50

c: 21/50

Step-by-step explanation:

on edge

Answer: 15 teams

Step-by-step explanation:

Total number of games played in the tournament = 105

Number of participating teams = p

Each team plays against every other team , then the total number of games played by each team = (p - 1) , since a team can't play itself

To obtain total number of games played =

(Number of teams × number of games played) [p × (p-1)]

However, the teams played against each other only once :

Therefore, total number of games played:

[p × (p-1)] / 2

Since we've been given the total number of games played :

[p × (p-1)] / 2 = 105

p × (p-1) = 105 × 2

p × (p-1) = 210

p^2 - p = 210

p^2 - p - 210 = 0

p^2 - 15p + 14p - 210 = 0

p(p - 15) +14(p-15) = 0

(p - 15) = 0 or (p + 14) = 0

p = 15 or p = - 14

Number of teams can't be negative

Therefore p = 15

Number of teams = 15

Answer:

B) 5 + 3√5 units

Step-by-step explanation:

The length of ZX is 2√5 units. What is the perimeter of triangle XYZ?  

A) 5 +√3 + 2 √5 units  

B) 5 + 3√5 units  

C) 5 + √6 + 2√5 units  

D) 10 + 2√5 units

From the diagram attached, point X is at (-1, 4), Y(3, 1), Z(1, 0).

The distance between two point

[tex]O(x_1,y_1)\ and\ A(x_2,y_2)\ is\ given\ as:\\\\OA=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

The lengths of the sides of the triangle are:

[tex]|XY| = \sqrt{(3-(-1))^2+(1-4)^2}=\sqrt{25} =5\ unit\\ \\|XZ|= \sqrt{(1-(-1))^2+(0-4)^2}=\sqrt{20} =2\sqrt{5} \ unit\\\\|YZ|= \sqrt{(1-3)^2+(0-1)^2}=\sqrt{5} \ unit[/tex]

The perimeter of the triangle is the sum of all the sides, i.e.

Perimeter = |XY| + |YZ| + |XZ| = 5 + 2√5 + √5 = 5 + 3√5  

Answer:

B

Step-by-step explanation:

Answer:

7.1 km

Step-by-step explanation:

Bien, este es un problema de conversión de unidades.

Procedemos de la siguiente manera;

Convirtamos todas las alturas que tenemos a metros.

Comenzamos con 23,000 decímetros a metros Matemáticamente, 1 metro = 10 decímetros Entonces 23,000 decímetros = 23,000 / 10 = 2,300 metros

En segundo lugar, convertimos 54 hectómetros a metros.

Matemáticamente; 1 hectómetro = 100 metros Entonces 54 hectómetros = 54 * 100 = 5400 metros Por lo tanto, su nueva altura sería; 14,800-2300-5400 = 7,100 metros Ahora, procedemos a convertir 7.100 metros a kilómetros.

Matemáticamente 1000 m = 1 km Entonces 7,100 m serán = 7100/1000 = 7.1 km

Responder:

Explicación paso a paso:

Altura inicial del avión = 14.800 m.

Como se redujo en 23,000 decímetros y luego en 54 hectómetros, la caída total de altura se obtiene al agregar 23,000 decímetros y 54 hectómetros

Antes de agregarlos, necesitamos convertir ambos valores a metros

1 decímetro = 0.1m

23,000 decímetros = x

x = 23,000 * 0.1

x = 2,300 metros

Además, si 1 hectómetro = 100 m

54 hectómetros = y

y = 54 * 100

y = 5400 metros.

Sumando ambas alturas;

x + y = 2300m + 5400m = 7700 metros

Esto significa que el avión cae por una altura total de 7700 metros

Para calcular la altura a la que volará el avión después de la caída, tomaremos la diferencia entre la altura inicial y la altura total caída.

La altura que el avión está volando ahora será 14,800 - 7,700 = 7,100 metros

Convirtiendo la respuesta final a kilómetros.

1000m = 1km

7.100m = z

z = 7100/1000

z = 7.1 km

Esto significa que el avión está volando a una altura de 7.1 kilómetros después de la caída.

Answer:

17.3 = AC

Step-by-step explanation:

Since this is a right angle, we can use trig functions

tan B = opp/ adj

Tan 68 = AC / 7

7 tan 68 = AC

17.32560797 = AC

To 1 decimal place

17.3 = AC

Answer:

Step-by-step explanation:

To find AC we use tan

tan ∅ = opposite / adjacent

From the question

AB is the adjacent

AC is the opposite

So we have

tan 68 = AC / AB

AC = AB tan 68

AC = 7 tan 68

AC = 17.32

AC = 17. 3 cm to one decimal place

Hope this helps you

Answer:

1/16.4616

Step-by-step explanation:

(1.9^2*2.4^-3) (1.9^3*2.4^-2)^-3

(1.9^2*2.4^-3) * 1 / (1.9^3*2.4^-2)^3

1.9^2*2.4^-3 / (1.9^3*2.4^-2)^3

1.9^2 * 1 / 2.4^3 ÷ (1.9^3* 1 / 2.4^2)3

1.9^2 / 2.4^3 × (2.4^2/1.9^3)^3

(1/2.4) (1/1.9)^3

(1/2.4) (1/6.859)

1/16.4616

Answer:

855.298 m^3

Step-by-step explanation:

The volume of a cylinder equation is piR^2H.

So pi5.5^2×9

855.298 m^3

Answer:

9/4n= 1.5/7

right now to find this equation it is a proportion so you cross multiply and you gonna get 63=6n and divide 6 on both sides and u get 10.5.

Check 9/4n= 9/42 and to simply u will get 1.5/7

Step-by-step explanation:

Answer:

the grade point average​ (GPA) of the student is 2.27

If the​ Dean's list requires a GPA of 3.00 or​ greater,  the student did not make the Dean's list.

Step-by-step explanation:

Given that:

A student grade are as follows:

B    ---   3

F   ---   0

B   ----   3

B  ----- 3

C ------- 2

Those courses had the corresponding numbers of credit hours 4​, 2​, 1​, 2​, and 2.

The grading system assigns quality points to letter grades as​ follows:

A = 4; B=​3; C=​2; D=​1; F=0

The sample mean simply implies the sum of the products of the value and the weights divided by the total weights;

i.e

[tex]\overline x = \dfrac{\sum xf}{n }[/tex]

[tex]\overline x = \dfrac{3(4)+0(2)+3(1)+3(2)+2(2)}{4+2+1+2+2 }[/tex]

[tex]\overline x = \dfrac{12+0+3+6+4}{11 }[/tex]

[tex]\overline x = \dfrac{25}{11 }[/tex]

[tex]\overline x =[/tex] 2.27

the grade point average​ (GPA) of the student is 2.27

If the​ Dean's list requires a GPA of 3.00 or​ greater,  the student did not make the Dean's list.

Answer:

So possibilities of zeroes are:

Positive       Negative       Imaginary

   1                    1                   2

   3                   1                   0

Zeroes = -1.4549, 1.2658, 0.34457-1.0503i, 0.34457+1.0503i.  

Step-by-step explanation:

Note: Descartes' Rule of Signs is used to find the signs of zeroes not the exact value.

The given function is

[tex]f(x)=4x^4-2x^3-3x^2+6x-9[/tex]

Degree of polynomial is 4 so number of zeroes is 4.

There are three sign changes, so there are either 3 positive zeros or 1 positive zero.

Now, put x=-x in f(x).

[tex]f(-x)=4(-x)^4-2(-x)^3-3(-x)^2+6(-x)-9[/tex]

[tex]f(-x)=4x^4+2x^3-3x^2-6x-9[/tex]

There is one variation in sign change, so there is 1 negative zero.

So possibilities of zeroes are:

Positive       Negative       Imaginary

   1                    1                   2

   3                   1                   0

Using graphing calculator the zeroes of given function are -1.4549, 1.2658, 0.34457-1.0503i and 0.34457+1.0503i.  

Answer:

1992.50 mL; 825 mL

Step-by-step explanation:

Given that :

Capacity of bottles in the attachment = 2L

Amount of soft drink in bottle 1 = 7.50mL

Amount of soft drink in bottle 2 = 1175mL

Converting liter milliliter

1Litre = 1000 milliliters

Therefore 2Litres = 2000 milliliters

Capacity each of bottle = 2000 milliliters

Volume of drink required to completely fill bottle 1:

2000mL - 7.50mL = 1992.50 mL

Volume of drink required to completely fill bottle 2:

2000mL - 1175mL = 825 mL

Answer:

3/2

Step-by-step explanation:

● (-3/8) ÷(-1/4)

Flip the second fraction by putting 1 instead 4 and vice versa.

● (-3/8)* (-4/1)

-4 over 1 is -4 since dividing by 1 gives the same number.

● (-3/8)*(-4)

Eliminate the - signs in both fractions since multiplying two negative numbers by each other gives a positive number.

●( 3/8)*4

● (3*4/8)

8 is 2 times 4

● (3*4)/(4*2)

Simplify by eliminating 4 in the fraction.

● 3/2

The result is 3/2

Step-by-step explanation:

It is given that,

Volume of the cylindrical can 1 is 2 litres and that of cylindrical can 2 is 6.75 litres. The diameter of the smaller can is 16 cm. We need to find the diameter of the larger can.

The formula of the volume of a cylinder is given by :

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

So,

[tex]\dfrac{V_1}{V_2}=\dfrac{r_1^2}{r_2^2}[/tex]

Diameter, d = 2r

[tex]\dfrac{V_1}{V_2}=\dfrac{(d_1/2)^2}{(d_2/2)^2}\\\\\dfrac{V_1}{V_2}=(\dfrac{d_1^2}{d_2^2})[/tex]

V₁ = 2 L, V₂ = 6.75 L, d₁ = 16 cm, d₂ = ?

[tex]\dfrac{2}{6.75}=(\dfrac{16^2}{d_2^2})\\\\d_2=29.39\ cm[/tex]

So, the diameter of the larger can is 29.39 cm.

Answer:

LN and NK

Step-by-step explanation:

trust

Answer: c

Step-by-step explanation:

Its correct

I believe it is C, as the graphs do look the same.

Answer:

1a (x + y)² = x² + 2xy + y²

1b. (x - y)² = x² - 2xy + y²

2. (x + y)² - (x - y)² = 4xy

3. 4² – 2² = 12

Step-by-step explanation:

1a. Expansion of (x + y)²

(x + y)² = (x + y)(x + y)

(x + y)² = x(x + y) + y(x + y)

(x + y)² = x² + xy + xy + y²

(x + y)² = x² + 2xy + y²

1b. Expansion of (x - y)²

(x - y)² = (x - y)(x - y)

(x - y)² = x(x - y) - y(x - y)

(x - y)² = x² - xy - xy + y²

(x - y)² = x² - 2xy + y²

2. Determination of (x + y)² - (x - y)²

This can be obtained as follow

(x + y)² = x² + 2xy + y²

(x - y)² = x² - 2xy + y²

(x + y)² - (x - y)² = x² + 2xy + y² - (x² - 2xy + y²)

= x² + 2xy + y² - x² + 2xy - y²

= x² - x² + 2xy + 2xy + y² - y²

= 2xy + 2xy

= 4xy

(x + y)² - (x - y)² = 4xy

3. Writing 12 as the difference of two perfect square.

To do this, we shall subtract 12 from a perfect square to obtain a number which has a perfect square root.

We'll begin by 4

4² – 12

16 – 12 = 4

Find the square root of 4

√4 = 2

4 has a square root of 2.

Thus,

4² – 12 = 4

4² – 12 = 2²

Rearrange

4² – 2² = 12

Therefore, 12 as a difference of two perfect square is 4² – 2²

Answer:

1.35 degrees per mg.

Step-by-step explanation:

The patient's temperature went from 105.85 to 99.1. That is a decrease of 6.75 degrees. You want to find the temperature decrease per milligram, which can be found by dividing the temperature by the number of mg of the drug.

6.75 / 5 = 675 / 500 = 1.35

So, the rate at which her temperature decreased per milligram is 1.35 degrees per mg.

Hope this helps!

A game is played using one die. If the die is rolled and shows 1, the player wins $5. If the die shows any number other than 1, the player wins nothing. If there is a charge of $1 to play the game, what is the game's expected value?

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

Let random variable "x" be a count of player gain.

X-values are: 4, -1

P(x=4) = 1/6; P(x= -1) = 5/6

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

E(x) = (1/6)(4) + (5/6)(-1)

E(x) = [4-5]/6

E(x) = -1/6 = -17 cents

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

Cheers,

Answer:

The answer is below

Step-by-step explanation:

A transformation of a point is the movement of an point from an initial position to a new position. If an object is transformed, all the point of an object is transformed. Two figures are said to be congruent if they have the same shape and the measure of each of their sides are the same.

An object is congruent to another object if the object can be mapped to the other object when transformed.

Answer:

The answer is c

Step-by-step explanation:

It is the correct solution because you are able to map circle m onto m

Answer: x Less-than-or-equal-to 2.25

Step-by-step explanation:

The given inequality: 47.75 + x Less-than-or-equal-to 50.

To determine: How much more weight can be added to Li’s suitcase without going over the 50-pound limit.

i.e. inequality for x.

[tex]47.75+x\leq50[/tex]

Subtract 47.75 from both the sides, we get

[tex]x\leq50-47.75\\\\\Rightarrow\ x\leq2.25[/tex]

So, the solution set is "x Less-than-or-equal-to 2.25"

Hence, the correct answer is "x Less-than-or-equal-to 2.25."

Answer

A x <_ 2.25

Step-by-step explanation:

Answer:

The amount of CD's she could buy would be 3.

Step-by-step explanation:

80-20=60

60÷18 = 3 CD's

Answer:

1,2,3

Step-by-step explanation:

Answer:

1. r = 2.82 cm

h = 5.6 cm

The maximum volume possible to the nearest 10 mL = 140 mL

2. Size side of square base of box is 5.64 cm

Height of box = 5.6 cm

The surface area of the box is 189.96 cm²

The volume of the box is 178.13 cm³

3.  The procedure for solving the problem was through noting that the shape of the cross-section of the pyramid is an isosceles triangle ans also that smallest possible box for the pretty perfume is one which fits the angle of inclination of the lid. This was found out by initially using the combined height of the perfume and the lid (placed to fit the spherical outline of the bottle) to calculate the dimensions of the pyramid, from which it was observed that the angle of inclination of the lid is larger than that of the calculated dimension, such that the lid outline would be visible and could eventually tear the perfume box  

With the inclination angle, β, which is the base angle of the isosceles triangle, the angle at the top of the pyramid cross-section is calculated and the following relations are used to calculate the triangular cross-section of the pyramid

h = a·cos(α/2)

b = 2·a·cos(β)

[tex]r = \dfrac{b}{2}\sqrt{\dfrac{2a - b}{2a + b}}[/tex]

[tex]R = \dfrac{a^{2}}{\sqrt{4a^{2}-b^{2}}}[/tex]

With the calculated dimensions, a, b, and h the area, A, of the square pyramid is calculated as 2×b×a + b² and the volume, V, as 1/3×b²×h

The attached diagram shows the the cross-section of the perfume in the pyramid box.

Step-by-step explanation:

1. The surface area of the cylinder = 2πr² + 2πrh = 150 cm².........(1)

The volume of the cylinder, V = πr²h = 100 mL = 100 cm³..............(2)

From equation (2), h = 100/(π·r²)

Substituting the value if h in equation (1), we have;

2πr² + 2πr100/(π·r²) = 150

2πr² + 200/r = 150

(2πr³ + 200)/r = 150

2πr³ + 200 = 150×r

2πr³ -150·r+ 200 = 0

150 = 2πr² + 2πrh

h = (150 - 2πr²)/(2πr)

h = (75- πr²)/(πr)

Substituting the value of h in the equation for the volume, we have;

V = πr²h =  πr²(75- πr²)/(πr)

V = 75·r - π·r³

At maximum volume, dV/dr = 0, we have

d(75·r - π·r³)/dr = 75 - 3·π·r²= 0

3·π·r²= 75

π·r² = 25

r = 5√π/π

h = (75- πr²)/(πr) = (75- π(5√π/π)²)/(π(5√π/π)) = (75 -25)/(5·√π)

h = 50/(5·√π)= 10·√π/π

The maximum volume = πr²h = π×25/π×10·√π/π =  250·√π/π = 141.05 cm³

The maximum volume possible = 141.05 cm³ = 141.05 mL

The maximum volume possible to the nearest 10 mL = 140 mL

The dimensions of the bottle are;

r = 2.82 cm

h = 5.6 cm

The surface area of the bottle = 2π(2.82)² + 2π×2.82 ×5.6 = 149.2 cm

2

Given that the cylindrical bottle has r = 2.82 cm and h = 5.6 cm, we have;

Size side of square base of box = 2 × 2.82 = 5.64 cm

Height of box = 5.6 cm

The surface area of the box = 2 × Area of base + 4 × Area of side

The surface area of the box = 2 *5.64^2 + 4 * 5.6 * 5.64 = 189.96 cm²

The volume of the box = Area of base × Height = 5.64^2*5.6 = 178.13 cm³

3. Diameter of spherical bottle = 7 cm = 2×r

Volume of the sphere  bottle = 4/3πr³ = 4/3*3.5^3*π = 343/6·π = 179.6 cm³

The surface area of the sphere  bottle = 4πr² = 4*(7/2)^2*π = 49·π = 156.94 cm²

3 i. The volume of a cone = 1/3πr²h = 1/3*(5/2)^2*4.5 = 9.385·π = 29.45 cm³

The  surface area of a cone = πrS

S = √(4.5^2 + (5/2)^2) = 5.15

The  surface area of a cone = π*2.5*5.15 = 40.43 cm²

3 ii. The depth of fitness of the lid on the bottle = 7/2 - √(7/2)^2 - 2.5^2) = 1.05

The total height of the spherical bottle with the conical lid = 7 + 4.5 - 1.05 = 10.45 cm

3 iii. Given that the box is shaped like a pyramid we have;

Width of the box at middle of the height of the spherical bottle = 7 cm

Height of the box = 10.45 cm

[tex]r = \dfrac{b}{2}\sqrt{\dfrac{2a - b}{2a + b}}[/tex]

[tex]R = \dfrac{a^{2}}{\sqrt{4a^{2}-b^{2}}}[/tex]

With the aid of a graphing calculator, the width of the square pyramid is found to be 12.12 cm

The volume = 1/3*12.12^2*10.45 = 511.68 cm²

The surface area = 2*12.12*√(12.12/2)^2 + 10.45^2) +12.12²= 439.7 cm²

The angle of inclination of the lid = tan⁻¹ (4.5/2.5) = 60.95°

The angle of inclination of the calculated box is tan⁻¹ (10.45/6.06) = 59.88

Since the lid is steeper, we make use of the angle of the lid

The base angles are thus = 60.95°

The angle at the top is thus 180 - 60.95*2 = 58.11°

Therefore, by the formula, we find that

a = 12.25 cm

b = 11.897 cm

h = a·cos(α/2)

h = 10.707 cm

The volume = 1/3*11.897^2*10.707 = 505.15 cm³

The surface area = 2*11.897*√(11.897/2)^2 + 10.707^2) +11.897²= 432.98 cm²

The angle at the top of the box = 2

Given that:

Then the maximum volume possible to the nearest 10 mL =

Given that:

Hence, the surface area of the box is

The volume of the box is :

This refers to the measure of the total area of an object.

The procedural method used to solve the problem was to identify the shape of the pyramid, then finding out the smallest possible box for the pretty perfume and then using the calculated dimensions, found the answers.

Read more about surface area here:
https://brainly.com/question/76387