A solid right pyramid has a regular hexagonal base with an area of 5.2 cm2 and a height of h cm.

A solid right pyramid has a regular hexagonal base with an area of 5.2 centimeters squared and a height of h centimeters.

Which expression represents the volume of the pyramid?

One-fifth(5.2)h cm3
StartFraction 1 Over 5 h EndFraction(5.2)h cm3
One-third(5.2)h cm3
StartFraction 1 Over 3 h EndFraction(5.2)h cm3

Given:

[tex]PQRS\sim TUVW[/tex]

In the given figure, PS=x, RS=35, UV=20, VW=25 and TW=15

To find:

The scale factor from PQRS to TUVW.

Solution:

We have,

[tex]PQRS\sim TUVW[/tex]

We know that the corresponding sides of similar figures are proportional. The scale factor is the ratio of one side of image and corresponding side of preimage.

The scale factor is:

[tex]k=\dfrac{VW}{RS}[/tex]

[tex]k=\dfrac{25}{35}[/tex]

[tex]k=\dfrac{5}{7}[/tex]

Therefore, the scale factor from PQRS to TUVW is [tex]k=\dfrac{5}{7}[/tex].

Answer:

x=0;y=2

Step-by-step explanation:

4(-x+2)=2x+8 -4x+8=2x+8 -4x-2x=8-8 -6x=0 x=0 y=-x+2 y=0+2 y=2

Answer:

7/5 is the scale factor

Step-by-step explanation:

Answer:

3c + 9

Step-by-step explanation:

Remember to multiply everything in the brackets by the number outside the brackets.

Answer:

Box Dimensions:

L  = 15.15 ul

W = 7.15 ul

h = x = 2.43 ul

V(max) =    263.22 cu

Step-by-step explanation:

We call x the length of the square to be cut in the corners then:

Are of the base of the box is:

(20 - 2*x)  is the future length of the box and

(12 - 2*x) will be the width

The heigh is x  then the volume of the box is:

V = ( 20 - 2*x )* ( 12 - 2*x ) * h

And the volume as a function of x is:

V(x) = ( 20 - 2*x) * ( 12 - 2*x ) * x     or   V(x) = (240 -40*x -24*x + 4*x²) * x

V(x) =  240*x - 64*x² + 4*x³

Taking derivatives on both sides of the equation we get:

V´(x) = 240 - 128*x + 12*x²

V´(x)  =  0              240 - 128*x + 12*x²  = 0    or     60 - 32*x + 3*x²

3*x²  -  32*x  +  60  = 0

Solving:

x₁,₂  =  32  ± √ (32)² - 4*3*60 ]/ 2*3

x₁,₂  =  32  ± √ 1024 - 720 )/6

x₁,₂  = ( 32  ± √ 304 )/6

x₁,₂  = ( 32  ± 17.44 )/6

x₁  =  8.23      ( we dismiss this solution because is not feasible 2*x > 12

x₂ = 2.43  u.l ( units of length)

Then

L  =  20 - 2*x      L  = 20  - 4.85     L  = 15.15 ul

W =  12 - 2*x      W = 12 - 4.85      W = 7.15 ul

h  =  2.43 ul

V = 2.43*7.15*15.15  cubic units

V =  263.22 cu

To see if when x = 2.43   function V has a maximum we go to the second derivative

V´´(x)  = - 128  + (24)*2.43

V´´(x) = - 69.68      as        V´´(x)  < 0   then we have a maximum for V(x) in the point x = 2.43

Answer:

Ben = $ 41

Kaden = $ 31

Step-by-step explanation:

Let initially Ben has $ p and then Kaden has $ (p  - 10).

After that

Ben has= $ (p + 4)

Kaden has = $ (p- 10 + 4) = $ ( p - 6)

According to the question,

[tex]p- 6 = \frac{7}{9}\times (p+4)\\\\9 p- 54 = 7 p + 28 \\\\2 p = 82\\\\p =41[/tex]

Initially Ben has $ 41 and Kaden has $ 31.  

Answer:

1, -3.5

Step-by-step explanation:

Answer:(0.5,-3.5)

Step-by-step explanation:

(-2+3/2)/2, (-5-2)/2

0.5,-3.5

Answer:

19

Step-by-step explanation:

Conditional probability formula: A|B (A given B)= (A∩B)/B

So cold drink | large (cold drink given large)=  (Cold∩Large)/Large

cold∩large= 5

large= 22+5= 27

5/27=.185185185

which i guess rounds to 19%

Answer:

gal = 663902.4

11 pavers

Step-by-step explanation:

V = l × w × h

V = 164 × 82 × 6.6

V = [tex]88757ft^3[/tex]

**********************************

The Swimming pool is a

rectangular prism. Write

the formula for its volume

and calculate it.

l...length of this prism

w...width of this prism

h...height of this prism

V ...volume

*********************************

To know how many

gallons are in the pool,

multiply the volume by

the number of gallons

in [tex]1ft^3[/tex] gal...number of

gallons

********************************

gal = 88757 × 7.48

gal = 663902.4

********************************

First to not confuse

anybody on this, we need

to convert the meters into

centimeters.

Rule: 1 m = 100 cm

        3 m = 300 cm

        2.5 m = 250 cm

********************************

so for every meter, we

multiply 100 to get the

amount of centimeters

********************************

so then add the

centimeters of 3 m and

2.5 m

Answer: 550 cm

so then now compare

the measurings...

3 m = 300 cm

50cm × y = 300cm

50cm × 6 = 300cm

y = 6

2.5 m = 250 cm

50cm × y = 250cm

50cm × 5 = 250cm

y = 5

6 + 5 = 11 pavers

so Oliver will need 11 pavers

Answer:

-.985

Step-by-step explanation:

Answer:

Step-by-step explanation:

If you look at the diagram, you notice there are two triangular bases and three rectangular faces.

Therefore, the surface area, or the total area of all the bases and faces, would be the area of one triangular base multiplied by 2 and the area of each rectangular face

area of triangle = (1/2)*height*base

area of triangular base = (1/2)*15*28 = 210 cm^2

area of rectangle = base*height

area of rectangular face #1 = 25*30 = 750 cm^2

area of rectangular face #2 = 17*30 = 510 cm^2

area of rectangular face #3 = 28*30 = 840 cm^2

total surface area = 2*210 + 750 + 510 + 840 = 2520 cm^2

Answer:

[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]

⏩ 107° angle will be an obtuse angle because its measurement is more than 90° but less than 180°.

⁺˚*･༓☾✧.* ☽༓･*˚⁺‧

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Answer:

An obtuse angle

Step-by-step explanation:

Angles are classified by how large their degree measure is. Here is a list of the basic classifications of an angle,

acute: degree measure between (0) and (90) degrees

right: exactly (90) degrees,

obtuse: degree measure between (90) and (180) degrees

reflex: degree measure between (180) and (360) degrees

Answer:

ANSWER IS 12

Step-by-step explanation:

Answer:

last term is 1536

Value of the geometric series is 3,069

Step-by-step explanation:

took one for the team

There are 10 terms in the geometric series.

And, The first term of the series is, 3

We know that;

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

The geometric series is,

⇒ S₁₀ = ∑ 3 (2)ⁿ⁻¹

Where, n is from 1 to 10.

Thus, We get;

There are 10 terms in the geometric series.

And, For first term;

Put n = 1;

⇒ S₁₀ = ∑ 3 (2)ⁿ⁻¹

⇒ S₁₀ = ∑ 3 (2)¹⁻¹

⇒ S₁₀ = ∑ 3 (2)⁰

⇒ S₁₀ = ∑ 3 × 1

⇒ S₁₀ = 3

Thus, The first term of the series is, 3

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Answer:, Joey will pay $117.18 for sneakers.

Step-by-step explanation:

Given: original price = $155

Discount rate = 30%

Tax rate = 8%

Price after discount = Original price - (Discount) x (original price)

[tex]= 155-0.30\times 155\\\\=155-46.5\\\\=\$\ 108.5[/tex]

Tax = Tax rate x (Price after discount)

[tex]= 0.08 \times 108.5[/tex]

= $ 8.68

Final price for sneakers = Price after discount + Tax

= $ (108.5+8.68)

= $ 117.18

Hence

Answer:

Our two numbers are:

[tex]2+4\sqrt{2} \text{ and } 4\sqrt{2}-2[/tex]

Or, approximately 7.66 and 3.66.

Step-by-step explanation:

Let the two numbers be a and b.

One positive real number is four less than another. So, we can write that:

[tex]b=a-4[/tex]

The sum of the squares of the two numbers is 72. Therefore:

[tex]a^2+b^2=72[/tex]

Substitute:

[tex]a^2+(a-4)^2=72[/tex]

Solve for a. Expand:

[tex]a^2+(a^2-8a+16)=72[/tex]

Simplify:

[tex]2a^2-8a+16=72[/tex]

Divide both sides by two:

[tex]a^2-4a+8=36[/tex]

Subtract 36 from both sides:

[tex]a^2-4a-28=0[/tex]

The equation isn't factorable. So, we can use the quadratic formula:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = 1, b = -4, and c = -28. Substitute:

[tex]\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-28)}}{2(1)}[/tex]

Evaluate:

[tex]\displaystyle x=\frac{4\pm\sqrt{128}}{2}=\frac{4\pm8\sqrt{2}}{2}=2\pm4\sqrt{2}[/tex]

So, our two solutions are:

[tex]\displaystyle x_1=2+4\sqrt{2}\approx 7.66\text{ or } x_2=2-4\sqrt{2}\approx-3.66[/tex]

Since the two numbers are positive, we can ignore the second solution.

So, our first number is:

[tex]a=2+4\sqrt{2}[/tex]

And since the second number is four less, our second number is:

[tex]b=(2+4\sqrt{2})-4=4\sqrt{2}-2\approx 3.66[/tex]

Answer:

[tex]2+4\sqrt{2}\text{ and }4\sqrt{2}-2[/tex]

Step-by-step explanation:

Let the large number be [tex]x[/tex]. We can represent the smaller number with [tex]x-4[/tex]. Since their squares add up to 72, we have the following equation:

[tex]x^2+(x-4)^2=72[/tex]

Expand [tex](x-4)^2[/tex] using the property [tex](a-b)^2=a^2-2ab+b^2[/tex]:

[tex]x^2+x^2-2(4)(x)+16=72[/tex]

Combine like terms:

[tex]2x^2-8x+16=72[/tex]

Subtract 72 from both sides:

[tex]2x^2-8x-56=0[/tex]

Use the quadratic formula to find solutions for [tex]x[/tex]:

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] for [tex]ax^2+bx+c[/tex]

In [tex]2x^2-8x-56[/tex], assign:

Solving, we get:

[tex]x=\frac{-(-8)\pm \sqrt{(-8)^2-4(2)(-56)}}{2(2)},\\x=\frac{8\pm 16\sqrt{2}}{4},\\\begin{cases}x=\frac{8+16\sqrt{2}}{4}, x=\boxed{2+4\sqrt{2}} \\x=\frac{8-16\sqrt{2}}{4}, x=\boxed{2-4\sqrt{2}}\end{cases}[/tex]

Since the question stipulates that [tex]x[/tex] is positive, we have [tex]x=\boxed{2+4\sqrt{2}}[/tex]. Therefore, the two numbers are [tex]2+4\sqrt{2}[/tex] and [tex]4\sqrt{2}-2[/tex].

Verify:

[tex](2+4\sqrt{2})^2+(4\sqrt{2}-2)^2=72\:\checkmark[/tex]

Answer:

−3x^2+2x /x−2

Step-by-step explanation:

4x−9x^3/ 3x^2−4x−4

=  −9x^3+4x /3x^2−4x−4

=  x(−3x+2)(3x+2) /(3x+2)(x−2)

=  −3x^2+2x /x−2

Step-by-step explanation:

there Are 120 possibilities for the top three positions

We will see that there are 120 different possibilities for the top 3 positions.

Here we need to count the number of options for each of the positions.

The total number of different combinations is given by the product between the numbers of options, we will get:

C = 6*5*4 = 120

There are 120 different possibilities for the 3 positions.

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Answer:

Step-by-step explanation:

Middle point of AB

x(m) = (6+1)/2 = 7/2

y(m) = (7+4)/2 = 11/2

slope of the line that contains AB

(4-7)/(6-1) = -3/5

eqaution of the perpendicular bisector

y-11/2 = 5/3(x-7/2)

y = 5/3x -35/6 + 11/2

y = 5/3x + (-35 + 33)/6

y = 5/3x -1/3

Middle point of AC

x(m) = (1+5)/2 = 3

y(m) = (7+5)/2 = 6

Slope of the line that contains AC

(5-7)/(5-1) = -1/2

equation of the perpendicular bisector

y-6 = 2(x-3)

y = 2x -6 + 6

y = 2x

Point of intersection

y= 5/3x -1/3

y = 2x

2x = 5/3x - 1/3

6x = 5x - 1

x = -1

y = -2

P(-1,-2)

Answer:

(1,7)

Step-by-step explanation:

Given:

A(1,7)

B(6,4)

C(5,5)

Solution:

Mid point of AB = M((1+6)/2,(7+4)/2) = M(3.5,5.5)

Slope of AB = (4-7)/(6-1) = -3/5

Perpendicular bisector of AB:

L1: y -  11/2 = -(3/5)(x-7/2) ............(1)

Mid point of AC, m= N((1+5)/2,(7+5)/2) = N(3,6)

Slope of AC, n = (5-7)/(5-1) = -2/4 = -1/2

perpendicular bisector of AC:

L2: y-6 = -(1/2)(x-3) ..........."(2)

To find the point of intersection,

(1)-(2)

-5.5 - (-6) = -(3/5)x +12/5 + x/2 - 3/2

1/2 = -x/10 + 6/10

x/10 = 1/10

x = 1

substitute x in (1)

y = 3/2+11/2 =7

Therefore Point of intersection is (1,7)

Answer:

[tex]x = \frac{7 + \sqrt{65}}{2} \ , \ x = \frac{7 - \sqrt{65}}{2}[/tex]

Step-by-step explanation:

[tex]x^2 = 7x + 4 \\\\x^2 - 7x - 4 = 0\\\\ a = 1 \ , \ b = - 7 , \ c \ = \ - 4 \\\\x = \frac{-b \pm \sqt{b^2 - 4ac }}{2a}\\\\Substitute \ the \ values : \\\\x = \frac{7 \pm \sqrt{7^2 - (4 \times 1 \times -4)}}{2 \times 1}\\\\x = \frac{7 \pm \sqrt{49 + 16}}{2 }\\\\x = \frac{7 \pm \sqrt{65}}{2 }\\\\x = \frac{7 + \sqrt{65}}{2}\ , \ x = \frac{7 - \sqrt{65}}{2}[/tex]

Answer: a = 7.5h + bn

Step-by-step explanation:

Since Ava works at a florist shop and earns $7.50 an hour plus a fixed bonus for each bouquet she arranges.

where,

a = total amount earned,

h= hours worked in one week,

n = number of bouquets she arranged

b= bonus amount for bouquets

Then, the formula that will help her determine how much she will make in a week will be:

a = (7.5 × h) + (b × n)

a = 7.5h + bn

The formula is a = 7.5h + bn.

Answer: 4

Step-by-step explanation: bc

Answer:

42

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

x = 6

7x

Step 2: Evaluate

Answer:

4 + (1/3)w + w = 24

subtract 4 from both sides

(1/3)w + w = 20

multiply both sides by 3 to clear the fraction

w + 3w = 60

4w = 60

Divide both sides by 4

w = 15

Answer:

36.87°

Step-by-step explanation:

Given the right angle triangle :

To obtain the value of Cosθ ; we use the trigonometric relation :

Cosθ = Adjacent / Hypotenus

The adjacent angle isn't given :

Opposite = 9 ; hypotenus = 15

Adjacent = √(hypotenus ² + opposite ²)

Adjacent = √(15² - 9²)

Adjacent = √(225 -81)

Adjacent = √144 = 12

Hence,

Cos θ = 12/15

θ = Cos^-1(12/15)

θ = 36.87°

Answer:

The fourth angles is 105

Step-by-step explanation:

The sum of the angles of a quadrilateral is 360

3*85 = 225

Let the fourth angle be x

225 +x = 360

x = 360 -225

x =105

Answer:

[tex]-\infty < x < \infty[/tex]

Step-by-step explanation:

Given

[tex]y = \sqrt[3]{x - 1}[/tex]

Required

The domain

The given function is cubic root; there are no restrictions on cubic root functions

Hence, the domain is:

[tex]-\infty < x < \infty[/tex]

Answer:

Step-by-step explanation:

This is a positive parabola so it opens upwards. The equation for the directrix of this parabola is y = k - p. k is the second number in the vertex of the parabola which is (0, 0), but we need to solve for p.

The form that the parabola is currently in is

[tex]y=a(x-h)^2+k[/tex] so that means that [tex]a=\frac{1}{8}[/tex]. We can use that to solve for p in the formula

[tex]p=\frac{1}{4a}[/tex] so

[tex]p=\frac{1}{4(\frac{1}{8}) }[/tex] which simplifies to

[tex]p=\frac{1}{\frac{1}{2} }[/tex] which gives us that

p = 2. Now to find the directrix:

y = k - p becomes

y = 0 - 2 so

y = -2, choice A.

Solution :

It is given that a company named  "Sugary Sweet" wishes to test about the sweet and the flavorful that their participants like the candy.

There are Two levels of the flavor and three levels of sugar.

Thus it is a Two Way ANOVA test.

A two-way ANOVA test is used to test the effect of any two independent variables on the dependent variable.

[tex]$H_{01} : \text{Mean effect of the sugar are equal}$[/tex]

[tex]$H_{02} : \text{Mean effect of the flavor are equal}$[/tex]

[tex]$H_{01} : \text{There is no interaction between the sugar and the flavor}$[/tex]

Answer: 700

Step-by-step explanation: 3 x 200 + 100

Answer:

c.$700

Step-by-step explanation:

3x+100 3 per chair=3x plus the additional 100 dollar fee

3(200)+100

600+100

700