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The Volume of the smaller prism is 37.5 ft³.

Prism is a three-dimensional structure that has identical polygon bases, and other faces are identical parallelograms.

The volume of the prism is determined by the formula

V = Bh

B is the base area and h is the height of the Prism.

The scale factor is given as 1/4, as the volume of the larger prism is given.

The volume of the larger prism is 2400 ft³

the side lengths will be multiplied by 1/4

Let the base area is for the larger prism the area for the smaller prism will be equal to

A = (1/16) a

The height of the larger prism is h.

Height of the smaller prism will be (1/4)h

The volume of the smaller prism = (1/16)*(1/4) Volume of the Larger Prism

The volume of the smaller prism = 2400 / (16*4)

The volume of the smaller prism = 37.5 ft³.

To know more about the Volume of Prism

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Answer:

73.18

Step-by-step explanation:

equilateral triangle means all sides are the same

A=(√3/4)a^2

A=(√3/4)*13^2

A=73.18 inches square

Answer:

73.18 square inches.

Step-by-step explanation:

To find the area of an equilateral triangle, we use a certain formula.

Where the side length is represented by s, the area is (sqrt(3))/4 * s^2.

Since s = 13, you will have (sqrt(3))/4 * 13^2 = 1.732050808/4 * 169 = 292.7165865/4 = 73.17914662. You can round that to 73.18.

So, the area of the triangle is 73.18 square inches.

Remember to use your units when presenting your answer, and hope this helps!

let's label each pump A, B, and C, just for convenience. A fills the tank by 1/50 every minute, B fills the tank by 1/60 every minute, and C drains it by 1/75 every minute. Now we can put them all into one function: t(1/50 + 1/60 - 1/75) = 1, where t = our time in minutes and 1 = the tank being full.

next, we solve for t: t = 300/7 minutes, or approximately 42.86 minutes.

Answer:

1.54

Step-by-step explanation:

The cotangent value is referred to as the reciprocal or the opposite of a given tangent value. Cotangent is also referred to as it's short form called cot

Mathematically, Cotangent (cot) = 1/tan

In the above question, we are given a value where:

tan = 33°

Cotangent (cot) = 1/tan 33°

Cotangent (cot) = 1.5398649638

We are told to approximate to the nearest hundredth

= 1.54

Answer:

377 choices

Step-by-step explanation:

From the above question, we are told that

A restaurant offers 6 choices of appetizer, 8 choices of main meal and 5 choices of dessert. A customer can choose to eat just one course, or two different courses, or all three courses.

Let us represent each choice by :

A = Appetizer = 6

M = Main meal = 8

D = Dessert = 5

a) The combination of the 3 choices together

AMD=6 × 8 × 5=240

b) AM= Appetizer and Main meal

= 6 × 8 = 48

c) AD= Appetizer and Dessert

= 6 × 5 = 30

d) MD = Main meal × Dessert

= 8 × 5 = 40

e) A,M,D (each alone)=

Appetizer + Main meal + Dessert

= 6 + 8 + 5

= 19

Assuming all choices are available, how many different possible meals does the restaurant offer?

This is calculated as:

AMD + AM + AD + MD + A,M,D

240 + 48 + 30 + 40 + 19

= 377 choices

Answer:

[tex]Total = 2.00mL[/tex]

Step-by-step explanation:

Given

Solution: NaCl

Flask 1: 0.25mL of NaCl

Flask 2: 1.75mL of Nacl

Required

Calculate the total amount of the solution

The total amount of the solution is calculated by adding the size of the contents in both flasks

i,e,

[tex]Total = Flask\ 1 + Flask\ 2[/tex]

[tex]Total = 0.25mL + 1.75mL[/tex]

[tex]Total = 2.00mL[/tex]

Answer:

yep it is 2.00

Step-by-step explanation:

Answer:

the slope is 2 and the y intercept is -2

Step-by-step explanation:

y=2x-2

This is in the form y = mx+b  where m is the slope and b is the y intercept

the slope is 2 and the y intercept is -2

Answer:

15=x

Step-by-step explanation:

a^2 + b^2=c^2

=9^2 +12^2 =x^2

=81 +144=x^2

=/225 =/x^2

=15=x

Answer:

x = 12

Step-by-step explanation:

Use the right triangle altitude theorem.

16/x = x/9

x^2 = 16 * 9

x^2 = 144

x = 12

Answer:

y = 21/5x

Step-by-step explanation:

y is directly proportional to x

y = kx

Find k constant.

21 = 5k

21/5 = k

Plug k as 21/5.

y = 21/5x

Answer:

y=21/5x

Step-by-step explanation:

When y is 21, x is 5.

5(21/5)=21, so we have y=21/5x

Answer:

Step-by-step explanation:

Answer:

( y + b - a - 3d)(y + b + a + 3d).

Step-by-step explanation:

y^2 + 2by + b^2 - a^2 - 6ad - 9d^2

= y^2 + 2by + b^2 - (a^2 + 6ad + 9d^2)

= (y + b)^2 - (a + 3d)^2

This is the difference of 2 squares so we have

(y + b - (a + 3d))(y + b + (a + 3d))

= ( y + b - a - 3d)(y + b + a + 3d)

Answer:

BD = 5

Step-by-step explanation:

∠A = 60°

Since AB = 20 = BC, Then ∠B = 60° resulting in a equilateral triangle with ∠C = 60°.  Then dividing ∠DAE into half gives 4 = angles of 15° yielding each secition of BC being equal to 20/4 = 5.  Do i don't think DE ≈ 9.28 cannot occur.

Answer:

1/5

Step-by-step explanation:

total number of socks= 10

randomly selects two socks.

2/10=1/5 probability

Answer:

14 units

Step-by-step explanation:

We apply the Theorem of reflection over parallel lines.

Theorem: The composition of two reflections over parallel lines that are h units apart is the same as a translation of 2h units.

Given that the two parallel lines are 7 units apart

h=7 units

2h= 2 X 7 =14 units

Therefore, the preimage and the final image will be 14 units apart.

Step-by-step explanation:

If you are not a gerbil, then you are not a pet owner. False; if you are not a gerbil, you can be a human who owns pets.

If you are not a pet owner, then you have a gerbil. False; if you are not a pet owner then you have no pets.

If you do not have a gerbil, then you are not a pet owner. False; you could have a dog or a cat.

If you are not a pet owner, then you do not have a gerbil. True, since if you do not own any pets, you will not have any animals, so you will not have a gerbil.

Hope this helps!

Answer:

If you are not a pet owner, then you have a gerbil. False; if you are not a pet owner then you have no pets

Step-by-step explanation:

Answer:

Step-by-step explanation:

MNOP is a parallelogram             Given

PM // ON                                     opposite sides of parallelogram are parallel

∠ NOM = ∠ONP                          Alternate angles theorem

MN // OP                                  opposite sides of parallelogram are parallel

∠NOP =∠ MNO                     Alternate angles theorem

ON = ON                               common to both triangles ΔOMN & ΔONP

ΔOMN ≅  ΔONP                   ASA congruent

PM ≅ ON                          CPCT -Corresponding Part of Congruent triangle

Answer:

x = 7.5

Step-by-step explanation:

2/3x + 2= 21/3

Subtract 2 from each side

2/3x + 2-2= 21/3-2

2/3x = 21/3 - 6/3

2/3x =15/3

2/3x = 5

Multiply each side by 3/2 to isolate x

2/3x * 3/2 = 5 *3/2

x = 15/2

Answer:

h(t)=-5t+-500

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

i took the test

Answer:

4x

Step-by-step explanation:

When you have a parallel line, the slope of the line is the same. So the slope of (-4,3),(-4,7)=4 would be the same as for example  4x+5  

Answer:

8.7 cm

Step-by-step explanation:

The question is a 2-two-step Pythagoras theorem. (c^2 = a^2 + b^2)

Consider as such, If I were to draw a diagonal line along the base of the cube what is the length of the diagonal line. To find out that we use the theorem. We can substitute a for 5 and b for 5 as well. So

a^2 +b^2 = c^2

5^2 + 5^2 = c^2

25 + 25 = c^2

√50 = c

Then since the line side of the cube is on a 3d angle we need to do the same process again but now using the imaginary diagonal line that we just calculated and the height (5).

a^2 +b^2 = c^2

√50^2 + 5^2 = c^2

50 + 25 = c^2

√75 = c

c = 8.6602...

when rounded to 1 d.p.

c = 8.7

Line AB is 8.7 cm long.

Answer:

A. tan(x) = 2.4/10

Step-by-step explanation:

The question is incomplete and lacks the required diagram. Find the question and diagram attached below.

Which equation can be used to solve for the measure of angle ABC? tan(x) = 2.4/10 tan(x) =10/2.4 sin(x) =10/10.3 sin(x) =10.3/10

We will use the SOH CAH TOA identity to calculate the equation needed to solve for angle ABC.

In a right angled triangle, the side facing the acute angle ABC is the opposite, the longest side is the hypotenuse and the third side (base) is the adjacent.

From the diagram shown;

AB = hypotenuse = 10.3cm

AC = opposite = 2.4cm

BC = adjacent  = 10cm

To get the angle x, we can use the SOH and TOA identity.

SOH means sin<ABC = opp/hyp

Sin(x) = AC/AB = 2.4/10.3

TOA ≈ Tan(x) = opp/adj

Tan(x) = 2.4/10

The equation that can be used to solve for the measure of angle ABC are therefore sin(x) = 2.4/10.3 OR tan(x) = 2.4/10

Based on the given option,

tan(x) = 2.4/10 is the only correct answer.

Answer:

in short its A.

Step-by-step explanation:

EDGE 2021

Step-by-step explanation:

you can split triangle in two 90-:80 triangles

Answer:

[tex]9.05 * 10^{7} kg[/tex]

Step-by-step explanation:

Given

[tex]Statue\ of\ Liberty\ =\ 2.04 * 10^5 kg[/tex]

[tex]Washington\ Monument\ =\ 9.07 * 10^7 kg[/tex]

To get the number of kilograms the Washington Monument weighs more than the Statue of Liberty, we simply calculate the difference;

Difference = Washington Monument - Statue of Liberty

[tex]Difference = \ 9.07 * 10^7 kg - \ 2.04 * 10^5 kg[/tex]

Expand [tex]10^7[/tex]

[tex]Difference = \ 9.07 * 10^{5+2} kg - \ 2.04 * 10^5 kg[/tex]

[tex]Difference = \ 9.07 * 10^{5} * 10^2 kg - \ 2.04 * 10^5 kg[/tex]

Take out the common factor in the above expression

[tex]Difference = 10^{5}\ (\ 9.07 * 10^2 kg - \ 2.04\ kg)[/tex]

[tex]10^2 = 100;[/tex] so we have

[tex]Difference = 10^{5}\ (\ 9.07 * 100 kg - \ 2.04\ kg)[/tex]

[tex]Difference = 10^{5}\ (\ 907 kg - \ 2.04\ kg)[/tex]

[tex]Difference = 10^{5}\ (904.96\ kg)[/tex]

Open bracket

[tex]Difference =904.96 * 10^{5} kg[/tex]

Write in standard form

[tex]Difference =9.0496 * 10^2 * 10^{5} kg[/tex]

[tex]Difference =9.0496 * 10^7 kg[/tex]

[tex]Difference =9.05 * 10^7 kg[/tex] (Approximated)

Hence, he Washington Monument weigh more than the Statue of Liberty by about [tex]9.05 * 10^{7} kg[/tex]

Answer:

it is d i just did the 4 quiestion assignment by the learning odessy

Step-by-step explanation:

Answer:

a) we know that:

the tens digit exeeds the units digit by 3, then if we have two digits

ab.

and b, the digit for units is equal to r.

then a, the digit for tens, is equal to r + 3.

Then, if r = 4, we have that the digit for tens is r + 3 = 7

and the number is 74.

b) if n is an integer, then we know that 2*n is an even number.

Now, the next even number is always 2 units away, then the next even number to 2*n is:

2*n + 2 = 2*(n + 1)

Answer: C

Step-by-step explanation:

y = ax + bx + c is the general equation for quadratic function. While the discriminant D is

D = b^2 - 4ac

You are given the equation:

y = x^2 + 3x - 4

Where a = 1, b = 3 and c = -4

Substitutes all the parameters into the discriminant D formula

D = 3^2 - 4 × 1 × -4

D = 9 - ( - 16 )

Open the bracket

D = 9 + 16

D = 25

Therefore, D = 25 and the roots are rational

Answerr:

Step-by-step explanation:

Answer: 10 for each side but in total is 20

Step-by-step explanation: u multiply 5 x 4 = 20 divided by 2 to get 10 meters and another is 4 divided by 2 is 2 x 5 is 10 meters times 2 is 20 total

Answer:

D.

[tex]u =3[/tex]

[tex]v =\sqrt{3}[/tex]

Step-by-step explanation:

Given

The triangle in the diagram above

Required

Find the missing lengths, u and v

To find the missing lengths, we have to check the relationship between the missing lengths, the given length and the given angle;

From trigonometry;

[tex]sin\ \theta = \frac{Opp}{Hyp}[/tex]; Where Opp = Opposite and Hyp = Hypotenuse

From the attached diagram;

[tex]\theta = 30[/tex]

[tex]Opp = v[/tex]

[tex]Hyp = 2\sqrt{3}[/tex]

[tex]sin\ \theta = \frac{Opp}{Hyp}[/tex]  becomes

[tex]sin\ 30 = \frac{v}{2\sqrt{3}}[/tex]

Multiply both sides by [tex]2\sqrt{3}[/tex]

[tex]2\sqrt{3} * sin\ 30 = \frac{v}{2\sqrt{3}} * 2\sqrt{3}[/tex]

[tex]2\sqrt{3} * sin\ 30 = v[/tex]

In radians, [tex]sin30 = \frac{1}{2}[/tex]

[tex]2\sqrt{3} * \frac{1}{2} = v[/tex]

[tex]\sqrt{3} = v[/tex]

[tex]v =\sqrt{3}[/tex]

Similarly, From trigonometry;

[tex]cos\ \theta = \frac{Adj}{Hyp}[/tex]; Where Adj = Adjacent

From the attached diagram;

[tex]\theta = 30[/tex]

[tex]Adj = u[/tex]

[tex]Hyp = 2\sqrt{3}[/tex]

[tex]cos\ \theta = \frac{Adj}{Hyp}[/tex]  becomes

[tex]cos\ 30 = \frac{u}{2\sqrt{3}}[/tex]

Multiply both sides by [tex]2\sqrt{3}[/tex]

[tex]2\sqrt{3} * cos\ 30 = \frac{u}{2\sqrt{3}} * 2\sqrt{3}[/tex]

[tex]2\sqrt{3} * cos\ 30 = u[/tex]

In radians, [tex]cos30 = \frac{\sqrt{3}}{2}[/tex]

[tex]2\sqrt{3} * \frac{\sqrt{3}}{2} = u[/tex]

[tex]\sqrt{3} * \sqrt{3} = u[/tex]

[tex]3 = u[/tex]

[tex]u =3[/tex]

Answer:

D. 2y < 2

Step-by-step explanation:

To find the equation with shaded area below the boundary line, all we need to do is to examine each inequality and find the one which gives

+y < ( a constant)

We can leave out the x term for this.

For example:

A. y>5  clearly it is shaded above the line (because of the > sign)

B. -3y <3 => 3y > -3    so again it is shaded above

C. -3y                   is not even an inequality

D. 2y < 2              clearly it is shaded BELOW

E. 4y >12              clearly it is shaded above

See also attached diagram.  The answer is represented by the purple area.  All the other areas are shaded above the boundary line.

Answer:

Option D is the correct option.

Step-by-step explanation:

Let the points be A and B

A ( 7 , 35 ) -----> ( x1 , y1 )

B ( 7 , 21 ) -------> ( x2 , y2 )

Now, finding the distance between these two points:

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

Plug the values

[tex] = \sqrt{(7 - 7) ^{2} + {(21 - 35)}^{2} } [/tex]

[tex] = \sqrt{ {0}^{2} + {( - 14)}^{2} } [/tex]

0 raised to any positive power equals 0

[tex] = \sqrt{0 + {( - 14)}^{2} } [/tex]

When adding or subtracting 0, the quantity doesn't change

[tex] = \sqrt{ {( - 14)}^{2} } [/tex]

Reduce the index of the radical and exponent with 2

[tex] = 14 \: units[/tex]

Hope this helps...

Best regards!

~ a music lover

Answer:

50

Step-by-step explanation:

The perimeter of a Triangle is the sum of it's 3 sides.

We are given two sides here which is side length 5.6 and a side of length 19.7

Let's us represent the third side as x

Therefore

x + 19.7 + 5.6 = Perimeter of the triangle

We would have this equation

But it is important to know that every side of a triangle must be less than the sum of the other two sides, hence

x < 19.7 + 5.6

x < 25.3

Adding 25.3 to both sides to make the left side equal to the perimeter

perimeter = x+25.3 < 25.3 + 25.3 = 50.6

Therefore, 50.6 is the smallest whole number that is larger than the perimeter of the triangle in the question above.

Therefore, the biggest whole number smaller than the perimeter of the above triangle is 50

Answer:

39

Step-by-step explanation:

25.3<x>14.1

Because 5.6 +19.7=25.3

Because 19.7-5.6=14.1

And 25.3+14.1=39.4

WE NEED WHOLE NUMBER A LITTLE BIT SMALLER (cause thats the question)

S0, 39.4 turns into 39