What is the volume of the composite figure

a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.

In base seven, we have the following conversions:

1 long = 1 unit

1 flat = 10 units

1 block = 10 flats

To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.

So, the fewest number of multibase blocks required would be 2 flats.

Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.

In base three, we have the following conversions:

1 long = 1 unit

1 flat = 3 units

1 block = 3 flats

To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.

So, the fewest number of multibase blocks required would be 3 flats and 1 unit.

Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

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Answer:

$0.75

Step-by-step explanation:

Step 1:

5 ibs for $3.75    Given

Step 2:

$3.75 ÷ 5     Divide

Answer:

$0.75

Hope This Helps :)

Answer:

-5i and 5i cannot be roots of the equation, since they are complex.

Step-by-step explanation:

A 3-degree polynomial equation must have 3 roots, if one of its roots is a complex number, then its conjugate must also be a root of the function. The problem already stated two roots, which are reals, therefore the last root must also be real. Using this line of thought we know that -5i and 5i cannot be roots of the equation, since they're complex.

The length of the two segments, written as radicals, are:

AB = √117

PQ = √244

Remember that for a segment whose endpoints are (x₁, y₁) and (x₂, y₂), the length of the segment is:

L = √( (x₂ - x₁)² + (y₂ - y₁)²)

First, for the segment AB the endpoints are:

A = (-4,  -4)

B = (2, 5)

Then the length is:

L =  √( (-4 - 2)² + (-4 - 5)²)

L = √117

For the segment PQ the endpoints are:

P = (-6, 8)

Q = (6, -2)

The length is:

L =  √( (-6 - 6)² + (8 + 2)²)

L = √244

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Answer:

70

Step-by-step explanation:

10[25-{8-6(16-13) }]÷5

10[25-{8-6*3)}]/5

10[25-{8-18}]/5

10[25-(-10)]/5

10[25+10]/5

10*35/5

70

Step-by-step explanation:

please mark me as brainlest

Using the pattern, n can represent the the increase of dots according to step.

In the given question we have to find what values make sense for n in this situation.

n is representing the number.

As we can see that there is a pattern given.

In the step 1 have 1 dot, in step 2 have 3 dots, in step 3 have 6 dots and in step 4 have 10 dots.

So if we see the pattern then according to number of step the dots increasing accordingly.

As In step 1 have 1 dot, in step 2, 2 dots increase, in step 3, 3 dots increase and in step 4, 4 dots increase.

So, n can represent the the increase of dots according to step.

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\(\\ \rm\Rrightarrow log_7(5-x)-log_7(3+x)=-1\)

\(\\ \rm\Rrightarrow log_7(5-x)=-1+log_7(3+x)\)

\(\\ \rm\Rrightarrow 7(5-x)=3+x\)

\(\\ \rm\Rrightarrow 35-7x=3+x\)

\(\\ \rm\Rrightarrow 35-3=x+7x\)

\(\\ \rm\Rrightarrow 32=8x\)

\(\\ \rm\Rrightarrow x=4\)

Answer:

x = 4

Step-by-step explanation:

\(\large \boxed{\begin{minipage}{7.5 cm}\underline{Log Laws} \\ \\$\textsf{Quotient law}: \quad \log_ax - \log_ay=\log_a\frac{x}{y} \\ \\\textsf{If }\: \log_ab=c\: \textsf{ then }\: a^c=b$\\\end{minipage}}\)

\(\large \begin{aligned}\log_7(5-x)-\log_7(3+x) & =-1\\\\\log_7\left(\dfrac{5-x}{3+x}\right) & =-1\\\\\left(\dfrac{5-x}{3+x}\right) & =7^{-1}\\\\\dfrac{5-x}{3+x} & =\dfrac{1}{7}\\\\7(5-x) & =3+x\\\\35-7x & =3+x\\\\35-3 & =x+7x\\\\8x & =32\\\\x & =\dfrac{32}{8}\\\\x & =4\end{aligned}\)

After eliminating the parameter, the rectangular equation is y = x³ – 3x² + 3x – 1. Option C is the correct option.

What is a rectangular equation?

An equation in rectangular form, also known as a rectangular equation, is a single equation written in the standard form in mathematics that uses variables like x, y, and z.

Given parametric equations are

y = t³  .......(i)

x = t + 1  .....(ii)

Calculate the value of t from equation (ii):

x = t + 1

t = x - 1

Putting t = x - 1 in equation (i):

y = (x - 1)³

Applying algebric identity (a - b)³ = a³ – 3a²b + 3ab² – b³:

y = x³ – 3x² + 3x – 1

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Answer:

c

cubic

all real numbers

Step-by-step explanation:

The work required to pump the water out of the spout is approximately 64,307,077 ft-lb

To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then convert it to work using the formula: work = force × distance.

First, let's calculate the volume of water in the tank. The frustum of a cone can be represented by the formula: V = (1/3)πh(r1² + r2² + r1r2), where r1 and r2 are the radii of the two bases and h is the height.

Given r1 = 3 ft, r2 = 6 ft, and h = 12 ft, we can calculate the volume:

V = (1/3)π(12)(9 + 36 + 18) = 270π ft³

Now, we can calculate the weight of the water using the density of water:

Weight = density × volume = 62.5 lb/ft³ × 270π ft³ ≈ 53125π lb

Next, we convert the weight to force by multiplying it by the acceleration due to gravity (32.2 ft/s²):

Force = Weight × acceleration due to gravity = 53125π lb × 32.2 ft/s² ≈ 1709125π lb·ft/s²

Finally, we can calculate the work by multiplying the force by the distance. Since the water is being pumped out of the spout, the distance is equal to the height of the frustum, which is 12 ft:

Work = Force × distance = 1709125π lb·ft/s² × 12 ft ≈ 20509500π lb·ft ≈ 64307077 lb·ft

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Answer:

0

Step-by-step explanation:

Answer:

(-2, 33) and (5, - 16)?

A. 7x- y=51

B. 7x+ y= -47

C. 7x+ y= -14 D. 7x+y= 19

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

I hope I helped have a great day.

Answer: depends if its about a tax deductable he can if its from his buisness account

Step-by-step explanation:

Answer:

Step 2

Step-by-step explanation:

from Step 1      4/3 - 1/3 = 3/3  = 1   =  q   =  q + 1/3 - 1/3

Answer:

-64

Step-by-step explanation:

By looking at the numbers, we can identify that this is a geometric sequence and the ratio would be 2. The formula to find the nth term in a geometric series is:

\(t *r^{n-1}\)

where t is the first term and r is the ratio. We can substitute in the information we know:

\(-\frac{1}{2} *2^{n-1}\)

We are looking for the eighth term, so we substitute 8 where n is:

\(-\frac{1}{2}*2^{8-1}\)

We can simplify:

\(-\frac{1}{2}*2^7\)

\(-2^6\)

\(-64\)

Answer:

Step-by-step explanation:

Points plotted.

See the graph attached.

Correct choice is:

OPTION A

#CcarryOnLearning

Answer:

C) 12(5-3w) and A) 6(10-6w)

Step-by-step explanation:

60-36w=12(5-3w)

60-36w = 60+ -36w

Answer:C

Step-by-step explanation:

Answer:

volume of a cylindrical water tank = 70,650cm³

Step-by-step explanation:

volume of cylinder, V = πr²h

where π = 3.14

h = 100cm

r = ?

given is diameter = 30cm

r = d/2 = 30/2 = 15cm

substituting the values in the formula,

V = 3.14 * 15² * 100

= 3.14 * 225 * 100

= 70,650cm³                        

Answer:

How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm

Volume: 706,500 cm³

Step-by-step explanation:

How much space it would take up:

To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.

The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.

To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(15 cm)²

A = π(225 cm²)

A ≈ 706.86 cm²

So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.

The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.

Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.

Volume:

To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to find the radius by dividing the diameter by 2:

Radius = 30 cm / 2 = 15 cm

Now we can calculate the volume:

V = π(15 cm)²(100 cm)

V = 3.14 * 225 cm² * 100 cm

V = 706,500 cm³

Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.

Answer: 52

Step-by-step explanation: use the calculator lol

Answer:

52

Step-by-step explanation:

The value that is not reasonable for the true mean weight of the residents of the town is 193 pounds

Given that the mean weight is 187 pounds with a margin of error of 3 pounds, we can construct the interval as follows:

Mean weight - Margin of error = 187 - 3 = 184 pounds

Mean weight + Margin of error = 187 + 3 = 190 pounds

So, the reasonable range for the true mean weight of the residents of the town is between 184 and 190 pounds.

Now, let's evaluate the options to identify the value that falls outside this reasonable range:

A. 170 pounds - This value falls below the lower limit of the reasonable range (184 pounds). Therefore, it is not a reasonable value for the true mean weight.

B. 188 pounds - This value falls within the reasonable range of 184 to 190 pounds. It is a reasonable value.

C. 193 pounds - This value falls above the upper limit of the reasonable range (190 pounds). Therefore, it is not a reasonable value for the true mean weight.

D. 186 pounds - This value falls within the reasonable range of 184 to 190 pounds. It is a reasonable value.

E. 182 pounds - This value falls below the lower limit of the reasonable range (184 pounds). Therefore, it is not a reasonable value for the true mean weight.

From the options provided, the value that is not reasonable for the true mean weight of the residents of the town is 193 pounds.

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

The volume of the two prisms compares that the volume of prism B will double.

We are given that side length of the cube measured 18 inches in length. She built another prism (Prism B) with the same dimensions as the cube, except she doubled its height.

When the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross-section is same as its base, then its volume is:

V = B x h

So, the volume of the two prism A= V = B x h

V = 18 x h = 18h

the volume of the two prism B= V = B x h

V = 18 x 2h = 36h

So, the volume of prism B will double thus the correct option is B.

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The complete question is;

Anna built a prism (Prism A) out of a cube of wood. The side length of the cube measured 18 inches in length. Anna built another prism (Prism B) with the same dimensions as the cube, except she doubled its height.

How does the volume of the two prisms compare?

The volume of prism B will triple.

The volume of prism B will double.

The volume of prism B will decrease.

The volume of prism B will be cut in half.

The number of tiles is 96

From the question, we have

The width of the room is 16 feet, 8 inches and the client has chosen a square tile that measures 4 inches on each side.

16 feet = 192 inches

Number of tiles = (192*8)/(4*4)

= 96 tiles

The number of tiles is 96.

Multiplication:

The product of two or more numbers is computed by mathematicians using multiplication. In everyday life, it is a basic mathematical operation that is frequently used. We employ multiplication when we must combine groups of like sizes. The operation of multiplication serves as a representation of the fundamental idea of adding the same number repeatedly. The product of two or more numbers is what is obtained when those numbers are multiplied, and the factors are the quantities that are multiplied. Multiplying the numbers simplifies the process of adding the same number repeated.

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Answer:

B and A

.......................

Answer:

M' and N'O'

Step-by-step explanation:

Answer:

B. 0.56

Step-by-step explanation:

A. 0.81  > 0.7

B. 0.56  < 0.7 & 0.56 > 0.15

C. 0.76  > 0.7

D. 0.005​ < 0.15

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs.

We have,

The Pythagorean theorem that relates to the sides of a triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (known as the legs). Mathematically, it can be expressed as a² + b² = c², where "a" and "b" are the lengths of the legs, and "c" is the length of the hypotenuse.

Now,

In a right triangle, the legs are the two sides that form the right angle, and the hypotenuse is the side that is opposite to the right angle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs. So, the relationship between the legs and the hypotenuse can be described by this theorem. In other words, if we know the length of the two legs of a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse, and vice versa. The hypotenuse is always the longest side of the right triangle, and it is also the side that connects the two legs.

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complete question:

Applying the Pythagorean Theorem In this activity, you will explain your understanding of mathematical relationships and use the Pythagorean theorem to solve real-world problems. Question 1 In your own words, explain the relationship between the legs and the hypotenuse of a right triangle.

Answer:

78.67

Step-by-step explanation:

The computation of the average for a student is shown below:

= Different Weights × different activities

= (3% × 81) + (9% × 90) + (9% × 92) + (17% × 86) + (17% × 71) + (17% × 93) + (28% × 62)

= 2.43 + 8.1 + 8.28 + 14.62 + 12.07 + 15.81 + 17.36

= 78.67

Hence, the average of the student is 78.67

We simply applied the above formula

Answer:

1. 4(x+1)  2. 9+x   3. 21+x  4. 15+x  5. 9x+2  6. 2(2x+13y) 7. 29y+5x  8. 75x  9. 28x

Answer:

1. 4x+4

2. 9+x

3. 21+x

4. 15+x

5. 13x+2

6. 4x+26y

7. 29y+5x

8. 75x

9. 28x

Answer:

(3z)^3

Step-by-step explanation:

27 = 3 * 3 * 3 = 3^3

3^3 z^3   = (3z)^3

Answer:

a ≈ 1.59

b ≈ 6.69

Step-by-step explanation:

Law of Sines: \(\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}\)

Step 1: Find c using Law of Sines

\(\frac{6}{sin58} =\frac{c}{sin13}\)

\(c = sin13(\frac{6}{sin58})\)

c = 1.59154

Step 2: Find a using Law of Sines

\(\frac{6}{sin58} =\frac{a}{sin109}\)

\(a = sin109(\frac{6}{sin58} )\)

a = 6.68961