The mystery number is a three-digit number. Its digits are 1, 8, and 4.
• The 4 and the 8 are not next to each other.
• The 1 comes before the 4.
What is the mystery number?

Answer:

4) Volume model = 1723 ft³

5) The percentage of the original tank is 51200% of the mock-up

Step-by-step explanation:

4) ∵ The volume of the main tank is 882,158 ft³

∵ The dimension of the scale model is 1/8 of the original model

∵ V model/v original = (dimension model/dimension original)³

∴ Volume model/882,158 = (1/8)³

∴ Volume model = (1/512) × 882,158 = 1722.965 = 1723 ft³

5) The percentage of the original tank is

    (882158/1722.965) × 100% = 51200%

Final answer:

The volume of the scale model tank is 1/512 of the original tank's volume, which is approximately 0.1953125%. The original tank's volume is 51200% of the scale model's volume.

Explanation:

Step-by-Step Solution for Volume of Scale Model Tank

Let's denote the original dimensions of the theater's main show tank as length L, width W, and height H. Therefore, the original volume V of the tank is V = L \times W \times H.

For the scale model, each linear dimension is scaled down to one eighth of the original. Thus, the dimensions of the model will be L/8, W/8, and H/8.

Now, the volume of the scale model V_{model} can be calculated as:

The volume of the scale model is 1/512 or about 0.1953125% of the original tank's volume.

Percentage Volume of Original Tank to Mock-up Tank

To find out what percentage the original volume is of the mock-up tank, we can set up a proportion.

The original volume is 51200% of the mock-up of the tank.

A. Prism

A prism has two bases

Step-by-step explanation:

[tex]n-a\ number\\\\3.145<n<3.146\Rightarrow 3.1450<n<3.1460\\\\n\in\{3.1451,3.1452,\ 3.1453,\ 3.1454,\ ...,3.1459\}[/tex]

Answer:

Step-by-step explanation:

3x3=9 For the second week

9x3=27 For the Third week

27x3=81 For the Forth week so

3 Min first week

9 Min second week

27 Min third week

81 Min forth week

b is the correct answer

Step-by-step explanation:

The symbolic notation that represents the statement 'Mary works at the water park or takes college classes' is P ∨ Q.

The symbolic notation that represents the statement 'Mary works at the water park or takes college classes' is P ∨ Q.

The '∨' symbol represents the logical operator 'or', which indicates that either statement P or statement Q (or both) can be true for the overall statement to be true.

In this case, Mary can work at the water park, take college classes, or do both.

https://brainly.com/question/32607178

#SPJ2

Final answer:

The sales price of the skirt was $15.60.

Explanation:

In this problem, we are given that the total cost of the skirt, pair of shoes, and pair of socks is $34.95 before tax. We are also given that the pair of socks costs $3.75. Since the original prices of the skirt and shoes were the same, we can assume they each cost x dollars.

Therefore, the equation we can set up is: x + x + 3.75 = 34.95.

We can solve this equation to find the value of x, which represents the original price of the skirt. Subtracting 3.75 from both sides, we get: 2x = 31.20. Dividing both sides by 2, we find that x = 15.60. Therefore, the sales price of the skirt was $15.60.

Answer:

D

Step-by-step explanation:

Since it is at least 90, it literally means that the lowest possible value is 90. Therefore the number can only be greater than or equal to 90. So, the answer is D.

Answer:

C. X is less than or equal to 90

Step-by-step explanation:

because as you can see  that the last sentence it says. A final grade of at LEAST 90?

Answer:

99

Step-by-step explanation:

Answer: 3.8

Step-by-step explanation: See the attached file!

Answer:

see explanation

Step-by-step explanation:

If the sequence is arithmetic then there will be a common difference d between consecutive terms, that is

8 - 4 = 4

16 - 8 = 8

22 - 16 = 6

32 - 22 = 10

The difference between terms is not common

Hence this is not an arithmetic sequence

Answer:

Step-by-step explanation: 50.27 is the area

Final answer:

The area of a circular rug with an 8 feet diameter, using the formula A = π[tex]r^2[/tex] and π approximated as 3.14, is 50.24 square feet.

Explanation:

The question seeks to determine the area of a circular rug with a diameter of 8 feet. To calculate the area of a circle, the formula used is A = π[tex]r^2[/tex], where A is the area and r is the radius of the circle. Since the diameter is twice the radius, we have a radius of 4 feet (8 feet divided by 2).

Using 3.14 for π, the calculation is:

First square the radius: 4² = 16.

Multiply this by π (approximated as 3.14): A = 3.14 × 16.

Complete the multiplication to find the area: A = 3.14 × 16 = 50.24 square feet.

Therefore, the area of the rug is 50.24 square feet.

Answer:

[tex]\large\boxed{x=\pm\sqrt{10}}[/tex]

Step-by-step explanation:

[tex]x^2=10\Rightarrow x=\pm\sqrt{10}\\\\\text{because}\ (-\sqrt{10})^2=10\ \text{and}\ (\sqrt{10})^2=10.\\\\\text{used}\ (\sqrt{a})^2=a[/tex]

Answer:

try the answer C

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

19.55 can be either 19 and 20, but it is closer to 20!

Answer: The answer is 20.

Step-by-step explanation: So anytime you are rounded if the number is 5 or over 5 it will round up. If it is under 5 it will round down and in this case it is over half or 5 so it would round up to 20 since 20 is a whole number.

Volume of sphere = 4/3 x PI x r^3

= 4/3 x 3.14 x 6^3

= 904.3 cubic meters

Volume of cone = PI x r^2 x h/3

h = √13^2-5^2 = 12

= 3.14 x 5^2 x 12/3

= 314 cubic meters

Answer:

Price before tax is $64

Step-by-step explanation:

It asks for price before sales tax, so ignore sales tax %.

P=original-[original•(20/100)]

=80-80•0.2

=80-16

P=64

Answer:

$64

Step-by-step explanation:

We have been given that an item regularly priced at $80 is on sale for 20% off. There is 3% sales tax. We are asked to find the sales price before sales tax.

The sales price would be 80 minus 20% of 80.

[tex]\text{Sales price}=80-\frac{20}{100}\times 80[/tex]

[tex]\text{Sales price}=80-\frac{1600}{100}[/tex]

[tex]\text{Sales price}=80-16[/tex]

[tex]\text{Sales price}=64[/tex]

Therefore, the sales price before sales tax would be $64.

Answer:

-[tex]\sqrt{\frac{2-\sqrt{2}}{4}[/tex]

Step-by-step explanation:

The cosine half-angle formula is

[tex]cos\frac{\pi }{2}[/tex]=±[tex]\sqrt{\frac{1+cosx}{2} }[/tex]

we can write

[tex]cos \frac{3\pi }{8}[/tex]

as

[tex]cos\frac{\frac{3\pi }{4} }{2}[/tex]

=-[tex]\sqrt{\frac{1+cos\frac{3\pi}{4} }{2}[/tex]

=-[tex]\sqrt{\frac{1-\frac{\sqrt{2}}{2}}{2}[/tex]

=-[tex]\sqrt{\frac{2-\sqrt{2}}{4}[/tex]

(cosine is negative is in second quadrant)

Using the half angle identity, the exact value of cos 3 pi / 8 is (√2 - 1) / 2√2.

Given a trigonometric expression,

cos 3π/8

We have to find the exact value of this using the half angle identity.

The half angle identity in terms of cosine function is,

cos (x/2) = ± √[(1 + cos x) / 2]

Here the angle is 3π/8.

This can be written as,

3π/8 = 3π/4 / 2

Substituting to the formula,

cos (3π/4/2) = √[(1 + cos 3π/4) / 2]

Now,

cos 3π/4 = cos (π - π/4)

               = -cos(π/4)

               = - 1/√2

Substituting to the formula,

cos (3π/4/2) = √[(1 - 1/√2) / 2]

                    = (√2 - 1) / 2√2

Hence the value is (√2 - 1) / 2√2.

Learn more about Half Angle identities here :

https://brainly.com/question/30404576

#SPJ6

Answer:

Final answer is $9000.

Step-by-step explanation:

Given that Alice took out a $15,000 loan for college. She is borrowing money from two banks. Bank A charges an interest rate of 6%, and Bank B charges an interest rate of 7%. After one year, Alice owes $960 in interest.

Now we need to find out about how much money did she borrow from Bank A.

So let's assume that money borrowed from bank A = x

then money borrowed from bank B = 15000-x

Interest from bank A = 6% of x = 0.06x

Interest from bank B = 7% of (15000-x) = 0.07(15000-x)

Given total interest is $960. So we can write equation:

0.06x+0.07(15000-x)=960

0.06x+1050-0.07x=960

1050-0.01x=960

-0.01x=960-1050

-0.01x=-90

[tex]x=\frac{-90}{-0.01}[/tex]

x=9000

Hence final answer is $9000.

Answer:

The amount borrowed from bank A = $9000

Step-by-step explanation:

Formula:

I = PNR/100

P - Principle amount

N - Number of years

R - Rate of interest

It is given that,Alice took out a $15,000 loan for college. Bank A charges an interest rate of 6%, and Bank B charges an interest rate of 7%. After one year, Alice owes $960 in interest.

Let 'x' be the amount borrowed from Bank A

Then the amount borrowed from Bank B = 15000 - x

To find the value of x

I = PNR/100

Here I = $960

(x*1*6)/100 + (15000 - x)*1*7/100 = 960

6x/100 + (15000*7)/100  - 7x/100 = 960

1050 - x/100 = 960

x/100 = 1050 - 960 = 90

x = 90 * 100 = 9000

Therefore the amount borrowed from bank A = $9000

Answer:

The answer is 8

Step-by-step explanation:

Answer:

The answer is C on edge (all real numbers except 1)

Step-by-step explanation:

Answer:

A)

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

0, 2, 4, 6, 8, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30 are even numbers.

mark as brainsliest♡

Answer:

28

Step-by-step explanation:

29, 28, 27

28 is before 29 and its even fam

Answer

16

Step by step

The triangles,PRS and PQT are similar.

PS:ST=15:3

=5:1

let PQ=x

PR:RQ

x+4:4

using the PS:ST ratio,

5:1=x+4:4

4×5=1(x+4)

20=x+4

collecting like terms

20-4=x

x=16.

Answer:

B

Step-by-step explanation:

There are 2 secant lines intersecting a circle. We can use far arc - near arc formula to find this.

Let far arc be arc AE, and near arc be arc BD. So the theorem tells us:

Measure of Angle C = half of the difference of far arc - near arc

so we can say:

∠ACE = half of (arc AE - arc BD)

or

∠ACE = [tex]\frac{1}{2}(172-58)[/tex]

Option B is right.

Answer:b

Step-by-step explanation:

Answer:

C. a 180° rotation about its center.

Answer:

The correct answer option is C. a 180° rotation about its center.

Step-by-step explanation:

We are to determine whether which of the transformations will always map a parallelogram onto itself.

We know that a parallelogram has a rotational symmetry of 2 so during a rotaion of 360 degrees, a parallelogram maps onto itself twice, which is at 180^{\circ} and 360^{\circ} about its center.

Therefore, the correct answer option is C. a 180° rotation about its center.

What are the statements?

Final answer:

The given statements about the points (3,0) and (-1,-3) are not true. One cannot determine if they are parallel to x-axis or mutually perpendicular without more information or a third point/vector.

Explanation:

The question describes two points, (3,0) and (-1,-3), and asks which statements are true regarding their position. To determine the relationship between these points, we can visualize them on a coordinate system. Point (3,0) lies on the x-axis, while point (-1,-3) does not. The statements provided suggest a scenario where the points either form parallel lines along the x-axis or are mutually perpendicular to each other.

Neither of the given statements is correct since one point lies on the x-axis, and the other does not, which means they cannot be parallel along the x-axis. Additionally, without a third point to form a triangle or a clear reference for perpendicular vectors, we cannot assert that they are mutually perpendicular. Therefore, we need additional information, such as the context for these points or the third reference point/vector, to make a proper determination.

Regarding the information about vectors and coordinates, remember that vectors can be used to define directions and magnitudes from one point to another. In this case, however, we are only given two points without clear instruction on how to interpret them as vectors.

For the statement 'Clearly, the three directions are mutually perpendicular to each other,' note that this applies to three-dimensional coordinate axes or where three vectors are given, which are specifically defined as perpendicular. This situation described with two points does not satisfy the conditions of that statement.

I thinks its 4 if that's one of your answers. It says of 3 people from a group of 12. And a 3 and 4 are both factors of 12. 3 x 4 = 12.

The number of possible committees of three people from a group of 12 can be found by using combinations, resulting in 220 possible committees.

The number of committees of three people possible from a group of 12 can be calculated using combinations.

To choose 3 people out of 12, you use the combination formula: C(12,3) = 220.

Therefore, there are 220 possible committees of three people from a group of 12.

Answer:

D) 180

Step-by-step explanation:

Keep in mind to properly use a percent you must set it to a decimal.

To do so simply move the . in 75. over to the left 2 times. Which will go to .75!

Now time to multiply 240 by .45.

240 x .45 =180

Answer:

D 180

Step-by-step explanation:

75/100*240=180

Find the length of the hypotenuse

34^2 + 27^2 = c^2

1156 + 729 = 1885

c^2 = 1885

sqrt(1885)

c = 43.42

Answer:

All sides of the triangle are a = 34, b = 27 and c = 46.7

and angles are A = 46°, B = 34.83° and C = 99.17°

Step-by-step explanation:

In a given triangle A = 46°, a = 34 units and b = 27 units

Then we have to find all angles and measure of the side left.

By sine rule,

[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

[tex]\frac{a}{sinA}=\frac{b}{sinB}[/tex]

[tex]\frac{34}{sin46}=\frac{27}{sinB}[/tex]

sinB = [tex]\frac{27\times sin46}{34}[/tex]

sinB = 0.5712

B = [tex]sin^{-1}(0.5712)[/tex]

B = 34.83°

Since in a triangle,

∠A + ∠B + ∠C = 180°

46°+ 34.83° + ∠C = 180°

80.83° + ∠C = 180°

∠C = 180 - 80.83 = 99.17°

[tex]\frac{b}{sinB}=\frac{c}{sinC}[/tex]

[tex]\frac{27}{sin34.83}=\frac{c}{sin99.17}[/tex]

[tex]\frac{27}{0.5711}=\frac{c}{0.9872}[/tex]

c = [tex]\frac{27\times 0.9872}{0.5711}=46.67[/tex]

Therefore, all sides of the triangle are a = 34, b = 27 and c = 46.7

and angles are A = 46°, B = 34.83° and C = 99.17°