The dimensions of the nations smallest post office are 8 ft 4 in x 7 ft 3 in. Why would you use the measurement 8 ft 4 in. instead of 7 ft 16 in?

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

Answer:

1/16 of the class are left handed boys but we do not know the amount of left handed girls so we cannot be sure.

Step-by-step explanation:

1/2 * 1/8 = 1/16

there is still no way to be sure of how many girls are left handed so you should probably make a note by the problem so the mistake on the test will be realized

By multiplying the fractions, we find that 1/16 of the students in Mrs. Wallace's science class are left-handed boys.

To solve this problem, we first need to understand that it involves fraction multiplication. We know that 1/2 of the students in Mrs. Wallace's science class are boys. Out of these boys, we know that 1/8 of them are left-handed.

When you want to find out a certain amount out of a fraction, you multiply fractions. In this case, 1/2 (the number of boys in class) times 1/8 (the fraction of boys who are left-handed) gives us 1/16. Therefore, 1/16 of the students in Mrs. Wallace's science class are left-handed boys.

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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: Last option.

Step-by-step explanation:

By definition, the square of a binomial is:

[tex](a+b)^2=a^2+2ab+b^2\\\\(a-b)^2=a^2-2ab+b^2[/tex]

Keeping the above on mind, you have the following expression given in the problem:

[tex](x+5)^2[/tex]

Therefore, if:

[tex]a=x\\b=5[/tex]

You obtain the following trinomial:

[tex](x+5)^2=x^2+2(x)(5)+5^2=x^2+10x+25[/tex]

Therefore, the answer is the last option.

Answer:

D. x2 + 10x + 25

Step-by-step explanation:

Answer:

0.3

Explanation:

We are given that:

Probability that a randomly chosen person lives in the East is 0.12

P(East) = 0.12 ..................> I

Probability that a randomly chosen person lives in the West is 0.18

P(West) = 0.18 ............> II

Now, we want to find the probability that the randomly chosen person lives in the East or West

To do this, we will use the following formula:

P(A or B) = P(A) + P(B)

Applying this rule to our givens:

P(East or West) = P(East) + P(West)

P(East or West) = 0.12 + 0.18

P(East or West) = 0.3

Hope this helps :)

Answer:

0.30

Step-by-step explanation:

The probability that a person chosen at random lives in the east region is 0.12

The probability that a person chosen at random lives in the west region is 0.18

The probability that a person chosen at random lives in east or west region;

[tex]P(E\:or\:W)=P(E)+P(W)[/tex]

This implies that;

[tex]P(E\:or\:W)=0.12+0.18[/tex]

[tex]P(E\:or\:W)=0.30[/tex]

Answer:

a) Neither arithmetic nor Geometric

Explanation:

Since 99-89.9= 9.1, and 89.9 - 78.8 = 11.1, the sequence is not arithmetic.

Like wise 89.9/99=0.908 and  78.8/89.9 = 0.876 makes it not a geomtric sequence

Step-by-step explanation:

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

99, 89.9, 78.8, 68.7, . . . . .

Here,

[tex]a_1=99\\\\a_2=89.9\\\\a_3=78.8\\\\a_4=68.7[/tex]

But we can see that there is minor difference between the consecutive terms:

So, we will go for common difference whether it is same or not.

[tex]a_2-a_1=89.9-99=-9.1\\\\a_3=a_2=78.8-89.9=-11.1\\\\a_4-a_5=68.7-78.8=-10.1[/tex]

Their difference are not common.

So, It is neither geometric nor arithmetic.

Hence, Option 'a' is correct.

B 'cause A return value equal to 0

Answer:

try the answer C

Step-by-step explanation:

Answer:

[tex]\large\boxed{The\ slope=\dfrac{3}{2}}[/tex]

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the points (0, 0) and (4, 6) - look at the picture.

Substitute:

[tex]m=\dfrac{6-0}{4-0}=\dfrac{6}{4}=\dfrac{6:2}{4:2}=\dfrac{3}{2}[/tex]

The slope of the line is [tex]\frac{3}{2}[/tex]

The change in y co-ordinate with respect to the change of x co-ordinate of a line is called the slope of the line.

Slope of a line is denoted by "m"

If two points on the line are [tex](x_{1},y_{1})[/tex] & [tex](x_{2} ,y_{2})[/tex], then m = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]

From the given graph, We take to points (2, 3) & (4, 6)

Now, Slope (m) = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]

                         = [tex]\frac{6-3}{4-2}[/tex]

                         = [tex]\frac{3}{2}[/tex]

The slope =  [tex]\frac{3}{2}[/tex]

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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: 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:

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

Answer:

Step-by-step explanation:

l=2w-5

2(l+w)=80

l+w=40

2w-5+w=40

3w=45

w=15 feet

l=25 feet.

the width is 15 feet and length is 25 feet.

Answer:

To get the x-intercepts of the function, f(x) = 4x2 – 24x + 20

It has to be equated to zero and the values of x are the x-intercepts. So,

4x2 – 24x + 20 = 0

The resulting equation is a quadratic equation which can be solved by different methods. The solution is

x = 5, 1

The average therefore is:

(1+5/)2 = 3

The equation that represents the average of the x-intercept is 3.

Option C is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

f(x) = 4x² - 24x + 20

x-intercept is f(x) = 0.

Now,

4x² - 24x + 20 = 0

4(x² - 6x + 5) = 0

x² - 6x + 5 = 0

x² - (5 + 1)x + 5 = 0

x² - 5x - x + 5 = 0

x(x - 5) - 1(x - 5) = 0

(x - 1)(x - 5) = 0

x = 1 and x = 5

The average of x-intercept.

= (1 + 5)/2

= 6/2

= 3

Thus,

The average of the x-intercept equation is 3.

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Answer:

99

Step-by-step explanation:

Answer:

he did better in his History test

Step-by-step explanation:

40-28 gives you 12 marks he lost

whereas

60-39 gives you 21 makes he lost

therefore he done better in his history test the he did in his geo test because he lost more marks in his geo test then her did in his history test

Make the denominators same

take LCM of 40 and 60

120

[tex]\frac{28*3}{40*3}\\\frac{84}{120} \\\\\frac{39*2}{60*2} \\\frac{78}{120}[/tex]

Phil did better in this history test

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:

200

Step-by-step explanation:

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

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:

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.

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.

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.

radius(r)=1cm

answer:-

diameter(d)=2r=2cm

Answer:

Step-by-step explanation:

A diameter is two times longer than a radius. Therefore, if the radius r = 1cm, then the diameter d = 2(1cm) = 2cm.

Answer:

The answer is 8

Step-by-step explanation:

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:

JM

Step-by-step explanation:

If it is equal to each other than all you do is look at what it will be like for the other one.

A is at the beginning and D is at the end.

J is at the beginning and M is at the end.

JM is your answer.

Answer:

JM corresponds to AD.

Step-by-step explanation:

Look at their relative positions in the 2 names.

A and D are the first and last letters.

So the answer is JM because they are the first and last letters in JKLM.

Answer:

A)

Step-by-step explanation: