The dimensions of the box below are reduced by half. What is the ratio of the volume of the new box to the volume of the original box?

please help!!!!
u will get 100 points!!!!

The given fraction can be converted into  whole  number as

16/5 +52/9 =9

99/7 -15/2=7

13/8+ 27/5=7

41/4-26/15=9

27/10+44/9=8

We can see that all the expression was given as a fraction the to convert to whole number we will need to solve them by performing the neccessary addition as well as substraction operations then it will converted to whole number.

16/5 +52/9

=404/45.

=8.977

=9

99/7 -15/2=

= 93/14

=6.643

7

13/8+ 27/5

= 281/40

=7.025

7

41/4-26/15

=511/60

=8.52

=9

27/10+44/9

= 683/90

=7.59

=8

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Florence was 0.16 m/s faster in the 100-meter race than in the 200-meter race

An equation is an expression that shows the relationship between numbers and variables using mathematical operators.

Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance / time

She completed the 100-meter race in 10.49 seconds and the 200-meter race in 21.34 seconds. Hence:

For 100 meters:

Speed = 100 m / 10.49 s = 9.53 m/s

For 200 meters:

Speed = 200 m / 21.34 s = 9.37 m/s

The speed difference = 9.53 m/s - 9.37 m/s = 0.16 m/s

Florence was 0.16 m/s faster

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The pressure using Pete's model based on the information will be 2.79 N/cm³

A trapezium (often known as a trapezoid in some parts of the world) is a four-sided figure with at least one set of parallel lines. These two lines are often referred to as the bases, and the other sides as its legs.

Isosceles Trapezium is a type of trapezium has its legs of equal length, and its base angles possessing an equivalent measure..

Pete has an anvil used for metal working, he models the base as two trapeziums the anvil applied of 834 newton's

The pressure using Pete's model based on the information will be:

= 834 / 299.25

= 2.79 N/cm³

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Answer:

1.54

Step-by-step explanation:

Trapezium=

12+24=36

36 x (length) 15 = 540cm^2

Pressure= force/area

832/540 = 1.54N/cm^2

The values of x, y, and z based on the system of equations will be (-2,4,7).

x + 3y + 5z = 45

6x - 3y + 2z = - 10

------------------------add

7x + 7z = 35

6x - 3y + 2z = -10

-2x + 3y + 8z = 72

----------------------add

4x + 10z = 62

7x + 7z = 35....multiply by 4

4x + 10z = 62...multiply by -7

---------------------

28x + 28z = 140 (result of multiplying by 4)

-28x - 70z = - 434 (result of multiplying by -7)

--------------------add

- 42z = - 294

z = -294/-42

z = 7

4x + 10z = 62

4x + 10(7) = 62

4x + 70 = 62

4x = 62 - 70

4x = - 8

x = -8/4

x = -2

x + 3y + 5z = 45

-2 + 3y + 5(7) = 45

-2 + 3y + 35 = 45

3y + 33 = 45

3y = 45 - 33

3y = 12

y = 12/3

y = 4

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Solve the following system of equations algebraically for all values of x,y and z

x+3y+5z=45

6x-3y+2z=-10

-2x+3y+8z=72

From the attached graph the solution set is (3, 3) for the inequalities

The first inequality is y < -(2/3)x + 5.

We can graph this by plotting the y-intercept of 5 and then using the slope of -2/3 to find additional points.

We then draw a dashed line through these points to indicate that the points on the line are not included in the solution set.

Since the inequality is y <, we shade the region below the line.

The second inequality is y ≥ (4/3)x - 1.

We can graph this by plotting the y-intercept of -1 and then using the slope of 4/3 to find additional points.

We then draw a solid line through these points to indicate that the points on the line are included in the solution set.

Since the inequality is y ≥, we shade the region above the line.

Hence, from the attached graph the solution set is (3, 3) for the inequalities

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The likelihood that a milkshake chosen at random will be a sloppy, thin, flavourless mess is 0.62.

The possibility or chance of an event occurring is measured by probability. It is a number between 0 and 1, where 0 denotes that the occurrence is impossible and 1 denotes that it is unavoidable. By dividing the number of favourable outcomes by the total number of potential outcomes, the probability of an occurrence is determined.

a. The milkshake will most likely turn out to be a watery, thin, flavourless mess (2, 4, 7).

The likelihood that a milkshake chosen at random would be a sloppy, thin, flavourless mess is equal to the final result of the milkshake will be a watery, thin, flavourless mess.

=2+4+7/21

=13/21

=0.62

b. No association can be removed from this table. We are unable to forecast the result of any event since the overall number of events is random.

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Answer:ABC(Done for you)
ACB
BAC
BCA
CAB
CBA

Step-by-step explanation:

Answer:

t = time in years

p(t) = population at time t

[tex]p(t) = 500000( {1.043}^{t} )[/tex]

[tex]p(10) = 500000( {1.043}^{10}) = 761751 [/tex]

The answer to the question about how many teams completed the escape room in 45 minutes or less is 6.

A dot plot is a type of chart used to display the distribution of a dataset. It is also known as a dot chart, strip plot, or dot graph. In a dot plot, each data point is represented by a dot placed along a horizontal or vertical axis.

Dot plots are useful for showing the distribution of a small to moderate-sized dataset, and are especially helpful when you want to compare the distribution of two or more datasets side by side. They are also useful for identifying outliers or gaps in the data

If we count the amount of dots on 45 and before 45 and add them up, the answer is 6

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The value of missing side lengths are,

m = 4/√3

h = 2 / √3

We have to given that;

A triangle is shown in figure.

Now, We can formulate;

sin 60° = 2 / m

√3/2 = 2 / m

m = 4/√3

cos 60° = h / m

1/2 = h / (4/√3)

1/2 = √3h / 4

2 = √3h

h = 2 / √3

Thus, The value of missing side lengths are,

m = 4/√3

h = 2 / √3

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Deviance is a term used in sociology to describe behavior that violates social norms or expectations. It refers to any behavior that is considered outside of the established rules and expectations of a society or culture.

Informal negative sanctions are the social disapproval or punishment that people receive for violating social norms. An example of informal negative sanctions could be a group of friends ostracizing another friend for breaking a social rule, such as not showing up to a planned event.

In terms of the act of deviance, it could be anything from breaking a minor social norm to committing a serious crime. The reaction of informal negative sanctions is often an attempt to maintain social control by encouraging conformity to the established norms of the group or society.

While physical violence is not necessary to maintain social control, the threat of punishment is an important part of any functioning society. People follow the rules and norms of society because they know that if they do not, there will be consequences. However, it is important to note that violence and punishment should not be the only means of social control. Positive reinforcement, such as rewards for good behavior, can also be an effective way of encouraging conformity to social norms.

In summary, deviance refers to behavior that violates social norms, and informal negative sanctions are a way of enforcing social norms. The threat of physical violence is not necessary to maintain social control, but consequences for deviant behavior are essential for any functioning society.

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Answer:

period :  π ; amplitude : 2

Step-by-step explanation:

Correct me if I'm wrong!!

Note that the angle measurements are given as follows:

A = 145° (Sum of angles on a straight line.

B = 35° Opposite angles

C = 145° Opposite angels

D) = 35° supplementary angels.

a) Note that Sum of angles on a straight line=180° and are therefore supplementary

b) All opposite angle are equal, since ∠b is opposite to 35°, then ∠b = 35°

c) 145° is also opposite to ∠c

d) when two angles are supplementary, it means that they sum up to 180°

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Full Question:

Solve for the missing angle measurements for angles a, b, c, and d
See the attached imge

1. Therefore, the exact value of cos(105°) is (√2 - √6)/4.

2. Therefore, the exact value of sin(75°) is (√6 + √2)/4.

3. Therefore, the exact value of tan(105°) is (√3 + 1)/(3 - √3).

4. Therefore, the exact value of cos(105°)cos(15°) is (2 + 2√3)/8.

A branch of mathematics known as trigonometry is concerned with the study of triangles and the correlations between their sides and angles.

It entails computing different triangle measurements and attributes using trigonometric functions including sine, cosine, and tangent.

Trigonometry is an essential component of calculus and other advanced mathematical studies, and it has applications in many disciplines including engineering, physics, navigation, astronomy, and architecture.

1. We can use the formula cos(A + B) = cos(A)cos(B) - sin(A)sin(B) with A = 60° and B = 45°. Then:

cos(105°) = cos(60° + 45°)

= cos(60°)cos(45°) - sin(60°)sin(45°)

= (1/2)(√2/2) - (√3/2)(√2/2)

= (√2 - √6)/4

Therefore, the exact value of cos(105°) is (√2 - √6)/4.

2. We can use the formula sin(A + B) = sin(A)cos(B) + cos(A)sin(B) with A = 45° and B = 30°. Then:

sin(75°) = sin(45° + 30°)

= sin(45°)cos(30°) + cos(45°)sin(30°)

= (√2/2)(√3/2) + (√2/2)(1/2)

= (√6 + √2)/4

Therefore, the exact value of sin(75°) is (√6 + √2)/4.

3. We can use the formula tan(A + B) = (tan(A) + tan(B))/(1 - tan(A)tan(B)) with A = 60° and B = 45°. Then:

tan(105°) = tan(60° + 45°)

= (tan(60°) + tan(45°))/(1 - tan(60°)tan(45°))

= (√3 + 1)/(3 - √3)

Therefore, the exact value of tan(105°) is (√3 + 1)/(3 - √3).

4. We can use the formula cos(A + B) = cos(A)cos(B) - sin(A)sin(B) with A = 60° and B = -45°. Then:

cos(105°)cos(15°) = cos(60° - 45°)cos(15°)

= [cos(60°)cos(-45°) - sin(60°)sin(-45°)]cos(15°)

= [(1/2)(√2/2) - (√3/2)(-√2/2)]cos(15°)

= (√2 + √6)/4 * cos(15°)

= (√2 + √6)/4 * (√6 + √2)/4

= (2 + 2√3)/8

Therefore, the exact value of cos(105°)cos(15°) is (2 + 2√3)/8.

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Step-by-step explanation:

A.

Sequence 2:

25-2×5=15

25-2×6=13

25-2×7=11

25-2×8=9

25-2×9=7

Ordered pairs :

(13,15)

(16,13)

(19,11)

(21,9)

(24,7)

B.

Sequence1 :

The rule is 3x+2 for x starts by 1, so:

3×1+2=5

3×2+2=8

3×3+2=11

3×4+2=14

3×5+2=17

Sequence2

The rule is 2x+3 forx starts by 6, so :

2×6+3=15

2×7+3=17

2×8+3=19

2×9+3=21

2×10+3=23

Ordered pairs

(5,15)

(8,17)

(11,19)

(14,21)

(17,23)

Wwe can reject the null hypothesis and deduce that there is sufficient empirical evidence to validate the presumption that seatbelts are competent for mitigating fatalities.

Null Hypothesis: There is no discernible distinction between the proportion of fatalities among occupants wearing seat belts and those without.

Alternative Hypothesis: The portion of fatalities experienced by those in vehicles donning seatbelts will be demonstrably lower in comparison to individuals not utilizing them.

The z-value was computed, finding that (0.0113 - 0.0024) / √(0.0047 * (1 - 0.0047) * (1/2915 + 1/7848)) = 12.43.

For a two-tailed test at a 0.05 significance level with 2915 plus 7848 less 2 = 10761 degrees of freedom, the critical value range would be ±1.96. With the calculated z-value of 12.43 surpassing the critical threshold, we can reject the null hypothesis.

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The result of the row 1 multiplication by 1/4 is determined as  [¹/₂  0 ].

The resultant of the row multiplication in the surd is calculated by applying the following method;

row 1 in the given surds = [2 0]

To multiply row by 1/4, we will multiply each entity by 1/4 as shown below;

[2 0] x 1/4 = 1/4(2 0)

= [¹/₂  0 ]

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, that 2, and 0 by 1/4.

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The probability of randomly selecting a red token would be 0. 30.

First, we know that the experiment was done 2, 000 times;

605 + 342 + 518 + 535 = 2000

The probability that a red token is randomly selected is therefore:

= Red token / Total times

= 605 / 2, 000

= 0. 3025

In fractions, we can make this:

= 605 / 2, 000

= 121 / 400

This is closest to the fraction 3 / 10 which is 0. 30.

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Answer:

Step-by-step explanation:

Given:

q(x) = -3x+4

r(x) = -4x

(r₀q)(4)   =>    r(q(4))     solve for q(4) first

q(4) = -3(4)+4       > substitute 4 in for x

q(4) = -12 +4

q(4) = -8           > now substitute this into r(q(4))

r(-8) = -4(-8)     > substitute -8 in for x

r(-8) = 32

(r₀q)(4) = 32

(q₀r)(4)   => q(r(4))    solve for r(4) first

r(4) = -4(4)        > substitute 4 for x

r(4) =-16            > substitute this into q(x)

q(-16) = -3(-16)+4

q(-16) = 48 +4

q(-16) = 52

(q₀r)(4) = 52

The value of the height of the entire climbing frame is 11.99 feet

To determine the value, we need to know the different trigonometric identities.

These identities are;

From the information given, we have that;

In the triangle, the parameters are;

Hypotenuse is the distance between the architect and frame

The angle is 63.43

Adjacent is 6 feet

Using the tangent identity, we have;

tan 63.43 = h/6

cross multiply, we get;

h = tan (63. 43) × 6

Find the tangent value and substitute, we have;

h = 1. 99 × 6

Multiply the values, we have;

h = 11. 99 feet

Then, the height of the entire climbing frame is 11. 99 feet

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Complete question:

'The architect stands 6 feet from climbing frame, looking up at the top of the frame at an angle of 63.43" It is 5 and half feet from ground to the architect's eyes: The vertical distance from eye level to the top of the climbing frame is feet: The height of the entire climbing frame is feet:'

The cost of each chair and table is $2.5 and $8.75 respectively.

Given that the total cost to rent 3 chairs and 2 tables is $25 and total cost to rent 5 chairs and 6 tables is $65.

We need to find the cost of each chair and table,

Let the cost of each chair and table be x and y respectively,

3x+2y = 25.......(i)

5x+6y = 65.........(ii)

Multiply the equation (i) by 3 and subtract ii from i,

9x+6y = 75 - (5x+6y = 65)

4x = 10

x = 2.5

Put x = 2.5 in any equation to find the value of y,

3(2.5)+2y = 25

2y = 17.5

y = 8.75

Hence, the cost of each chair and table is $2.5 and $8.75 respectively.

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The ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder is 4:3, or 4/3.

To find the ratio of the surface areas of the two similar cylinders, we need to consider the ratio of their corresponding dimensions. Since the two cylinders are similar, their radii are proportional to their heights. Let's denote the height of the smaller cylinder as h1, the height of the larger cylinder as h2, the radius of the smaller cylinder as r1, and the radius of the larger cylinder as r2.

Given:

h1 = 15 inches

h2 = 20 inches

The ratio of the heights is:

h2 / h1 = 20 / 15 = 4 / 3

Since the cylinders are similar, the ratio of their radii is the same as the ratio of their heights:

r2 / r1 = 4 / 3

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The maximum cardinality of S is 20.

To increase the number of subsets within S, our goal must be to find as many non-empty subset intersections as possible. This is achieved by constructing subsets that possess only one shared element. In this particular case, any two sets contained in the collection will include the element 2000 in their intersection causing it to become a valid subset.

Now, we shall investigate whether an additional subset can be added to S. If an extension exists without including 2000, its intersection with the previous 20 subsets would negligibly have no common elements and would hence not be regarded as a valid subset for addition into S.

As a result, a total of 20 subsets represent maximum cardinality for set S per these conditions.

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The correct option is B: The result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

Once kids have a firm grasp on right fractions, they are exposed to mixed numbers and improper fractions.

Divide the numerator and denominator to create a mixed fractions from an incorrect fraction. The solution to this problem is the whole number portion; the leftover portion is the numerator; its denominator stays the same.

We can convert the two fractions to decimal form in order to compare them.

7.375 is equivalent to 7 3/8, and

4/5 is equivalent to 0.8.

7.375 multiplied by 0.8 results in:

7.375 × 0.8 = 5.9

Since the result is 5.9, which is less than 7.375, it follows that 7 3/8 multiplied by 4/5 is less than 7 3/8.

Thus, the result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

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The Taylor polynomial t3(x) for f(x) = cos(x) centered at a = pi/2 is t3(x) = -(x-pi/2) + (x-pi/2)³/3!.

A polynomial is  described as an expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

The Taylor polynomial of degree n for a function f(x) centered at a is given by the formula:

We get the derivatives :

pn(x)=f(c)+f′(c)(x−c)+f′′(c)2!....

f(x) = cos(x)

f'(x) = -sin(x)

f''(x) = -cos(x)

f'''(x) = sin(x)

We the  evaluate these derivatives at x = pi/2:

f(pi/2) = cos(pi/2) = 0

f'(pi/2) = -sin(pi/2) = -1

f''(pi/2) = -cos(pi/2) = 0

f'''(pi/2) = sin(pi/2) = 1

We substitute  these values into the formula for the Taylor polynomial, and simplify to get Taylor polynomial T3(x) for the function:

the Taylor polynomial t3(x) for f(x) = cos(x) centered at a = pi/2 is t3(x) = -(x-pi/2) + (x-pi/2)³/3!.

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Based on the information, we can infer that the correct graph/table is option D.

To identify the correct chart or table, we must identify the information about the data that Emily uses each year. She uses 360GB each year, in this case, to identify the relationship we must divide the amount of data she uses by the number of months she has in a year:

360GB / 12 months = 30 GB/month

In accordance with the above, we must identify the table or graph that represents this relationship. In this case it would be table D because it shows an increasing relationship of 1 month with 30gb, 2 months with 60gb, 3 months with 90gb, 4 months with 120gb, and so on.

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Answer:

-8√3

Step-by-step explanation:

[tex] - 2 \sqrt{48} \\ = - 2 \sqrt{16 \times 3} \\ = - 2 \sqrt{16} \times \sqrt{3} \\ = - 2 \times 4\sqrt{3} \\ = - 8 \sqrt{3} [/tex]

The calculated values of the actual lengths of the walls are AB = 144 ft, CD = 288 ft, EF = 528 ft and EF = 240 ft

From the question, we have the following parameters that can be used in our computation:

Scale of blueprint = 1 in : 48 ft

This means that

Scale = 48 ft/1in

Calculating the actual lengths of the walls, we have

AB = 3in * 48 ft/1in

AB = 144 ft

CD = 6in * 48 ft/1in

CD = 288 ft

EF = 11in * 48 ft/1in

EF = 528 ft

FG = 5in * 48 ft/1in

EF = 240 ft

Hence, the actual lengths of the walls are AB = 144 ft, CD = 288 ft, EF = 528 ft and EF = 240 ft

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