The Length, breadth and height of a room are 825cm, 625cm and 450 cm. Determine the longest rod which can measure the 3 dimensions exactly

Answer:

The answer is 912

Step-by-step explanation:

Answer:

87.6m²

Step-by-step explanation:

From the above question, we are given the following information

The dimensions of the base were 3 m by 5 m:

Length = 3m

Width = 5m

The pyramid was 3.6 m high

Height = 3.6m

To calculate the amount of ice needed for this sculpture, we would have to find the Surface Area of the Rectangular Prism

This is calculated as:

Surface Area =2(wl+hl+hw)

= 2(3 × 5 + 3.6 × 3 + 3.6 × 5)

= 2(15 + 10.8 + 18)

= 2(43.8)

= 87.6m²

The amount of ice needed for this sculpture is 87.6m²

The correct statement for Linda's test is: the P-value would be less than 0.08, and H0 would be rejected if α = 0.05.

For Linda's test, she is testing the hypothesis that u1 < u2. Since Linda had reason to believe that either u1 = u2 or u1 < u2 based on an earlier study, her alternative hypothesis is one-sided.

Given that Sam's two-sample t test resulted in a P-value of 0.08 for the two-sided alternative hypothesis, we need to consider how Linda's one-sided alternative hypothesis will affect the P-value.

When switching from a two-sided alternative hypothesis to a one-sided alternative hypothesis, the P-value is divided by 2. This is because we are only interested in one tail of the distribution.

Therefore, for Linda's test, the P-value would be 0.08 divided by 2, which is 0.04. This means the P-value for Linda's test is smaller than 0.08.

Now, considering the significance level α = 0.05, if the P-value is less than α, we reject the null hypothesis H0. In this case, since the P-value is 0.04, which is less than α = 0.05, Linda would reject the null hypothesis H0: u1 = u2 in favor of the alternative hypothesis HA: u1 < u2.

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Answer:

Question 1172264: How old am I if 500 reduced by 4 times my age is 256? How old am I if 500 reduced by 4 times my age is 256? A is our age. 500 - 4A = 256.

Step-by-step explanation:

thank me later

The relationship between b (the number of years since the start of the study) and y (the mass of the sample in milligrams) using the exponential function:

y = 750(0.955)ᵇ

The rate of decay is given as 4.5% per year, which means that after one year, the sample will have decayed to 95.5% of its original mass.

After two years, it will have decayed to 95.5% of that amount, and so on. We can express this relationship between b (the number of years since the start of the study) and y (the mass of the sample in milligrams) using the exponential function:

y = 750(0.955)ᵇ

Here, the initial mass of the sample is 750 milligrams, and the factor of 0.955 represents the proportion of the original mass that remains after one year.

Taking this factor to the power of b gives us the proportion of the original mass that remains after t years, which we can multiply by the initial mass to get the current mass of the sample in milligrams.

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Answer:

Equation:  2x + 5 + 6x + 15 = 92

Solution:  x = 9

m∠A =23°  m∠B = 69°

Step-by-step explanation:

measure of ∠B = 3(2x + 5) = 6x + 15

The sum of the angles = 92 = 2x + 5 + 6x + 15

92 = 8x + 20

72 = 8x

x = 9

m∠A = 2(9) + 5 = 18 + 5 = 23

m∠B = 6(9) + 15 = 54 + 15 = 69

Check:  23 + 69 = 92  and 23(3) = 69

The solution is :

Equation:  2x + 5 + 6x + 15 = 92

Solution:  x = 9

m∠A =23°  

m∠B = 69°

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here we have,

given that,

measure of ∠B = 3(2x + 5) = 6x + 15

The sum of the angles = 92 = 2x + 5 + 6x + 15

92 = 8x + 20

72 = 8x

x = 9

m∠A = 2(9) + 5 = 18 + 5 = 23

m∠B = 6(9) + 15 = 54 + 15 = 69

Check:  23 + 69 = 92  and 23(3) = 69

Hence, The solution is :

Equation:  2x + 5 + 6x + 15 = 92

Solution:  x = 9

m∠A =23°  

m∠B = 69°

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Answer:

Translation: Shift the trapezoid 5 units to the right.

Dilation: Enlarge the trapezoid vertically by a factor of approximately 3.365.

Reflection: Reflect the trapezoid across the y-axis.

Note: The order of transformations may vary depending on the convention used.

Step-by-step explanation:

To determine the series of transformations that result in the unshaded trapezoid being the image of the shaded trapezoid, we can analyze the changes in the coordinates.

Translation:

The shaded trapezoid is shifted horizontally by 5 units to the right to become the unshaded trapezoid. Therefore, the first transformation is a translation.

Translation vector = (5, 0)

Dilation:

The shaded trapezoid is enlarged in the vertical direction. To determine the dilation factor, we compare the corresponding side lengths.

The length of side AB in the shaded trapezoid is given by the distance formula:

AB = sqrt((-4 - (-5))^2 + (5 - 1)^2) = sqrt(1^2 + 4^2) = sqrt(17)

The length of side A'B' in the unshaded trapezoid is given by the distance formula as well:

A'B' = sqrt((1.5 - 0)^2 + (9 - 1)^2) = sqrt(1.5^2 + 8^2) = sqrt(66.25) = 2.5sqrt(26)

The dilation factor is the ratio of the corresponding side lengths:

Dilation factor = A'B' / AB = (2.5sqrt(26)) / sqrt(17) = 2.5sqrt(26/17) ≈ 3.365

Reflection:

The unshaded trapezoid is a reflection of the shaded trapezoid across the y-axis. This transformation reverses the sign of the x-coordinates.

Answer:

3 meters per second

Step-by-step explanation:

Average speed = Total distance/ Total time

Answer:

107.25cm²

Step-by-step explanation:

Area of triangle = 0.5 * base * height

Base = 14.3 cm

Height = 15 cm

Hence, Area of triangle :

Area = 0.5 * 14.3 * 15

Area = 107.25cm²

Answer:

z = \(\frac{-ax-by-d}{c}\)

Step-by-step explanation:

ax+by+cz+d=0

cz = -ax-by-d

z = \(\frac{-ax-by-d}{c}\)

Answer

the third side can measure 2 in, 3 in, or 4 in

Explanation

inequality theorem

a + b > c

a + c > b

b + c > a

2 = a

b = 3

c = x

a + b > c

2 + 3 > x

5 > x

x= 4, 3, 2, or 1 in

a + c > b

2 + x > 3

x = 4, 3, or 2

b + c > a

3 + x > 2

x = 4, 3, or 2

Answer:

x = 4

Step-by-step explanation:

To see when g(x) = f(2)

First, find f(2)

f(2) = 3(2) - 1 = 5

Now g(x) = 2x-3  = f(2) = 5

2x - 3 = 5

Adding 3 to both sides

2x = 8

Dividing 2 on both sides

x = 4

Answer:

option 4, linear pairs

Step-by-step explanation:

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180° (known as supplementary angles)

\( \frac{f}{g} = \frac{ \sqrt[3]{2x} }{2x + 1} \)

According to the given information Ling has enough string to produce at least 20 bracelets.

Numbers serve the purpose of counting, measuring, organising, indexing, and other purposes. Natural numbers, whole numbers, rational and irrational numbers, integers, actual values, complex numbers, even and odd numbers, and so on are all distinct forms of numbers.

A number is really a numerical value that is used to express quantity. As a consequence, a number seems to be a mathematical idea that may be used to count, measure, and name objects. As little more than a result, numbers are the foundation of mathematics. Here is one butterfly, and here are four butterflies.

Each bracelet requires 7 1/2 inches of string. So, the total length of string required to make 20 bracelets is:

20 × 7 1/2 = 150 inches

Therefore, Ling needs to buy at least 150 inches of string.

We can write the inequality to represent this situation as:

length of string ≥ 150

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The linear function of the scenario is y = 33x

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

Time = 5.5 hours

Cost = $180

This means that

x = 5.5 and y = 180

The constant of proportionality is calculated as

k = Cost/Time

Substitute the known values in the above equation, so, we have the following representation

k = 180/5.5

Evaluate

k = 33

The equation is calculated as

y = kx

So, we have

y = 33x

Hence, the equation is y = 33x

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Check the picture below.

Answer:

H

Step-by-step explanation:

Answer:

it's h because in the molecular level it just makes sense

a) The air pressure at sea level is given by the formula when n = 0, so P = 1013 × 0.887 = 900.71 millibars.

b) To find the percentage decrease in air pressure for each kilometre above sea level, we can use the formula for percentage change:

(New Value - Original Value) / Original Value * 100

Air pressure, also known as atmospheric pressure, is the force exerted on a surface by the weight of the air above it. Air pressure is typically measured in units such as millibars (mb) or inches of mercury (inHg). It plays an important role in weather patterns and can affect things like airplane flight and altitude sickness.

Sea level refers to the average level of the surface of the ocean. It is used as a reference point for measuring elevation, and for measuring air pressure at a specific location. At sea level, the air pressure is approximately 1013 millibars or 29.92 inches of mercury (inHg). Air pressure decreases as the altitude increases above sea level.

The new value is P = 1013 × 0.887^n and the original value is P = 1013 (at sea level)

So, the percentage decrease in air pressure for each kilometre above sea level is:

(1013 × 0.887^n - 1013) / 1013 * 100 = (-0.113n) * 100 = -11.3n %

So, the air pressure decreases by -11.3 % for each kilometre above sea level.

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The value of the expressions will be:

x + y + x + y + 2x + 2z.= 4x + 2y + 2z

6a² - 5a²b - 4a² - 3a²b = 2a² - 8a²b

2(x + 3y) - 2x = 6y

3x(2 + x) - x² = 2x² + 6x

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

The value of the expressions will be:

x + y + x + y + 2x + 2z

= 4x + 2y + 2z

6a² - 5a²b - 4a² - 3a²b

= 2a² - 8a²b

2(x + 3y) - 2x

= 2x + 6y - 2x

= 6y

3x(2 + x) - x²

6x + 3x² - x²

= 2x² + 6x

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The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. Therefore, the correct answer is C.

A pivot column is a column of the matrix that has a non-zero entry in the pivot position and all entries below the pivot are zero. In row echelon form, every row below a pivot column has a zero in the corresponding position. The pivot columns correspond to the linearly independent columns of the original matrix and the number of pivot columns determines the rank of the matrix.

The rank of a matrix is defined as the number of linearly independent columns or rows in the matrix. If the columns of a matrix span Rn, then the rank of the matrix must be equal to n. This means that the matrix must have n linearly independent columns. To ensure that the columns of A span R5, A must have at least 5 pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have a non-trivial solution, meaning that the columns of A would not be linearly independent and would not span R5.

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Complete question :

Mikel creates the table below to help her determine 40% of 70. She writes the expression Which change in Mikel’s expression will lead her to the correct answer?

Corresponding chart for the problem is attached below.

Answer:

The 0.2 in the expression could be changed to 2.

Step-by-step explanation:

40% of 70

Directly working this out, we obtain :

0.4 * 70 = 28

From the table :

To obtain same from the columns, 0.2 is adjusted to 2.

Hence, 2 * 14 = 28

Answer: 22 people will be riding the lady trip on the ferry

The optimal values are x* = 8 - 2y = 8 - 2(8) = -8 and y* = 8.

To solve for x* and y* in terms of Pₓ, Pᵧ, and I, we need to maximize the utility function U(x, y) = 3x + 4y subject to the budget constraint Pₓ * x + Pᵧ * y = I.

Given I = $24, Pₓ = $3, and Pᵧ = $6, we can substitute these values into the utility function and the budget constraint:

U(x, y) = 3x + 4y

Pₓ * x + Pᵧ * y = I

Substituting the given values, we have:

U(x, y) = 3x + 4y

3x + 6y = 24

Now, we can solve the system of equations to find x* and y*.

Rearranging the budget constraint equation, we get:

3x = 24 - 6y

x = 8 - 2y

Substituting this expression for x into the utility function, we have:

U(y) = 3(8 - 2y) + 4y

U(y) = 24 - 6y + 4y

U(y) = 24 - 2y

To maximize U(y), we need to find the value of y that maximizes U(y).

Taking the derivative of U(y) with respect to y and setting it equal to zero, we have:

dU/dy = -2 = 0

Since the derivative is a constant, there is no value of y that maximizes U(y). Instead, we need to evaluate U(y) at the endpoints of the feasible range.

When y = 0, we have:

U(0) = 24

When y = (24 - 8) / 2 = 8, we have:

U(8) = 24 - 2(8) = 8

Comparing the utility values at the endpoints, we find that U(0) = 24 > U(8) = 8.

Therefore, the optimal values are x* = 8 - 2y = 8 - 2(8) = -8 and y* = 8.

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Solve for x  ∗  (P  x ​  ,P  y ​  ,I) and y  ∗  (P  x ​  ,P  y ​  ,I) when U(x,y)=3x+4y, if I=$24,P  x ​  =$3 and,P  y ​  =$6.

Answer:

The largest angle is 102

Step-by-step explanation:

2x + 3x + 10 = 180

5x + 10 = 180

5x = 170

x = 34

2(34) = 68

3(34) + 10 = 102

Answer:

Step-by-step explanation:

102

The reasons for the steps are ;

step1 ; collect like terms

step2 : dividing both sides by 6

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

For example , in an equation 6x +5x = 3x + 24 , to find x in this equation we need to follow some steps;

First we collect like terms

6x +5x - 3x = 24

8x = 24

then we divide both sides by the coefficient of x

x = 24/8

x = 3

Similarly , solving 18 - 2x = 4x

collect like terms

18 = 4x +2x

18 = 6x

divide both sides by coefficient of x

x = 18/6 = 3

x = 3

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Answer:

The right option is option e.T-shaped.

Step-by-step explanation:

The molecular geometry or shape of clf3 is T-shaped. It acquires such shape because of presence of two lone pairs which take equatorial position and there are greater repulsions. The hybridisation is sp3d and it has 2 lone pairs

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Option e) T-shaped

The shape or molecular geometry  of ClF₃ is T-shaped. It acquires such a shape due to the presence of two lone pairs in the equatorial position and has greater repulsion. The hybrid is sp³d and it has 2 lone pairs.

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Answer:

bk

Step-by-step explanation:

jlvlivh

Answer:

dunno what the other guy said but I'm pretty sure the answer is -12/11, or -1.09.

A table or spreadsheet used to systematically evaluate options according to specific criteria is a decision matrix.

A decision matrix is a table or spreadsheet used to systematically evaluate options based on specific criteria. It is a tool commonly used in decision-making processes to objectively assess and compare different choices.

The decision matrix organizes the criteria in rows and the options in columns. Each cell in the matrix represents the evaluation or score of an option based on a particular criterion. The criteria can be weighted to reflect their relative importance in the decision-making process.

By filling out the decision matrix with scores or ratings for each option and criterion, a comprehensive evaluation can be performed. The matrix allows decision-makers to visualize and compare the performance of different options against the criteria, helping them make more informed and structured decisions.

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The number of unique ways to complete a quiz with 5 questions and 4 possible answers to each question is \(4^5\), or 1024.

This can be calculated using exponential notation, which states that a number raised to the power of another number is equal to the number multiplied by itself that many times. In this case, 4 to the power of 5 is equal to 4 x 4 x 4 x 4 x 4, or 1024.

In other words, the number of unique ways to answer a quiz with 5 questions and 4 possible answers to each question is equal to 4 multiplied by itself 5 times. This can also be written using the exponential notation as \(4^5\). There are 1024 unique ways to complete a quiz with 5 questions and 4 possible answers to each question.

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