A factory makes sheets of metal that are 7/10 of an inch thick. If a worker at the factory makes a stack of 71 of the sheets, how many inches thick will the stack be?

Write your answer as a fraction or as a whole or mixed number.

Step-by-step explanation:

\( { ({3}^{3} )}^{4} \)

\( = {3}^{3 \times 4} \)

\( = {3}^{12} \)

\(or \)

\( = 531441\)

The range of time values describes the entire interval over which Georgiana would be interpolating is 0 to 30 minutes.

What is the domain and range of a function?

The domain of a function is the set of x values for which it is defined, whereas the range is the set of y values for which it is defined.

As in the table, the minimum time for which the distance is defined is 0 minutes while the maximum time is 30 minutes. Therefore, the range of time values describes the entire interval over which Georgiana would be interpolating is 0 to 30 minutes.

Learn more about Domain and Range here

https://brainly.com/question/9740428

#SPJ4

Answer:

C

Step-by-step explanation:

Answer:

The order of arithmetic calculations is

B - Bracket

O - off

D - Division

M - Multiplication

A - Addition

S - Subtraction

Use this to solve

Answer:

x=5

Step-by-step explanation:

since it’s isosceles trapezoid, diagonals are equal.

x+10=2x+5

x=5

Answer:

f(x + 1) + 2

Step-by-step explanation:

All the points are translated 1 unit to the left and 2 units up.
To write a translation along the x-axis, movement to the right would be written as f(x - a), where a is the amount translated, and movement to the left would be written as f(x + a). In this case, we would need to write the translation as f(x + 1), since it is moving 1 unit to the left.
As for translations along the y-axis, movement upward would be written as f(x) + a, and movement downward would be written as f(x) - a. Thus, the transformation rule to describe the path the pre-image made to arrive at the image would be f(x + 1) + 2.

P.S. I'm a bit rusty with this stuff, so I apologize in advance if I messed something up.

Answer:

There are 60 pieces of 20 cent coins

Step-by-step explanation:

Let the number of 50 cent coins be x.

Let the number of 20 cent coins by y.

Now, we are told that value of all coins is $27.

Also, 50 cent = $ 0.5 and 20 cents = $0. 2

Thus;

0.5x + 0.2y = 27 - - - - - (eq 1)

Now, we are told that there are twice as many 20 cent coins as there are 50 cent coins. So,

y = 2x - - - - (eq 2)

Putting 2x for y in eq 1,we have;

0.5x + 0.2(2x) = 27

0.5x + 0.4x = 27

0.9x = 27

x = 27/0.9

x = 30

Thus, y = 2 * 30 = 60

Thus,there are 60 pieces of 20 cent coins

a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

Learn more about subspace

brainly.com/question/30318872

#SPJ11

Answer:

152.4 centimeters.

Step-by-step explanation:

1 inch = 2.54 centimeters

60 inches = x centimeters

Where x is the number of centimeters equivalent to 60 inches.

To solve for x, we can set up a proportion:

1 inch / 2.54 centimeters = 60 inches / x centimeters

Cross-multiplying, we get:

1 inch * x centimeters = 2.54 centimeters * 60 inches

Simplifying, we get:

x = (2.54 cm/in) * (60 in)

x = 152.4 cm

Therefore, 60 inches is equivalent to 152.4 centimeters.

According to the rules of significant figures:



1.25 × 200 = 300

the answer is

TRue

Answer:

1/805

Step-by-step explanation:

4/3220 = 1/805 = 0.00124223....

Let \(n=abcba\) be such a number. If 18 divides \(n\), then both 2 and 9 divide \(n\).

To be divisible by 2, we must have \(a\in\{2,4,6,8\}\). Meanwhile we can have \((b,c)\in\{0,1,2,\ldots,9\}^2\).

To be divisible by 9, we the sum of the digits of \(n\) must itself be divisible by 9, or

\(2a+2b+c=9k\)

for some integer \(k\).

The largest value of \(2a+2b+c\) is 2•8 + 2•9 + 9 = 43, so we must have \(k\in\{1,2,3,4\}\).

I'm not sure what the best way to get the final count may be, but there are 44 such numbers. It's rather tedious to do by hand.

• If \(k=1\), then \(2a+2b+c=9\), and we can do this in 4 ways.

For example,

2•2 + 2•0 + 5 = 9 \((n = 20502)\)

• If \(k=2\), then \(2a+2b+c=18\) and can be done in 16 ways.

2•2 + 2•3 + 8 = 18 \((n = 23832)\)

• If \(k=3\), then \(2a+2b+c=27\) and can be done in 18 ways.

2•2 + 2•7 + 9 = 27 \((n = 27972)\)

• If \(k=4\), then \(2a+2b+c=36\) and can be done in 6 ways.

2•6 + 2•8 + 8 = 36 \((n = 68886)\)

The most precise name for ABCD with vertices A(−5, 2), B(−3, 6), C(6, 6), and D(4, 2) is quadrilateral.

The given quadrilateral ABCD can be classified as a trapezoid. By definition, a trapezoid is a quadrilateral with at least one pair of parallel sides. In this case, sides AB and CD are parallel, which satisfies the definition of a trapezoid.

Furthermore, based on the given coordinates of the vertices, we can see that sides AC and BD are equal in length. An isosceles trapezoid is a special case of a trapezoid in which the non-parallel sides are congruent. Therefore, quadrilateral ABCD can also be classified as an isosceles trapezoid.

To summarize, the most precise name for quadrilateral ABCD is a trapezoid, and more specifically, an isosceles trapezoid.

Learn more about quadrilaterals here:

brainly.com/question/29934440

#SPJ1

Answer:

parallelogram

Step-by-step explanation:

The given equation T=(2*Z2/(Z2+Z1)) represents the transmission coefficient for an acoustic impedance-matching layer. An impedance matching layer is a thin layer of material placed between two media with different acoustic impedances .

This layer allows sound waves to efficiently pass from one medium to another. The transmission coefficient of an acoustic impedance matching layer is given by the equation T = (2*Z2/(Z2+Z1)) where Z1 and Z2 are the acoustic impedances of the two media that are being interfaced by the matching layer.In ultrasound transducers, the matching layer is used to couple the piezoelectric element to the tissue being imaged.

This allows for the maximum transfer of acoustic energy from the piezoelectric element to the tissue being imaged.The relationship between the transmission coefficient and the impedance matching layer with impedance % is given by the equation .5where Zpc is the acoustic impedance of the piezoelectric element, and Ztis is the acoustic impedance of the tissue being imaged.Substituting Zm1 into the equation for T,  Therefore, the equation for the transmission coefficient for an acoustic impedance-matching layer is T=(2*Z2/(Z2+Z1)), and the equation for the impedance matching layer with impedance .

To know more about equation visit :

https://brainly.com/question/29657983

#SPJ11

Answer:

x=2

Step-by-step explanation:

7x=14

divide by 7 on each side to get x by itself

x=14/7

x=2

Therefore, when two lines begin parallel but later diverge, it implies that the geometry involved is non-Euclidean.

I understand that you would like an explanation related to parallel lines in geometry and the final answer should be concise, covering the main point in the last two lines.
In geometry, parallel lines are lines in a plane that never intersect or touch each other at any point. These lines always maintain the same distance from one another. However, if two lines start as parallel but later diverge, it indicates that they are no longer maintaining the same distance from each other. In such a case, the geometry under consideration is non-Euclidean.

Therefore, when two lines begin parallel but later diverge, it implies that the geometry involved is non-Euclidean.

To learn more about scale factors visit:

https://brainly.com/question/29967135

#SPJ11

Answer:

(7, -1)

Step-by-step explanation:

3x + 7y = 14

y = x - 8

3x + 7(x - 8) = 14

3x + 7x - 56 = 14

10x - 56 = 14

Add 56 to both sides.

10x = 70

Divide both sides by 10.

x = 7

3(7) + 7y = 14

21 + 7y = 14

Subtract 21 from both sides.

7y = -7

Divide both sides by 7.

y = -1

(7, -1)

Simone is descending at a slower rate than Natalie is ascending. Therefore, Natalie is hiking at a faster (greater) rate than Simone.

The slope shows how steep the line is.It is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.

The slope of the elevation-time graph represents the rate of change of elevation over time, or the constant proportionality between the two variables. To find the slope, we can use the formula:

slope = (change in elevation)/(change in time)

For Simone, from 0 to 30 minutes, the change in elevation is 2500 - 1700 = 800 ft, and the change in time is 30 - 0 = 30 min. Therefore,

slope = 800 / 30 = 26.67 ft/min

For Natalie, from 0 to 60 minutes, the change in elevation is 0 - 2500 = -2500 ft, and the change in time is 60 - 0 = 60 min. Therefore,

slope = -2500 / 60 = -41.67 ft/min

Since the slope for each person is not the same, there is no proportional relationship between their elevations and time. Therefore, we cannot write an equation of the form Y = kX for their elevations and time.

To know more about elevation-time graph visit:

https://brainly.com/question/13139707

#SPJ1

The probability of selecting a yellow and then a yellow without replacement is 3/10.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of red marbles = 1

Number of green marbles = 1

Number of yellow marbles = 3

Total number of marbles = 5

The probability of selecting a yellow and then a yellow without replacement.

= 3/5 x 2/4

= 6/20

= 3/10

We are using 2/4 since yellow marbles become 2 and the total marbles become 4 when the condition of without replacement is given.

Thus,

The required probability is 3/10.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ1

Answer:

Step-by-step explanation:

First, we want to note two things:

We can describe this with an inequality:  x ≥ -10
Be sure you use ≥ and not >, since -10 is included.

We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.

You can also use set-builder notation: { x | x ≥ -10 }

The probability that the spinner lands on red and the coin toss is tails is 0.4

The sections on the spinner are

Yellow = 4

Red = 16

This means that

P(Red)=Red/Total

So, we have the following representation

P(red) = 16/20

Also, we have

Coin = {H, T}

This means that

P(T) = 1/2

So, we have

P(Red and Tail) = P(Red) * P(T)

So, we have

P(Red and Tail) = 16/20 * 1/2

Evaluate

P(Red and Tail) = 0.4

So, the probability is 0.4

Read more about probability at

https://brainly.com/question/251701

#SPJ1

The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

know more about Bedrock.

https://brainly.com/question/2948854

#SPJ11

(a) A basis for the solution space of the homogeneous system of linear equations is:

{(-3, 1, 0, 0), (-5, 0, -5, 1)}

(b) The dimension of the solution space is 2.

To find a basis for the solution space, we first write the augmented matrix of the system and row-reduce it to its echelon form or reduced row-echelon form.

Then, we identify the free variables (variables that can take any value) and express the dependent variables in terms of the free variables. The basis for the solution space consists of the vectors corresponding to the free variables.

In this case, after performing row operations, we obtain the reduced row-echelon form:

[1 0 -1 -1 0]

[0 1 3 2 0]

[0 0 0 0 0]

The first and second columns correspond to the free variables x3 and x4, respectively. Setting these variables to arbitrary values, we can express x1 and x2 in terms of x3 and x4 as follows: x1 = -x3 - x4 and x2 = -3x3 - 2x4. Therefore, a basis for the solution space is {(-3, 1, 0, 0), (-5, 0, -5, 1)}.

Since the basis has 2 vectors, the dimension of the solution space is 2.

For more such answers on Linear Equation

https://brainly.com/question/2030026

#SPJ8

Answer:

5)m=11/10

6)m=-17/2

7)m=18.13

8)m=-26/9

BTW The M is an EXAMPLE

Step-by-step explanation:

F(x) is a degree 6 polynomial having roots at x = 0, I -5, and 3.

As F(x) contains six elements in the form of (x-a), where an is a root, the degree of F(x) is 6. We discover that the roots are x=0, I -5, and 3 when we set each component to zero. By resolving each issue independently, their roots can be discovered. For instance, x=0, I is obtained from x(x2+1)=0. We obtain x=-5 from (x+5)=0. We get x=3 from (x2-3)=0. The roots of F(x) are significant because they reveal where the function crosses the x-axis and where its extrema are.

learn more about root here:

https://brainly.com/question/16932620

#SPJ11

For a penetrated confined aquifer:

(a) Pressure:

The pressure can be calculated using the hydrostatic pressure formula:

Pressure = density × gravity × height

Given:

Density of water = 1000 kg/m³ (assuming water density)

Acceleration due to gravity = 9.8 m/s²

Height above the confined aquifer = 8.8 m

Using the formula:

Pressure = 1000 kg/m³ × 9.8 m/s² × 8.8 m

Pressure ≈ 86,240 N/m²

(b) Pressure Head:

The pressure head is the height equivalent of the pressure. Calculate by dividing the pressure by the product of the density of water and acceleration due to gravity:

Pressure Head = Pressure / (density × gravity)

Using the values:

Pressure Head = 86,240 N/m² / (1000 kg/m³ × 9.8 m/s²)

Pressure Head ≈ 8.8 m

(c) Elevation Head:

The elevation head is the difference in height between the top of the confined aquifer and the reference level (sea level). Given that the top of the confined aquifer is 545 m above sea level, the elevation head is 545 m.

(d) Hydraulic Head:

The hydraulic head is the sum of the pressure head and the elevation head:

Hydraulic Head = Pressure Head + Elevation Head

Hydraulic Head = 8.8 m + 545 m

Hydraulic Head ≈ 553.8 m

(e) Velocity of Water:

To calculate the velocity of water, Bernoulli's equation. However, to determine if the velocity term is significant, compare it to the pressure term. Assume a value for the flow rate and see if the resulting velocity is significant.

Assuming a flow rate of 1 m³/s, calculate the cross-sectional area of the well casing:

Area = π × (diameter/2)²

Area = π × (0.10 m/2)²

Area ≈ 0.00785 m²

Using the equation for flow rate: Q = velocity × Area, rearrange it to solve for velocity:

Velocity = Q / Area

Velocity = 1 m³/s / 0.00785 m²

Velocity ≈ 127.39 m/s

Considering a significant velocity term to be equal to or greater than 1% of the pressure term, check if the velocity (127.39 m/s) is 1% or more of the pressure term (86,240 N/m²):

Percentage of velocity term = (Velocity / Pressure) × 100

Percentage of velocity term = (127.39 m/s / 86,240 N/m²) × 100

Percentage of velocity term ≈ 0.15%

The velocity term (0.15%) is significantly smaller than 1% of the pressure term. Therefore, the velocity term can be considered insignificant.

In terms of realism, a flow rate of this magnitude (1 m³/s) is not typical for groundwater flow. Groundwater flow rates are generally much lower, usually on the order of liters per second or even less.

Find out more on confined aquifer here: https://brainly.com/question/14784268

#SPJ1

Step-by-step explanation:

It is possible, however, that some individuals in the sample may have had heights that were close to the average, either slightly above or slightly below it.

It is unlikely that any individual in Dr. Vickers' sample (or anyone at all) would have had the exact average number of feet, as the average is typically calculated as a mathematical mean that may or may not correspond to an actual measurement.

For example, if the average (mean) number of feet in a sample of 10 people is calculated to be 6 feet, it is highly unlikely that any individual in the sample actually has a height of exactly 6 feet. Rather, the average is a statistical summary of the data that provides insight into the central tendency of the sample as a whole.

It is possible, however, that some individuals in the sample may have had heights that were close to the average, either slightly above or slightly below it.

Learn more about "mathematical mean" : https://brainly.com/question/130657

#SPJ11

Answer:

x = 24

Step-by-step explanation:

if a and b are parallel then

62 and 5x - 2 are same- side interior angles and sum to 180° , that is

5x - 2 + 62 = 180

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

thus for a to be parallel to b , then x = 24