Martin is an artist who molds plaster into unique shapes. How much plaster can Martin fit into the mold shown? Cuboid with length as 1 ft, height as 2 ft and width as 1 ft. Is placed above the cuboid with length, height and width as 4 ft. A. 66 ft3 B. 80 ft3 C. 128 ft3 D. 256 ft3

Xavier's average speed is 1 kilometer per minute.

To calculate Xavier's average speed, we need to determine the total time it took him to reach Terminal B and the distance traveled.

Given that Henry had completed 3/4 of the journey when Xavier reached Terminal B, it means Xavier took 1/4 of the total time for the journey. Since Xavier reached Terminal B 30 minutes earlier than Henry, we can infer that Xavier took 30 minutes for his part of the journey.

Since Henry was 30 km away from Terminal B when Xavier reached it, we can assume that Xavier traveled the remaining 30 km to reach Terminal B.

Therefore, Xavier's average speed can be calculated as the distance divided by the time:

Average Speed = Distance / Time = 30 km / 30 minutes = 1 km/minute.

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Step-by-step explanation:

Part A:

4x² - 7x - 15

a, b, c = 4, -7, -15

ac = -60

factors that add up to -7 and multiply to -60 are (-12, 5)

rewrite equation

(4x² - 12x) + (5x - 15)

factor out GCF from both groups

4x(x - 3) + 5(x - 3)

(4x+5)(x-3)

Part B:

Using the factored form from the previous part we can set both factors equal to 0 to solve for x.

4x+5 = 0

4x = -5

x = -5/4

x-3 = 0

x = 3

the two x-intercepts are -5/4 and 3

Part C:

Since the leading coefficient is positive, the right side of the function will be going up or to positive infinity as x goes towards positive infinity. Since the degree is even both sides go in the same direction so on the left side it also goes towards positive infinity as x goes towards negative infinity.

Answer:

7/10 pi (radians)

Step-by-step explanation:

The formula for sector area is (angle * r^2)/2

140pi = angle*r^2/2

multiply both sides by 2

280pi = angle * r^2

r = 20 cm (substitute)

280pi = angle * (20)^2

280pi = angle * 400

Divide both sides by 400

7/10 pi = angle

Answer:

the value of 2/3 ^-2 is 18

To create a system with no solutions, we need to find a parallel line to the given one.

If the given line is y = a*x + b

Our line will be: y  = a*x + 1

Sadly we don't have the other equation for the system, but we can say that it is a general linear equation of the form:

y = a*x + b

Now we want to find another equation that passes through (0, 1) such that the system has no solutions.

Then we just need to find another linear equation with the same slope, a (so the lines are parallel and never intersect), and an y-intercept of 1, so the other linear equation is:

y = a*x + 1

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Answer:

A. 112.5°C

Step-by-step explanation:

Use the inverse variation equation, y = \(\frac{k}{x}\)

Replace y with T, and replace x with V:

T = \(\frac{k}{V}\)

Plug in 90 as T and 25 as V, then solve for k:

T = \(\frac{k}{V}\)

90 = \(\frac{k}{25}\)

2250 = k

So, the equation is T = \(\frac{2250}{V}\)

Plug in 20 as V and solve for T:

T = \(\frac{2250}{V}\)

T = \(\frac{2250}{20}\)

T = 112.5

So, the temperature will be A. 112.5°C

Answer:

\(\mbox{\large y = -\dfrac{3}{5}x - 4}\)

Step-by-step explanation:

The given equation is
\(\mbox{\large 6x + 10y = - 40}\)

The slope-intercept form of the equation of a line is
\(y = mx +b\)

where
m = slope

b = y-intercept

Subtract 4x from both sides of \(\mbox{\large 6x + 10y = - 40}\)

\(6x - 6x + 10y = - 6x-40\\\\\rightarrow \quad 10y = -6x - 40\\\\\text{Divide both sides by 10}\\\rightarrow \quad \dfrac{10y}{y} = -\dfrac{6}{10}x - \dfrac{40}{10}\\\\y = -\dfrac{6}{10}x - 4\\\\\dfrac{6}{10} = \dfrac{3}{5}\\\\\text{Equation of the line in slope-intercept form is: }\\\\y = -\dfrac{3}{5}x - 4\)

Answer:

If you meant 3.5 then its 3.5.

Answer: The y-intercept is -12

The x-intercept is 8

Step-by-step explanation: Factor out 3

Divide all by 3 to simplify.

9x - 6y = 72 is equivalent to

3x - 2y = 24

At this point, you can substitute 0 for x and solve for y

3(0) -2y = 24. -2y/-2 = 24/-2

y = -12

And substitute 0 for y and solve for x.

3x -2(0) = 24. 3x/3 = 24/3

x = 8

OR Change to slope intercept form:

y = mx + b. b is the y intercept.

-2y = -3x + 24. Solve for y.

Divide all by-2

y = 3x/2 - 12.

The y-intercept is -12

To find the x-intercept, substitute 0 for y and solve for x.

0 = 3x/2 -12 Add 12 to both sides.

12 = 3x/2. Multiply both sides by 2/3

8 = x

The x-intercept is 8

The perimeter of triangle is 66.24 units.

What is triangle?

In Euclidean geometry, any 3 points, once non-collinear, verify a unique triangle and at the same time, a unique plane

Main body:

according to question :

c = 28

let the vertices be A,B,C

∠A= 30°

by using trigonometric ratios,

BC/ AB = sin30°

AB = C = 28

BC/28 = sin30°

BC = 28*sin30°

BC= 28*(1/2)

BC = 14

similarly

AB /CA = cos 30°

28/CA = √3/2

CA = 28*√3/2

CA = 14/√3

CA = 24.24

Hence , perimeter = AB +BC +CA = 28+14+24.24

                              =66.24 units

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For a normal distribution with mean 0 and standard deviation 1 the python line will be 0.627409464153

What is mean?

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. It is known as the "average" and is the most widely used central tendency measure.

What is standard Deviation?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Appropriate function and output are given below

import scipy.stats as st

print(st.norm.cdf(0.325,0,1)

0.627409464153

The python line will be 0.627409464153 for a normal distribution with a mean of 0 and a standard deviation of 1.

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The 28th term in the sequence of positive rationals produced by the counting process described in Theorem 5.3.1 is 3/2.

Theorem 5.3.1 describes a counting process in which positive rationals are listed in increasing order. The process starts with 1/1, followed by all rationals of the form m/1, 1/m, where m is a positive integer.

Next, all rationals of the form m/(m+1), (m+1)/m are listed, where m is a positive integer. This process continues, with all remaining rationals listed in increasing order.

To find the 28th term in this sequence, we need to determine which rational number is listed in the 28th position. Following the described counting process, we can list out the first few rationals in the sequence:

1/1, 1/2, 2/1, 1/3, 3/1, 2/3, 3/2, 1/4, 4/1, 3/4, 4/3, 2/5, 5/2, 3/5, 5/3, 4/5, 5/4, ...

Counting through this list, we see that the 28th term is 3/2.

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Answer:

Step-by-step explanation:

The the age of Sarah be x and the amount she has be y:

When Sarah was 5 and her amount is $50

When x1 = 5, y1 = $50

Also when Sarah was 6, her amount is $100

When x2 = 6, y2 = $100

Find the slope which is also the constant of proportionality

x= ky

k = y2-y1/x2-x1

k = 100-50/6-5

k = 50/1

k = 50

Substitute the value of k in the formula:

x = 50y

This means that Sarah's age is directly proportional to the amount she have. Hence, it can be concluded that it is a direct relationship

The given order of integration is in the form of triple integrals, where the integration is performed first over the z-coordinate, then over the y-coordinate, and finally over the x-coordinate.

To obtain an equivalent integral in the given order of integration, we can use the substitution method and change the order of integration.

First, we integrate with respect to z from 0 to √(4-x^2), then we integrate with respect to y from -√(4-x^2) to √(4-x^2), and finally, we integrate with respect to x from 2 to 0. This can be expressed as:

∫2 0 ∫-√(4-x^2) √(4-x^2) ∫0 f(x,y,z) dz dy dx

We can then change the order of integration to obtain an equivalent integral in the form ∫ba∫g(z)f(z)∫k(x,z)h(x,z)f(x,y,z)dydxdz by integrating w.r.t. x first, then w.r.t. y, and finallyw.r.t. z.

This gives us:

∫0 √4-y^2 ∫-√(4-x^2) √(4-x^2) ∫0 f(x,y,z) dz dx dy

Using the limits of integration for each variable, we can rewrite this as:

∫0 2 ∫-√(4-y^2) √(4-y^2) ∫0 f(x,y,z) dz dy dx

Therefore, the equivalent integral in the given order of integration is ∫0 2 ∫-√(4-y^2) √(4-y^2) ∫0 f(x,y,z) dz dy dx.

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Answer:

Step-by-step explanation:

Note : we have a proportional relationship between the two variables

_______________________________________

He used 3/4 gallon of gas to mow 3/10 of the lawn

Then

He has to use 1/4 gallon of gas in order to mow 1/10 of the lawn

( we divided both sides by 3)

Then

He has to use 10 × 1/4 gallons of gas to mow 10/10 of the lawn

What that means is :

He has to use 10/4 gallons of gas to mow the entire lawn

In other words :

He has to use 2.5 gallons of gas to mow the entire lawn

________________

Alex is mowing a 145.5 square feet lawn. He used 3/4 gallon of gas to mow 3/10 of the lawn. How many gallons of gas are needed to mow the entire lawn

The given expression [csc^2(-θ) - 1] / [1 - cos^2(-θ)] equals 0. We are given the expression [csc^2(-θ) - 1] / [1 - cos^2(-θ)], and we need to determine its value.

We'll start by simplifying the expression using trigonometric identities.

The reciprocal of sine is cosecant, so we can rewrite csc^2(-θ) as 1/sin^2(-θ).

Using the Pythagorean identity sin^2(-θ) + cos^2(-θ) = 1, we can substitute sin^2(-θ) with 1 - cos^2(-θ).

Substituting these values into the expression, we get:

[1/(1 - cos^2(-θ))] - 1 / [1 - cos^2(-θ)]

To simplify further, we'll find a common denominator for the fractions.

The common denominator is (1 - cos^2(-θ)).

Multiplying the first fraction by (1 - cos^2(-θ)) / (1 - cos^2(-θ)), we get:

[1 - cos^2(-θ)] / [1 - cos^2(-θ)]^2 - 1 / [1 - cos^2(-θ)]

Expanding the denominator in the first fraction, we have:

[1 - cos^2(-θ)] / [1 - 2cos^2(-θ) + cos^4(-θ)] - 1 / [1 - cos^2(-θ)]

Now, we can combine the fractions over the common denominator:

[1 - cos^2(-θ) - 1 + cos^2(-θ)] / [1 - 2cos^2(-θ) + cos^4(-θ)]

Simplifying further, we find:

0 / [1 - 2cos^2(-θ) + cos^4(-θ)]

Since the numerator is 0, the expression simplifies to:

0

Therefore, the given expression [csc^2(-θ) - 1] / [1 - cos^2(-θ)] equals 0.

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Answer:

Step-by-step explanation:

A cube has 6 faces so:

Area of 1 face = 486/6 = 81 cm^2.

Lateral area = 4 * face area

= 4 * 81

= 324 cm2.

Answer:

one face = 81 cm²

lateral area = 324 cm²

Step-by-step explanation:

486/6 = 81 cm²

81 x 4 = 324 cm²

Answer:

Yes

Step-by-step explanation:

In the equation, -1.3 is the y-intercept. The y-intercept always has a x value of 0. On the point (0,-1.3), it matches the y-intercept and is therefore part of the function/equation.

Hope this helps :)

The graph of function f(x) = 3x -1.3 passes through the point (0,-1.3)

A function is a set of rules that assigns each element of a set a unique element of another set.

If f is a function and f(x) = x+2, then if we have to check x= 1 , y=3 put these values in y = x + 2 , 3 =1+2 (true). Thus, (1,3) satisfies y = x + 2

Given that y=f(x) = 3x - 1.3

put x  =0 , y = -1.3

y = 3x- 1.3 ⇒ -1.3 = 3 (0)-1.3 ⇒ -1.3 = -1.3, which is true

As the point (0, -1.3) satisfies the given equation.

Therefore, the graph f(x) = 3x -1.3 passes through the point ( 0,-1.3)

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problem decoded dude

follow meh

The AFC represents the fixed portion of the total cost, while the difference between ATC and AFC represents the variable cost per unit.

To determine the relationship between average fixed cost (AFC) and average total cost (ATC) at a quantity of output of 1,000 units, we need to understand the formulas for AFC and ATC.

AFC is calculated by dividing total fixed cost (TFC) by the quantity of output (Q). ATC is calculated by dividing total cost (TC) by the quantity of output (Q). Mathematically, we have:

AFC = TFC / Q

ATC = TC / Q

Given that AFC is $8 at a quantity of output of 1,000 units, we can substitute the values into the AFC formula:

$8 = TFC / 1,000

Multiplying both sides of the equation by 1,000, we find:

TFC = $8,000

Now, we are given that ATC is $12 at the same level of output. Substituting the values into the ATC formula, we have:

$12 = TC / 1,000

Multiplying both sides of the equation by 1,000, we find:

TC = $12,000

To summarize:

Total fixed cost (TFC) = $8,000

Total cost (TC) = $12,000

Therefore, it follows that the difference between AFC and ATC lies in the variable cost component. The AFC represents the fixed portion of the total cost, while the difference between ATC and AFC represents the variable cost per unit.

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Answer:

X=3

Step-by-step explanation:

-5x-4(x-6)=-3

-5x-4x+24=-3

-9x=-27

x=3

The total space that the cargo will take up is 7 x 10⁷ cubic feet.

In geometry, a prism is a three-dimensional solid shape that consists of two congruent bases (which can be any polygon) and a set of parallel line segments that connect the corresponding vertices of the two bases. The bases are usually parallel and of the same shape and size, and the line segments connecting the vertices are known as the lateral faces of the prism.

Prisms are commonly found in architecture and engineering, where they are used to create structures such as buildings, bridges, and towers. They are also used in optics, where they are used to refract and reflect light, and in mathematics, where they are used to study geometric properties and relationships.

To find the total space that the energy prisms will take up, we need to multiply the number of prisms by the amount of space each prism takes up. We can use scientific notation to simplify the calculation:

3.5 x 10⁵ energy prisms * 2 x 10² cubic feet per prism

= (3.5 * 2) x 10⁵⁺² cubic feet

= 7 x 10⁷ cubic feet

Therefore, the total space that the cargo will take up is 7 x 10⁷ cubic feet.

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Answer:

S = 3

S = 5

S = 7

S = 9

Step-by-step explanation:

t = 3s + 2

when t = 11

11 = 3s + 2

11 – 2 = 3s

9 = 3s

s = 3

t = 3s + 2

when t = 17

17 = 3s + 2

17 – 2 = 3s

15 = 3s

s = 5

t = 3s + 2

when t = 23

23 = 3s + 2

23 – 2 = 3s

21 = 3s

s = 7

t = 3s + 2

when t = 29

29 = 3s + 2

29 – 2 = 3s

27 = 3s

s = 9

I HOPE ALL THIS HELPS

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Answer:

Step-by-step explanation:

rational integer and real

it is rational because it is a perfect root of 2

it is a integer because every positive and negative numbers are integers.

Answer:

  42, 38, 34, 30

Step-by-step explanation:

You want the first 4 terms of the sequence described by ...

  an = 42 -4(n -1), n ∈ ℕ

You can write the first 4 terms of the sequence by evaluating the 'an' expression for n = 1, 2, 3, 4.

Or, you can recognize the expression describes a sequence with a first term of 42 and a common difference of -4. That is, each term is 4 less than the one before.

The terms you want are ...

  42, 38, 34, 30

__

Additional comment

The equation for the n-th term of an arithmetic sequence is ...

  an = a1 +d(n -1)

where a1 is the first term, and d is the common difference. Comparing this to the given equation, we see a1 = 42, d = -4.

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Answer:

(-2,3)

Step-by-step explanation:

This equation describes the displacement d of the object as it oscillates back and forth in SHM with a period of 7 minutes and amplitude of 18m.

Simple Harmonic Motion (SHM) is a motion that can be defined by a sine or cosine function with a fixed period and amplitude. The motion of a mass on a spring, the motion of a pendulum, and the motion of a mass on an inclined plane are examples of SHM.

The equation representing the displacement d of an object in SHM can be given said= A sin (2π/ T) where A is the amplitude of the SHM, T is the period of the SHM, and t is the time elapsed since the object was released from rest. In this problem, the object is moving in SHM with a period of 7 minutes and amplitude of 18m.

This equation describes the displacement d of the object as it oscillates back and forth in SHM with a period of 7 minutes and amplitude of 18m.

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Answer:

355.94 cm2

Step-by-step explanation:

if it is the area of the shaded part, you have to find the area of rectangle and the area of the circle, then subtract the rectangle's area from the circle's.

area of circle = 3.14( i used this π because the radius is not divisible by 7) × 11 × 11 = 379.94.

area of rectangle = 6 × 4 = 24cm

379.94 - 24.00 = 355.94cm2.

Answer:

1. no 2: yes 3: yes 4. no 5.no 6. no

Step-by-step explanation:

The difference between the sample and the population that occurs by chance is known as sampling error. The term "sampling error" refers to the discrepancy that arises between a sample statistic and a population parameter due to chance sampling variation

.A sample is a subset of a population that is chosen to represent the entire population. The population is the complete set of data that the researcher is interested in. It is impossible to collect information from every member of a population, so samples are used instead.Sampling error arises because the sample used to make inferences or generalizations about a population is never an exact representation of the entire population.

Sampling error may also be caused by differences in the measuring instrument used to collect data or the procedures used to collect data.The difference between the sample and the population that occurs by chance is known as sampling error. So, option B is correct.

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