Three rectangular-shaped holes have been drilled passing all the way through a solid 3 × 4 x 5 cuboid. The diagrams show the front, side and top views of the resulting block. What fraction of the original cuboid remains?

Three Rectangular-shaped Holes Have Been Drilled Passing All The Way Through A Solid 3 4 X 5 Cuboid.

Answers

Answer 1

The volume of a cuboid implies the product of its length, width, and height. So that the fraction of the original cuboid that would remain is [tex]\frac{7}{15}[/tex].

A cuboid is a solid derived from a rectangle, thus it has rectangular faces. Its volume can be determined by;

volume of a cuboid = length x width x height

In the given question, the volume of the original cuboid can be determined as;

  volume = 3 x 4 x 5

                = 60 Cubic units

Since holes can not be drilled at the intersection of the holes, then the volume of the hole has to be determined.

To determine the volume of the hole drilled, we have:

(6 x 3) + (3 x 2) + (2 x 2) = 28 Cubic units

So that the fraction of the original cuboid that would remain = [tex]\frac{28 cubic units}{60 cubic units}[/tex]

                                                                   = [tex]\frac{7}{15}[/tex]

Therefore,  [tex]\frac{7}{15}[/tex] of the original cuboid would remain.

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Related Questions

Find an equation of a line with slope -3/4 and that passes through P(-4,6) in standard, form.

Answers

Answer:

[tex]y = - \frac{3}{4}x + 3[/tex]

Step-by-step explanation:

the standard form of any straight line is:

y = m × x + c

where: y is the y value of the point

x is the x value of the point

m is the gradient/slope

SOLUTION

[tex]y = mx + c \\ 6 = - \frac{3}{4} ( - 4) + c \\ c = 3[/tex]

1/2+3/2=2^x
What is the solution to the equation?

Answers

Answer: x=1

Step-by-step explanation:

1/2+3/2=2^x

4/2=2^x

2=2^x

x=1

f is an even function. a = A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 3. Column 2 is labeled f (x) with entries 4, 5, a, 7. g is an odd function b = A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 3. Column 2 is labeled f (x) with entries b, 0, negative 3, negative 4.

Answers

The values of a and b are 4 and -3

How to solve for (a) and (b)?

To solve for a, we make use of the function f(x).

x    f(x)

2     4

0     5

2     a

3     7

Remove the x values 0 and 3

x    f(x)

2     4

2     a

The above table implies that:

f(2) = 4 and f(2) = a

Substitute 4 for f(2) in f(2) = a

4 = a

Rewrite as:

a = 4

To solve for b, we make use of the function g(x).

x    g(x)

2     b

0     0

2     -3

3     -4

Remove the x values 0 and 3

x    g(x)

2     b

2     -3

The above table implies that:

f(2) = b and f(2) = -3

Substitute -3 for f(2) in f(2) = b

-3 = b

Rewrite as:

b = -3

Hence, the values of a and b are 4 and -3

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Complete question

Use the Symmetry of a Function to Find Coordinates

f is an even function             g is an odd function

x    f(x)                                        x             g(x)

2     4                                          2              b

0     5                                          0              0

2     a                                          2              -3

3     7                                          3              -4

Find a and b

Answer:

4, 3

Step-by-step explanation:

Which function is graphed below?

Answers

The graphed rational function is:

[tex]f(x)= \frac{6}{x + 2}[/tex]

Which function is graphed below?

Here we can see that we have a rational function of the form:

[tex]f(x) = \frac{q(x)}{p(x)}[/tex]

Now we notice two things, as x increases, we have a horizontal asymptote that tends to zero.

Then q(x) is a constant, let's say:

q(x) = k

We also can see that we have a vertical asymptote at x = -2, then:

p(x) = (x + 2)

So the rational function is:

[tex]f(x) = \frac{K}{x + 2}[/tex]

Now, notice that when x = 0, the curve intercepts the y-axis at y = 3, then if we evaluate the function in x = 0 we must get:

[tex]f(0) = 3 = \frac{K}{0 + 2} = \frac{K}{ 2} \\\\3*2 = K = 6[/tex]

Then the rational function is:

[tex]f(x)= \frac{6}{x + 2}[/tex]

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Given the function h of x equals three times the square root x plus 1 end root minus 2, which statement is true about h(x)? The function is increasing on the interval (–∞, –2). The function is decreasing on the interval (–3, ∞). The function is decreasing on the interval (–∞, –3). The function is increasing on the interval (–2, ∞).

Answers

The function is decreasing on the interval (–3, ∞). Therefore, the correct option is B.

How to illustrate the function?

A linear function can be represented by a line. The standard form for this equation is: ax+b where,

a= the slope

b= the constant term that represents the y-intercept.

The domain of a function is the set of input values for which the function is real and defined.

Here, the function is decreasing on the interval (–3, ∞).

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What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)? f(x) = 2x2 + x + 4 x g(x) –2 1 –1 3 0 5 1 7 2 9

Answers

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is

[tex](\sqrt{2},\sqrt{-2}  )[/tex] and [tex]((7+\sqrt{2)} ,(7+\sqrt{-2}))[/tex]

We have given that,

f(x) = 2x^2 + x + 4

x                          g(x)      

-2                               1      

  -1                              3        

  0                              5      

  1                              7

  2                              9

What is a polynomial function?

A polynomial function is a relation where a dependent variable is equal to a  polynomial expression.

A polynomial expression is an expression including numbers and variables, where variables are raised to non-negative powers.

The general form of a polynomial expression is:

a₀ + a₁x + a₂x² + a₃x³ + ... + anxⁿ.

The highest power to a variable is the degree of the polynomial expression. When degree = 2, the function is a quadratic function.

When degree = 1, the function is a linear function.

How do we solve the given question?

The quadratic function is given to us:f(x) = 2x^2 + x + 4.

We need to determine the linear equation g(x).

Since it's a linear equation we use the two-point method to determine the equation.

What is the two-point?

y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)

We take the points g(-2) =1, g(-1) = 3

g(x) - g(1) = ((g(-2)-g(-1))/(-2+1))*(x-1)or,

g(x) - 1 = ((-2-(-1))/(-2+1))*(x-1)or, g(x) - 1 = -1(-x+1)or,

g(x) = x - 1 + 1 = x

∴ g(x) = x , is the linear function g(x)

We are asked to find the solution to the system of equations f(x) and g(x).To find the solution we need to check what is the common solution to both f(x) and g(x).

For that, we equate f(x) and g(x).2x^2 + x + 4 = x or, 2x² - x +x- 4 = 0or, 2x^2  - 4 = 02(x^2-2)=0x^2-2=0[tex]x^2-\sqrt{2}=0[/tex][tex](x-\sqrt{2}) (x+\sqrt{2})=0[/tex][tex](x-\sqrt{2})=0 \\x=\sqrt{2}  or x=-\sqrt{2}[/tex]g(-1) = 3(from the table)[tex]g(\sqrt{2})=\sqrt{2}  \ and \ g(\sqrt{-2}) =-\sqrt{2}[/tex][tex]f(\sqrt{2}) = 2(\sqrt{2} )^2 + (\sqrt{2} ) + 3\\=2(2)+\sqrt{2} +3\\=7+\sqrt{2}[/tex][tex]g(-\sqrt{2} )= 2(\sqrt{-2} )^2 + (\sqrt{-2} ) + 3\\=2(2)+\sqrt{-2} +3\\=7+\sqrt{-2}[/tex]

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is [tex](\sqrt{2},\sqrt{-2}  )[/tex] and [tex]((7+\sqrt{2)} ,(7+\sqrt{-2}))[/tex]

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someone please help me slove this its due tmrw somebody help, i will give brainlisest answer please​

Answers

Answer:

Question 5:

a) 65 degrees

b) 11

Question 6:

a) 15.6

b) 6.4

Question 7:

a) 10

b) 20

Question 8:

a) EF = 14.4

Question 9:

a) x = 6

b) y = 22.5

Step-by-step explanation:

Help Me Asap Please And Thank You!

Answers

In this case using the elimination method is actually easier, but the question asks you to use substitution method so....

2x+y= -10

3x-y=0

1st equation: It is better to isolate 2x on both sides because the y is going to be positive no matter what, 2x+y=-10 => y=-2x-10

If you isolated 3x for the 2nd equation, the y will be negative, and you have to divide the whole equation by -1 to make it positive

Now we got y=-2x-10, lets substitute it in the 2nd equation and solve for x:

3x-(-2x-10) = 0

5x+10=0

5x=-10

x=-2

Now lets solve for y:

3(-2)-y=0

-6-y=0

y=-6

Lets see if the same is applicable for 1st equation

2(-2)+(-6)=-10

-10=-10

Yess!!

(-2,-6) is the solution

The answer to the question is explained at the beginning

Hope it helps!

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?

y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2

Answers

Answer:

y < 3x + 2

Step-by-step explanation:

We will be solving this in slope-intercept form, which is a form that gives us the slope and the y-intercept of the graph explicitly:

[tex]y=mx+b[/tex], m is the slope and b is the y-intercept

We are given that everything to the left of the resulting line is shaded, so we know that the inequality sign will be < (less than). That already eliminates the second and fourth options. We also know the y-intercept, or the point where the graph crosses the y-axis and x is 0. because it is given to us (2, which comes from the point (0,2)). To figure out the slope, we can use the formula since we are given two points [(-3, -7) and (0, 2)] the line passes through. The formula, which is mapped out below, tells us that the slope is just the difference in rise (vertical movement) divided by the difference in run (horizontal movement).

[tex]m=\frac{-7-2}{-3-0} =\frac{-9}{-3} =3[/tex]

Now we have all the information we need to find the inequality. The slope is 3, the y-intercept is 2, and the sign is <. The first inequality fits these criteria, meaning the correct linear inequality is y < 3x + 2

What are the restrictions for y
X=10/5+y

Answers

Answer:

[tex]y\ne-5[/tex]

Step-by-step explanation:

So you have the equation:

  [tex]x=\frac{10}{5+y}[/tex]. As you may know, you cannot divide by 0, so y has to be restricted in a way that the denominator is never equal to 0. So to find when y makes the denominator 0, simply set the denominator equal to 0, and solve for y. This gives you the equation: 5+y = 0, y=-5. So the y value CANNOT be equal to -5. Because it makes the denominator 0. so [tex]y\ne-5[/tex] would be the restriction.

Pls I will get spanked if you don't help me.

How many meters are equal to 3 kilometers? Use the pattern in the number of zeros of the product when multiplying by a power of 10 to help you.

Answers:
30 meters
300 meters
3,000 meters
30,000 meters

Answers

1KM = 1000metres

3KM =3000metres

cos(x)=2cos^2(x)-1 0≤x≤2π

Answers

Answer:

[tex]x=0,~x=\frac{2\pi }{3},\:x=\frac{4\pi }{3},~x=2\pi[/tex]

Step-by-step explanation:

The given equation:

[tex]\cos(x)=2\cos^2(x)-1[/tex]

Let [tex]\cos(x)[/tex] be [tex]y[/tex]:

[tex]y=2y^2-1[/tex]

Rewrite as:

[tex]2y^2-y-1=0[/tex]

After solving quadratic equation, the solutions are:

[tex]y=1~~~~y=-\frac{1}{2}[/tex]

Substitute back [tex]\cos(x)[/tex], it follows:

[tex]\cos(x)=1~~~~\cos(x)=-\frac12[/tex]

For the first equation, the solution is [tex]x=0[/tex] and [tex]x=2\pi[/tex].

For the second equation, general solution is:

[tex]x=\frac{2\pi }{3}+2\pi n,\:x=\frac{4\pi }{3}+2\pi n[/tex]

But for the given interval, we must substitute n=0 into the equations so that the values of x must be within interval. Therefore:

[tex]x=\frac{2\pi }{3},\:x=\frac{4\pi }{3}[/tex]

So, the answers are:

[tex]x=0,~x=\frac{2\pi }{3},\:x=\frac{4\pi }{3},~x=2\pi[/tex]

using addition rules ,show how to add the two real numbers 7+(-14)

Answers

The answer is -7 because you add 7 to -14

Answer:

Step-by-step explanation:

14+(−7)+7

Now −7 is the idea or the construct that is the complete opposite of 7, when it comes to additive regions. So, they would cancel out.

And we are left with

14.

rewrite each expression without using absolute value notation |x-y| if x>y

Answers

The expression |x - y| without using absolute value notation is x - y

How to rewrite the expression?

The expression is given as:

|x - y|

Also, we have:

x > y

This means that:

|x - y| > 0

Remove the absolute notation

x - y

Hence, the expression |x - y| without using absolute value notation is x - y

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cos 0 = 8/17. Find tan 0.​

Answers

tan is 15/8

How to determine the identity

Since cos = adjacent/ hypotenuse

Adjacent = 8

Hypotenuse = 17

Let's find opposite

Using the Pythagoras theorem

Opposite ^2 = Hypotenuse^2 - adjacent^2

Opposite = [tex]\sqrt{17^2 - 8^2}[/tex]

Opposite = [tex]\sqrt{289 - 64}[/tex]

Opposite = [tex]\sqrt{225}[/tex]

Opposite = 15

Tan = opposite/ adjacent

Tan = 15/ 8

Thus, tan is 15/8

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1. Nasim thinks of a number.
When he multiplies his number by 5 and subtracts 16 from the result, he gets the same
answer as when ads 10 to his number and multiplies that result by 3.
Find the number Nasim is thinking of.

Answers

Step-by-step explanation:

5x-16 = 3 (10+x)

=> x= 23

Help me asap find the area for each letter and find the surface area

Answers

Surface area of A = 50 square inches, S.A of B = 120 square inches, S.A of C = 60 square inches, S.A of D = 50 square inches, S.A of E = 60 square inches, S.A of F = 120 inches.

S.A of the box = 460 square inches.

What is a cuboid?

A cuboid is a three dimensional solid shape made of 6 rectangles.

Analysis:

surface area of A = surface area of D which is the smallest from the diagram = 5 x 10 = 50 square inches

surface area of C = surface area of E = the second largest = 5 x 12 = 60 square inches

surface area of B = surface area of F = 10 x 12 = 120 square inches

surface area of shape = 2( 50 + 60 = 120) = 2(230) = 460 square inches.

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Write the equation of an ellipse with center (-2,-3), vertical major axis of length 14, and minor axis of
length 8.

Answers

Step-by-step explanation:

Since we have a vertical major axis, our ellipse is vertical.

The equation of a vertical ellipse is

[tex] \frac{(y - k) {}^{2} }{ {a}^{2} } + \frac{(x - h) {}^{2} }{ {b}^{2} } = 1[/tex]

where

(h,k) is the center

a is the semi major axis,

b is the semi minor axis

First, let plug in our center

[tex] \frac{(y + 3) {}^{2} }{ {a}^{2} } + \frac{(x + 2) {}^{2} }{ {b}^{2} } = 1[/tex]

Semi means half, so

a is half of 14 which is 7

B is half of 8, which is 4.

[tex] \frac{(y + 3) {}^{2} }{49} + \frac{(x + 2) {}^{2} }{16} = 1[/tex]

look at image.........

Answers

Answer:

first of all its not d since the y intercept is negitive

then its not b since its sloping down

so the slop is either 7/5 or 5/7

since rise/run it has to be 7/5

Hope This Helps!!!

The function f(x) = 5* is reflected over the y-axis. Which equations represent the reflected function? Select two
options.
f(x) = -(5)-*
0x==3(2)
Of(x) = 5(2)
f(x) = 5(5)
f(x) = 5(5)-*

Answers

Step-by-step explanation:

To reflect a function about the vertical axis, just negate the variable.

For example, if we want to reflect this function

[tex] y = log(x) [/tex]

about the y axis or vertical axis, we just make the x negative

[tex]y = log( - x) [/tex]

Another example,

[tex]y = |x| [/tex]

To reflect about y axis or vertical axis,

[tex]y = | - x| [/tex]

So here l,the answer with negative variables are function that are reflected about the y axis.

The options are the first and the fifth option.

Solve for Y

V = −4y + 4x

Answers

Answer:

Y=−4y/v +4x/v

Step-by-step explanation:

Divide each term in by v and simplify.

A 20-ft ladder leans against a building so that the angle between the ground and the ladder is 72 degrees. How high does the ladder reach on the building?

Answers

The height of the building is 19.02 feet, for a 20-ft ladder to lean against the building at an angle of 72 degrees.

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angle triangle.

Let h represent the height of the building, hence:

sin(72) = h/20

h = 19.02 feet

The height of the building is 19.02 feet, for a 20-ft ladder to lean against the building at an angle of 72 degrees.

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The height reached by the ladder of height 20-ft. inclined at 72° is approximately 19.02-ft.

How can the height reached by the ladder be found?

Length of the ladder = 20 feet

Angle between the ground and ladder = 72°

Height reached by the ladder = Required

Solution:

From the definition of the sine of an angle, we have;

[tex]sin (\theta) = \mathbf{ \frac{opposite \: side}{hypotenuse}} [/tex]

The length of the ladder = The hypotenuse side = 20 ft.

The opposite side to the angle 72° = The height reached by the ladder

Which gives;

[tex]sin (72 ^ {\circ})= \frac{height \: reached}{20} [/tex]

Height = 20 × sin(72°) = 19.02

The height reached by the ladder on the building ≈ 19.02-ft.

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Jillian had 2/9m of a cloth. she used 1/9m of it for sewing a blanket. how much of the cloth does she have remaining?

Answers

Hello,

2/9 - 1/9 = (2 - 1)/9 = 1/9

If you have a cube with the volume of 73.560059, what is the length of the cube?

Answers

If the side of a cube is x, then the volume is x3.
The problem to be solved is: x3
So: x = cube root ( 73.560059 (
x = 4.19

Select the correct answer.
Which statement best defines perpendicular lines?
A.
lines that lie in the same plane
B.
lines that intersect and form right angles
C.
lines that lie in the same plane and do not intersect
D.
lines that share a point

Answers

Answer:

c or b

Step-by-step explanation:

Answer:

Answer:B

Step-by-step explanation:

I did the test and got it right the person above help thx

Rounded to the nearest hundredth what is a positivite solution to the quadratic equation 0=2x^(2)+3x-8

OPTIONS
1.39
2.00
2.89
3.50

Answers

Step-by-step explanation:

the equation is

2x² + 3x - 8 = 0

the generic solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 2

b = 3

c = -8

x = (-3 ± sqrt(9 - 4×2×-8))/(2×2) =

= (-3 ± sqrt(9 + 64))/4 = (-3 ± sqrt(73))/4

x1 = (-3 + sqrt(73))/4 = (-3 + 8.544003745)/4 =

= 1.386000936... ≈ 1.39

x2 = (-3 - sqrt(73))/4

but that would negative, and therefore not a wanted solution.

x ≈ 1.39

is the targeted solution.

can someone please help me

Answers

Answer: A

Step-by-step explanation:

Answer:

A

I solved on paper it took me 45 mins

Sec6A - tan6A = 1+3tan2A.sec2A

Answers

sec ^6 A−tan ^6A=(1+tan ^2A−tan ^2 A)(1+tan ^4

A+2tan ^2 A+tan ^2 A+tan ^4 A+tan ^4 A)

sec ^6 A−tan ^6 A=1+3tan ^2 A+3tan ^4A

L.H.S. = R.H.S.

Hence proved

Step-by-step explanation:

♡´・ᴗ・`♡

A grab bag contains 12 packages worth $.70 each, 15 packages $.40 cents each, and 25 packages worth $.30 each. what is the expected value if you have to pay $.50 to pick one package at random?
group of answer choices

$0.47

-$0.08

$0.00

$0.01

Answers

The expected value of the discrete distribution, if you have to pay $.50 to pick one package at random, is of -$0.08.

What is the mean of a discrete distribution?

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

For this problem, considering the cost of $0.5, the distribution is given as follows:

P(X = 0.2) = 12/(12 + 15 + 23) = 12/50 = 0.24.P(X = -0.1) = 15/(12 + 15 + 23) = 15/50 = 0.3.P(X = -0.2) = 23/(12 + 15 + 23) = 23/50 = 0.46.

Hence the expected value is given by:

E(X) = 0.2 x 0.24 - 0.3 x 0.1 - 0.2 x 0.46 = -$0.08.

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Jim has 10 used books and 12 used DVD's to sell at a garage sale for $1.50 and $5.00 each respectively.

Let x be the number of books and y be the number of DVD's Jim ends up selling.

Which of the following systems of linear inequalities represents this situation if Jim wants to make at least $40.00?

a.)
x ≥ 10
y ≥ 12
1.5x + 5y ≥ 40

b.)
x ≤ 10
y ≤ 12
1.5x + 5y ≥ 40

c.)
x ≥ 1.5
y ≥ 5
10x + 12y ≥ 40

d.)
x ≤ 1.5
y ≤ 5
10x + 12y ≥ 40

Answers

Answer:

The correct system of inequalities is b.

Other Questions
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