Bradley cut a square hole out of a block of wood in wood shop. If the block was cube-shaped with side lengths of 8 inches, and the hole had side lengths of 5 inches, how much wood was left after the hole was cut out?
A.
387 cubic inches
B.
512 cubic inches
C.
39 cubic inches
D.
312 cubic inches

Step-by-step explanation:

the volume of a rectangular block or tank is

length × width × height

so, it is like all regular 3D objects

base area × height.

so, we get

120 × 75 × 48 = 374,400 m³ = 3.744 × 10⁵ m³

why ?

374,400 = 374400 × 10⁰ = 37440 × 10¹ =

= 3744 × 10² = 374.4 × 10³ = 37.44 × 10⁴ =

= 3.744 × 10⁵

Answer:

Slope = 1

Step-by-step explanation:

The limit of the expressions [tex]3^{2n} + 1[/tex] and [tex]4^{n + 2} - 3[/tex] for n to infinity is infinity

The expressions are given as:

[tex]3^{2n} + 1[/tex]

[tex]4^{n + 2} - 3[/tex]

The limits of the expressions as they approach infinity are represented as:

[tex]\lim_{n \to \infty} 3^{2n} + 1[/tex] and [tex]\lim_{n \to \infty} 4^{n + 2} - 3[/tex]

Substitute [tex]\infty[/tex] for n in both expressions

[tex]\lim_{n \to \infty} 3^{2 * \infty} + 1[/tex] and [tex]\lim_{n \to \infty} 4^{\infty + 2} - 3[/tex]

Solve both expressions independently;

[tex]\lim_{n \to \infty} 3^{2n} + 1 = 3^{2 * \infty} + 1[/tex]

Evaluate the product

[tex]\lim_{n \to \infty} 3^{2n} + 1 = 3^{\infty} + 1[/tex]

Evaluate the exponent

[tex]\lim_{n \to \infty} 3^{2n} + 1 = \infty + 1[/tex]

Evaluate the sum

[tex]\lim_{n \to \infty} 3^{2n} + 1 = \infty[/tex]

Also, we have:

[tex]\lim_{n \to \infty} 4^{n + 2} - 3 = 4^{\infty + 2} - 3[/tex]

Evaluate the sum

[tex]\lim_{n \to \infty} 4^{n + 2} - 3 = 4^{\infty} - 3[/tex]

Evaluate the exponent

[tex]\lim_{n \to \infty} 4^{n + 2} - 3 =\infty - 3[/tex]

Evaluate the difference

[tex]\lim_{n \to \infty} 4^{n + 2} - 3 =\infty[/tex]

Hence, the limit of the expressions for n to infinity is infinity

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Answer:

18 centimeters

Step-by-step explanation:

Divide the circumference by π, or 3.14 for an estimation. The result is the circle's diameter.

Divide the diameter by 2.

There you go, you found the circle's radius

Answer:

6h

Step-by-step explanation:

If Olivia teaches 6 classes that are 1 hour, she teaches 6×1 is 6 hours.

If the classes are two hours, she teaches 6×2 is 12 hours.

Try with numbers to see what math operation you are doing. Its times.

6×h is written 6h

6h is the  expression that shows the total number of hours she teaches

An expression is combination of variables, numbers and operators.

Given,

Each painting class Olivia teaches is h hours long.

The number of classes teached by Olivia in a week is 6.

We need to find an expression that shows the total number of hours she teaches

6h is the required expression.

h is the variable because its value will be changed.

Hence, 6h is the  expression that shows the total number of hours she teaches

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Considering the piece-wise function, the value of the function at x = 2, that is, g(2), is given by:

C. 1.

It is a function that has different definitions based on the input.

In this problem, the function is defined by:

Due to the equal sign, x = 2 is part of the second definition, hence:

g(2) = 2³ - 9(2)² + 27(2) - 25 = 1.

Which means that option C is correct.

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Answer:

13 m

Step-by-step explanation:

Answer:

si es funcion radical al final se pondra con raiz y las raizes son como potenciacion pero al revez es como multiplicacion y su opuesto en divicion haci que 5 mas 5 es 10 mas 4 es 14 pero sigue al raiz haci que se tiene que buscar una raiz a 14 seria 3,7288 y haci pero si no tenemos entonces una divicion 7 por 2 14 pero no se puede haci que 4 entre 7 la respuesta la pondrias como 4 (imagen de raiz encima del 7) 7

Step-by-step explanation:

espero ayudarte utilice un 64/1 de mi cabeza

Answer:

B

Step-by-step explanation:

y is first so, 8,1 6,2 4,3 2,4 0,5

The equation that represents the solution of x is x = 2 - y/2

The equation is given as:

14x + 7y = 28

Divide through by 7

2x + y = 4

Subtract y from both sides

2x = 4 - y

Divide both sides by 2

x = 2 - y/2

Hence, the equation that represents the solution of x is x = 2 - y/2

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Answer:

43.96 or C

Step-by-step explanation:

c=(pi)(d)

pi --> 3.14

d --> diameter (in your case 14.)

c=3.14*14

c= 43.96

Both formulas work, 2(pi)r and (pi)(d)

But, if they give you the diameter then use (pi)(d).

If they give you the radius then use 2(pi)r

P(the recipient is male)= 40.5%

p(the degree is a bachelors) = 52%

p(the recipient is female, given that the degree is advanced)  = 56.2%

p( the degree is not an associates, given that the recipient is male) = 78.4%

Probability determines the chances that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

P(the recipient is male) = total number of males / total number of recipients

1136/2803 = 40.5%

p(the degree is a bachelors) = total number of bachelors degree / total number of degree

= 1456 / 2803 = 52%

p(the recipient is female, given that the degree is advanced) = total number of females with advanced degree / total number of advanced dgree

376 / 669 = 56.2%

p( the degree is not an associates, given that the recipient is male) = number of males that that have degrees other than associates / total number of males

891 / 1136 = 78.4%

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Answer:

Step-by-step explanation:

I don't know what is meant by "analyze the function," but I can draw the functions.

Answer:

x=4

or

x=36

Step-by-step explanation:

I am wondering if you mean 3x=12 or x/3=12

if 3x=12, then x=4

if x/3=12, then x=36

Answer:

D. None of these

Step-by-step explanation:

(5×10^8)(4×10^3)

=20 × 10^11

All the terms are being multiplied. There is no distributive property (FOIL) here. Rearrange the numbers in any order that helps you.

5 × 4 × 10^8 × 10^3

Add exponents to multiply the 10's.

and in proper scientific notation, one last change would give you

2.0 × 10^12

Answer:

78.55cm^2

Step-by-step explanation:

area of a circle = πr^2

where π= 3.142

r= radius= diameter/2

radius= 10/2= 5

area= 3.142×(5)^2

area= 3.142×25=78.55cm^2

Answer:

18cm

Step-by-step explanation:

Given:

- The length of AB is 9 centimeters

- A dilation with a scale factor of 2

The length of the image AB after the dilation is applied:

9 x 2 = 18

dilation is used to make an image or in this case AB, with a scale factor of 2 means that its doubling in size. If the scale factor was 1/2 that it would be decreasing in size since it will be half of the original size

[tex]\csc \theta \tan \theta - \tan \theta \sin \theta \\\\\\=\dfrac 1{\sin \theta} \cdot \dfrac{\sin \theta }{\cos \theta }- \dfrac{\sin \theta }{\cos \theta} \cdot \sin \theta\\\\\\=\dfrac{1}{\cos \theta}-\dfrac{\sin^2 \theta}{\cos \theta}\\\\\\=\dfrac{1- \sin^2 \theta}{\cos \theta}\\\\\\=\dfrac{\cos^2 \theta}{\cos \theta}~~~~~~~~~~~~~~;[\sin^2 \theta + \cos^2 \theta =1 ]\\\\\\=\cos \theta[/tex]

Let's write out some trigonometric identities that we can use:

Now let's try solving them out:

  [tex]csc(x)tan(x)-tan(x)sin(x)=\frac{1}{sin(x)}tan(x)-sin(x)tan(x)\\\\ csc(x)tan(x)-tan(x)sin(x)=tan(x)(\frac{1}{sin(x)}-sin(x))\\\\ csc(x)tan(x)-tan(x)sin(x)=tan(x)(\frac{1}{sin(x)} -\frac{sin^2(x)}{sin(x)} )\\\\csc(x)tan(x)-tan(x)sin(x)=tan(x)*(\frac{1-sin^2(x)}{sin(x)} )\\\\csc(x)tan(x)-tan(x)sin(x)=\frac{sin(x)}{cos(x)}*\frac{cos^2(x)}{sin(x)} \\\\csc(x)tan(x)-tan(x)sin(x)=\frac{sin(x)}{sin(x)}*\frac{cos^2(x)}{cos(x)}\\\\csc(x)tan(x)-tan(x)sin(x)=1 * cos(x)\\\\ csc(x)tan(x)-tan(x)sin(x)=cos(x)[/tex]

  *I used a different variable, but that doesn't change the answer

Answer: cos(x)

Hope that helps!

Answer:

-2

Step-by-step explanation:

3(a+1.5)=-1.5

a+1.5 = - 1.5/3 = - 0.5

a = - 0.5 - 1.5 = - 2

Answer:

Step-by-step explanation:

3a + 4.5 = -1.5

3a = -6

a = -2

[tex]\boxed{ x= 2}[/tex]

[tex]4x+3=3x+5[/tex]

Subtract 3 from both sides :

[tex]4x + 3 = 3x + 5[/tex]

[tex]4x + 3-3 = 3x + 5-3[/tex]

[tex]4x = 3x + 2[/tex]

Subtract 3x from both sides :

[tex]4x = 3x + 2[/tex]

[tex]4x-3x = 3x + 2-3x[/tex]

[tex]x = 2[/tex]

[tex]\sf{\qquad\qquad\huge\underline{{\sf Answer}}}[/tex]

The value that satisfies the first degree equation is: x = 2.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf Verification:[/tex]

[tex] \qquad \sf \dashrightarrow42 + 3 = 32 + 5[/tex]

[tex] \: \: \qquad \sf \dashrightarrow 8 + 3 = 6 + 5[/tex]

[tex] \: \: \qquad \sf \dashrightarrow11 = 11[/tex]

Solving a first degree equation

The objective of the problem is to know what is the number that allows the stated equality to be fulfilled, for this it is necessary to clear the value of x.

The formulation is first degree:

[tex] \: \: \: \: \: \: \: \: \: \: \: \boxed{ \Rrightarrow\bf 4x + 3 = 3x + 5}[/tex]

The variables must be grouped in the same term, in this case we will do it in the left term, and the constants (numbers) in the right.

1) Subtract -3x from both terms:

[tex] \qquad \sf \dashrightarrow4x + 3 - 3x = 3x - 3x + 5[/tex]

[tex] \qquad \sf \dashrightarrow \: x + 3 = 5[/tex]

2) Subtract three units for each term:

[tex] \qquad \sf \dashrightarrow \: x + 3 - 3 = 5 - 3[/tex]

[tex] \qquad \sf \dashrightarrow \: {x =2 \: ✔}[/tex]

I hope I've helped : )

Answer:

Step-by-step explanation:

Multiplying or dividing an inequality by a negative number requires that the inequality symbol be reversed.

__

To solve this inequality, we can divide by the coefficient of x, which is -8. Dividing by -8 means we need to reverse the inequality symbol.

_____

Additional comment

Actually, applying any function that has a negative slope means the ordering is reversed. That is the more general case.

Here, we're specifically concerned with division by a negative number. You can see the effect on the ordering relation by considering ...

Answer:

Number of terms  = 31.

Step-by-step explanation:

Sum of n terms of an A S with first term 1 and common difference 1:-

496 = (n/2)(2(1) + 1(n - 1))

496 = (n/2)(n + 1)

n^2/2 + n/2 = 496   Multiply through by 2:-

n^2 + n = 992

n^2 + n - 992 = 0

(n - 31)(n + 32) = 0

n = 31   (we ignore the negative).

Answer:

y=ab^x

y=6.0.8^x

Step-by-step explanation:

find exponential function by substituting given values into y=ab^x and the solve

The total number of inches yards that she have is 6.95 yards

Given the following parameters

Amount of red yards = 4.2 inches

Amount of blue yards = 2.75inches

In order to determine the total yards, the sum of the yards is expressed as:

Total yards = 4.2 + 2.75

Total yards = 6.95 yards

Hence the total number of inches yards that she have is 6.95 yards

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Answer: B

Step-by-step explanation: There are many less face cards in the deck than other cards, you would think youre getting 3 points each time rather than thinking 10 points each time

Answer:

52 units^2

Step-by-step explanation:

Given:-

Length(L): 4

Width(W): 3

Height(H): 2

Surface area = 2(LW+WH+HL)

2(4×3+3×2+2×4)

2(12+6+8)

52 units^2

Hope this answers your question!!

Answer:

A) 6

B) 14

C) 4

D) 7

Hope it helps :))

Answer:

1/5x^4

Step-by-step explanation:

To change a negative exponent to a positive one, flip it into a reciprocal. This is what I have done here.