DIG DEEPER! A cube is removed from a rectangular prism. Find the surface area of the figure after removing the cube.


A rectangular prism with length 9 feet, width 8 feet, and height 5 feet. A cubic hollow runs to the height of the rectangular prism and has the side length of 5 feet.


The surface area is ______ square feet

Answer:

[tex]\frac{2t-4}{3}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3}[/tex][tex](t-2)\\[/tex]
=> [tex](\frac{2}{3} * t ) + (\frac{2}{3} * -2)[/tex]
=> [tex]\frac{2t}{3} + (-\frac{4}{3})[/tex]
=> [tex]\frac{2t-4}{3}[/tex]

Hope you understood!!

An undecidable problem is one for which it has been demonstrated that it is impossible to develop an algorithm that always leads to the correct yes-or-no answer. Two examples are:

The halting problem is the problem of determining whether a computer programme will finish running or continue to run indefinitely based on a description of the programme and an input. Alan Turing demonstrated in 1936 that a general algorithm for solving the halting problem for all possible program-input pairs does not exist.

A "pathological" programme g, when called with some input, can pass its own source and input to f and then specifically do the opposite of what f predicts g will do. This case cannot be handled by any f. A key part of the proof is a mathematical definition of a computer and programme, known as a Turing machine; the halting problem is intractable over Turing machines.

Learn more about undecidable problem

https://brainly.com/question/27345304

#SPJ4

The deposit to be made to save $10,000 in 5 years is $8189.67 when compounded monthly.

Compound interest is interest on a loan or deposit that is calculated on both the principal amount and the interest accumulated in previous periods. It differs from simple interest, which is calculated on the principal only. Compound interest can be more favorable to the lender and more expensive to the borrower. The frequency of compounding (annual, quarterly, monthly, etc.) also affects the total amount of interest earned or paid.

Given that:

A = $10,000

r = 4% = 0.04

t = 5 years

n = 12 (since the compounding is monthly)

P = ?

The compound interest is given as follows:

[tex]A= P(1+\frac{r}{n} )^{nt}[/tex]

Substituting the values in the formula we have:

[tex]10000= P(1+\frac{0.04}{12} )^{(12)(5)}\\\\10000= P(1+0.0033 )^{(60)}\\\\10000= P(1.0033 )^{(60)}\\\\10000= P(1.2185)\\\\P= \frac{10000}{1.2185} \\\\P=8189.67[/tex]

Learn more about compound interest here:

brainly.com/question/14295570

#SPJ4

Intercept = 1

Equation - y = -(2/5)x + 1

The person that will finish the series first is;

Ravi will finish first, because even though Manish has read more as of today, Ravi reads faster overall.

The general equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Total pages manish has read as at today = 544 pages

He reads at the same pace and after 8 days he has read 928 pages. Thus, the equation that represents the number of pages that Manish has read is; 928 = 8m + 544

922 - 544 = 8m

m = 378/8

m = 47.25

Thus, his rate is 47.25 pages per day

The equation for Ravi is y = 51x + 594

This shows a rate of 51 pages per day

Thus, Ravi will finish first

Read more about Linear Equation Problems at; https://brainly.com/question/13738662

#SPJ1

Answer:

Each child will have 3/16 pound of Halloween candy.

Step-by-step explanation:

To find out how much candy each sibling gets, we need to divide 3/4 by 4

3/4 divided by 1/4 = 3/16

Therefore, our answer is 3/16.

Answer:

3.2 hours

Step-by-step explanation:

182.4÷57=3.2

time divided by speed equals time

A pentagonal prism have 35 diagonals.

We know tha in a polygon or polyhedron the formula for finding the number of diagonals is: n(n-3)/2,

where n= the number of sides

We find the number of diagonals of a pentagonal prism.

As we know a pentagonal prism has two pentagonal bases like top and bottom and five rectangular sides.

For a pentagonal prism n = 10

So, using above formula the total number of diagonals would be,

d = [10 × (10 - 3)] / 2

d = (10 × 7) / 2

d = 70/2

d = 35

Therefore, the total number of diagonals would be = 35

Learn more about diagonal here:

https://brainly.com/question/23032581

#SPJ4

The solution of the fraction 3/4 is 0.75

The term fraction is defined as represent the parts of a whole or collection of objects

Here we have given the fraction 3/4.

Now, we have to do the following steps in order to find the decimal equivalent for the fraction.

First of all we just need to divide the numerator by the denominator.

Then we get the fraction is 3/4 which means we need to divide: 3 ÷ 4.

The division process is illustrated on the following image.

Then the decimal equivalent to the fraction written as 3/4 is expressed as 0.75 in the decimal form.

To know more about fraction here.

https://brainly.com/question/10354322

#SPJ4

The coefficient of [tex]x^{2}[/tex] in [tex](2x^{2}-3x-4)-(5x^{2}+6x-7)[/tex] is -3.

A coefficient is a multiplicative factor in a polynomial, series, or expression in mathematics. It is typically a number, although it can also be any expression (including variables such as a, b and c). They may also be referred to as parameters if the coefficients are variables in and of themselves. The coefficient in an expression that is not related to any variables is called the constant coefficient (also known as constant term or free coefficient).

Given equation,

[tex](2x^{2}-3x-4)-(5x^{2}+6x-7)[/tex]

= [tex]2x^{2}-3x-4-5x^{2}-6x+7[/tex]

= [tex]-3x^{2}-9x+3[/tex]

Hence, coefficient of [tex]x^{2}[/tex] is -3.

To learn more about coefficient here:

https://brainly.com/question/28975079

#SPJ4

Answer: To determine the correct statement, you need to find a pattern in the values of D(t). You can do this by finding the difference between consecutive values of D(t).

The difference between -60 and 0 is 60.

The difference between 0 and 10 is 10.

The difference between 10 and 90 is 80.

The difference between 90 and 100 is 10.

The difference between 100 and 130 is 30.

The difference between 130 and 150 is 20.

The pattern that emerges is that the difference between consecutive values of D(t) is always 25. This means that the correct statement is "The function is D(t)=25t−60". The correct answer is therefore d.

Step-by-step explanation:

To find the third angle of a triangle if you know the measures of the other two angles, you can use the fact that the sum of the measures of the angles in any triangle is always 180 degrees.

For example, let's say you know that angle A measures x degrees and angle B measures y degrees. To find the measure of angle C (the third angle), you can use the following equation:

x + y + C = 180°

To solve for C, you can subtract x and y from both sides of the equation:

C = 180 - x - y

So, the measure of angle C is equal to 180 degrees minus the measure of angle A and angle B.

To know more on Angle sum property of a triangle

https://brainly.com/question/8492819

#SPJ4

The value of the PU in the given triangle is 19.

The center of the thing is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians intersect. It can alternatively be described as the location where the three medians come together. A line connecting a side's midpoint and the triangle's opposite vertex is called the median.

Given,

'p' is the centroid of triangle XYZ and XU is 57.

Since p is the centroid the 'U', 'V', and 'W' are the mid pint of side'YZ', 'XZ', and 'XY'

from the centroid Theorem, we can write;

XP = 2/3 * XU

plug the values 'XU' in the above equation:

XP = 2/3 *57

XP = 2*19

XP = 38

from figure:

XP + PU = XU

PU = XU - XP

Plug 'XU' and 'XP'

PU = 57 -38

PU = 19

therefore, the PU of the given triangle is 19 units.

Learn more about centroid here:

#SPJ1

Complete question:

On solving the provided question we can say that equation formed is x/y = k, x = ky => y₂ = (10.5 × 3.2) / 5.6 => y₂ = 6

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

x/y = k, x = ky

where k is a constant.

Thus, x₁ / y₁ = x₂ / y₂

5.6 / 3.2 = 10.5 / y₂

5.6 × y₂ = 10.5 × 3.2

y₂ = (10.5 × 3.2) / 5.6

y₂ = 6

To know more about equation visit:

https://brainly.com/question/649785

#SPJ4

The two posters will cover 776 square inches of Melody's bedroom wall.

To find this, you add the area of the two posters together. Poster A has an area of 450 square inches, and poster B has an area of 326 square inches. By adding these two values together, we get 450 + 326 = 776 square inches. This is the total area that the two posters will cover on Melody's bedroom wall. It is important to note that this is assuming that the posters do not overlap each other and that they are placed next to each other, covering an equal area of the wall.

Learn more about Simple Addition here:

https://brainly.com/question/28954094

#SPJ4

The Third side of the right triangle with two sides can be found by Pythagoras Theorem that means by adding the square of other two sides .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the , in a Right Triangle, the square of the hypotenuse side (longest side) is equal to the sum of squares of the other two sides“.

The sides of this triangle are named as Perpendicular, Base and Hypotenuse. where , the hypotenuse is longest side of the triangle , because ,  it is opposite to the angle 90°.

Therefore , the third side (longest side) of a right triangle with two sides can be found by adding the square of the other two sides .

Learn more about Triangles here

https://brainly.com/question/30106737

#SPJ4

Answer:

  1/2log₂(a-1) -log₂(9)

Step-by-step explanation:

You want the expanded form of log₂(√(a-1)/9).

The relevant rules of logarithms are ...

  log(a^b) = b·log(a)

  log(a/b) = log(a) -log(b)

The rules are applicable for any base.

  [tex]\log_2{\dfrac{\sqrt{a-1}}{9}}=\log_2{(\sqrt{a-1})}-\log_2{(9)}=\boxed{\dfrac{1}{2}\log_2{(a-1)}-\log_2{(9)}}[/tex]

the child's percentile rank is 93 th percentile. It means he performed better than [tex]$93 \%$[/tex]of the total number of students.

Need to find the percentile rank for child's score.

Let[tex]$\mathrm{X}$[/tex]denote marks obtained by the child in the achievement test.

The [tex]$\mathrm{Z}$[/tex]value is given as,

[tex]$$Z=\frac{X-\mu}{\sigma}$$[/tex]

Using equation (1), the required percentile rank for child's score is expressed as,

[tex]& Z=\frac{148-125}{15} \\[/tex]

[tex]& Z=1.533[/tex]

The probability value corresponding to the Z=1.533, obtained from the Z table is 0.93736.

Thus, the percentile is 0.93736.

Therefore, the child's percentile rank is 93 th percentile. It means he performed better than [tex]$93 \%$[/tex]of the total number of students.

To learn more about  Percentile rank refer to:

https://brainly.com/question/24245405

#SPJ1

The mean number of rooms = 6

We know that the formula for the mean.

mean = sum of all observations / total number of observations

First we find thr total number of rooms, from given frequency table.

Number of Rooms        Frequency          Total number of rooms

           4                             4                              16

           5                             7                              35

           6                             10                            60

           7                             12                             84

           8                             5                              40

           9                             2                               18

So, the total number of rooms of 40 houses in a town would be,

16 + 35 + 60 + 84 + 40 + 18 = 253

And the total number of houses = 40

Using above formula of mean,  the mean number of rooms would be,

x = 253/40

x = 6.325

Therefore, on an average there are 6 rooms in each house.

Learn more about the mean here:

https://brainly.com/question/15323584

#SPJ4

Answer: , P = 2 +3g

Step-by-step explanation:

Answer:

Step-by-step explanation:

scale,= 1 : 5000000

it means 1 cm depicts 5000000cm

or 50000m else 50km

the distance between two towns in map = 7cm

so the distance between two towns = 7 *50

                                                      = 350km

What the height would need  for this curve to be a density curve is; One-half

The criteria for a curve to be a density curve is as follows;

1. The curve must always be non-negative. This tells us that the y-value of the curve must be greater than or equal to 0 at every given point.

2. The area under the curve must always be equal to 1.

Now, we are told that the curve starts at (-2, 0) and then goes to (5, question mark), and then goes down to (6, 0),.

This means that the area under the curve will be a trapezoid that has a height of question mark and then bases of length 3 (from -2 to 5) and length 1 (from 5 to 6).

The area of this trapezoid will be equal to the sum of the bases times the height divided by 2, or:

Area = ((3 + 1) × question mark)/2

Since the area under the curve must be equal to 1, we can set up the equation:

1 = ((3 + 1)  ×  question mark) / 2

Solving for question mark, we will:

The question mark = 2/4

The question mark = 1/2

Therefore, we can conclude that the height of the curve is  1/2

Read more about Density Curves at; https://brainly.com/question/27990511

#SPJ1

The angles that would make triangle ABC congruent to triangle PDF by AAS are ∠ ACB and ∠ PFD i.e. ∠ ACB = ∠ PFD.

Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.

Given:

The triangle ABC and PDF are concurrent by AAS,

The AAS concurrency required two angles and one side to be equal,

Here,

AB = PD,

∠ ABC = ∠ PDF

Now one more angle is required to be equal,

∠ ACB = ∠ PFD  

Thus, the missing angle is ∠ ACB and ∠ PFD.

To know more about Triangles:

https://brainly.com/question/16886469

#SPJ1

Answer:

The value of g(4) of the given function is 56.

Parallelogram M'N'P'Q' is larger than parallelogram MNPQ because MN and M'N' have lengths of 2 and 5 respectively, and parallelogram MNPQ is dilated by a factor of 5/2 to give parallelogram M'N'P'Q'.

A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two sets of parallel sides. In a particular kind of quadrilateral known as a parallelogram, both sets of opposite sides are parallel and equal. There are four different kinds of parallelograms, including three unique kinds. Parallelograms, squares, rectangles, and rhombuses are the four different shapes. Having two sets of parallel sides makes a quadrilateral a parallelogram. In a parallelogram, the opposing sides and angles are both the same length. On the same side of the horizontal line, the interior angles are additional angles as well. 360 degrees is the total number of interior angles.

To make parallelogram M'N'P'Q, parallelogram MNPQ was enlarged.

Points include M(2, 2), N(4, 2), P(3, 3), and Q. (1,-3)

M'(5, 5), N'(10, 5), P'(8, 7), and Q' (3,-7)

A) First, determine Minnesota's length:

|MN| = 2

|M'N'| = 4

To know more about parallelograms visit:

https://brainly.com/question/29147156

#SPJ4

Answer:

15

Step-by-step explanation:

to determine the number of plants per row, take the square root of 225

sqrt(225) = 15

There should be 15 plants per row

Answer:

Step-by-step explanation:

Since the formation of the strawberry plants should represent a square, it implies that the dimensions of the formation (i.e length and breadth) must be equal.

To achieve this, we have to calculate its square root as the formula for the area of any square is given as (side)^2.

Now, [tex]\sqrt{225}[/tex] = 15

implies that each as well as each column will contain 15 strawberry plants  

On solving the provided question we cans ay that - the value of the following exponent is

Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where

here,

= [tex]10^2 X 10^-3[/tex] X 32

= 100 X 1/1000 X 32

=1/10 X 32

=3.2

To know more about exponents visit:

brainly.com/question/3987569

#SPJ1

The number of gloves selected for each cases is 11 and 19 gloves respectively.

How is selection done?

In mathematics, most of the times selection is done using permutation and combination.

Putting things or numbers in order is known as a permutation.

Combinations are a means to choose items or numbers from a collection of items or groups of items without regard to their order.

Given,

       Total black gloves = 5 left hand+ 5 right hand

       Total brown gloves = 3 left hand + 3 right hand

        Total gray gloves = 2 left hand + 2 right hand

Now to find the least number of gloves for the given conditions, we start with the worst condition.

a) To get at least one matching pair, we first consider no matching pair, which is (5 +3+2) gloves of only left only or right only hand of each colour.

Now to make one pair, we need to select only one glove of the opposite hand of any colour.

Therefore to get atleast one matching pair, smallest number of gloves to be selected = 5 + 3 + 2 + 1 = 11 gloves

b) In this case also we start with worst case.

   For no matching pair of each colour we have to take 10 black gloves, 6 brown gloves and  2 gray gloves of any one hand.

Therefore to get matching pair of each colour, we have to take one more gray glove.

Therefore to get atleast one matching pair of each colour, smallest number of gloves to be selected = 10 + 6 + 2 + 1 = 19 gloves.

To learn more about selection by permutation and combination, follow the link.

https://brainly.com/question/4658834

#SPJ4

Answer: 15

Step-by-step explanation: In ΔNOP,

m

∠

N

=

(

9

x

+

8

)

∘

m∠N=(9x+8)

∘

,

m

∠

O

=

(

4

x

+

13

)

∘

m∠O=(4x+13)

∘

, and

m

∠

P

=

(

2

x

−

6

)

∘

m∠P=(2x−6)

∘

. Find

m

∠

N

.

m∠N