The Figure below shows a rectangular prism and a cube:
How many such cubes are required to completely pack the prism without any gap or overlap?

A. 288
B. 576
C. 1,152
D. 1,636

Answer:

True

Step-by-step explanation:

Answer:

(7, 4)

Step-by-step explanation:

One-to-one function means that for every value of y in the range there is associated only one value in x in the domain.

If the point (x, y) belongs to f(x), then point (y, x) belongs to f^-1(x) (its inverse). In this case, (4,7)  is on the graph of f(x), therefore (7, 4)  is on the graph of f^-1(x)

Answer:

Step-by-step explanation:

most probably secant

hope it helps

Answer:

42

Step-by-step explanation:

In a rectangle, the diagonals have the same length. Therefore:

[tex]3x+6=5x-18 \\\\3x+24=5x \\\\ 24=2x \\\\x=12 \\\\BD=5(12)-18=60-18=42[/tex]

Hope this helps!

Answer:

BD = 42

x=12 is found below as a way to find x

We can find 42 by adding together the equations

3x+6 = 5x-18

+18 = 5x(-3x-6)

18 + 6 = 2x

24 = 2x

x= 12  

We can then plug in for 5x and 3x

as BD = 5x-18 = 3x+6

5(12) = 60 -18 = 42 and 3(12) =36+6 = 42

To find line BD = 42

Step-by-step explanation:

3x+6= 42

3x = 42-6

3x = 36

x = 12

5x-18 = 60

5x = 60- 18

5x = 42

x=12

Answer:

the ball takes 3.1944 sec

Step-by-step explanation:

Answer:

It takes 3.498 seconds.

Step-by-step explanation:

To calculate free fall you must use the formula: h=1/2gt^2

Anna:

1st month = 18 + [tex]\frac{3}{4}[/tex] = 18[tex]\frac{3}{4}[/tex] inches

2nd month = 18[tex]\frac{3}{4}[/tex] + [tex]\frac{3}{4}[/tex] = 19[tex]\frac{1}{2}[/tex]

3rd month = 19[tex]\frac{1}{2}[/tex] + [tex]\frac{3}{4}[/tex] = 20[tex]\frac{1}{4}[/tex]

4th month = 20[tex]\frac{1}{4}[/tex] + [tex]\frac{3}{4}[/tex] = 21

5th month = 21 + [tex]\frac{3}{4}[/tex] = 21[tex]\frac{3}{4}[/tex]

Grace:

Because Anna is [tex]\frac{9}{4}[/tex] inches shorter than Grace, we can start the count from the third month:

1st month = 20[tex]\frac{1}{4}[/tex]

2nd month = 21

3rd month = 21[tex]\frac{3}{4}[/tex]

4th month = 21[tex]\frac{3}{4}[/tex] + [tex]\frac{3}{4}[/tex] = 22[tex]\frac{1}{2}[/tex]

5th month = 22[tex]\frac{1}{2}[/tex] + [tex]\frac{3}{4}[/tex] = 23

Answer:

9ab - 9a +1

Step-by-step explanation:

first, we can distribute the negative sign to the second set of parentheses.

-(-4ab + 5) becomes + 4ab - 5

now let's put the values in (5ab-9a-4) side by side with the corresponding values in + 4ab - 5

5ab + 4ab - 9a - 4 - 5

= 9ab - 9a - 9, because 5ab + 4ab = 9ab, -9a is alone, and -4 - 5 = -9.

Answer: 28

Step-by-step explanation:

Since this is an isosceles triangle, two of the angles are congruent.

180 - 124 = 56

56/2 = 28

Answer:

Step-by-step explanation:

y(x) and f(x) are similar in meaning; they both state that the dependent variable is a function of the independent variable x.

f(x) = 5x = y(x).

Answer: The bakery made 3 batches of biscuits.

Step-by-step explanation:

To find how many batches the bakery made  set up a proportional relationship .

so if  [tex]\frac{3}{10}[/tex]   can make 1 batch of biscuit

is asking how many batch of biscuits  can [tex]\frac{3}{5}[/tex]  cup of flour make

so solve this divide 3/5 by 3/10 to find the number of batches

[tex]\frac{3}{5} /\frac{3}{10}[/tex]  = [tex]\frac{30}{15 }[/tex]  = 2 +1

Answer:

the bakery made 3 batches of bicuits.

3/10=0.3

3/5=0.6

if 0.3 is 1 batch then 0.6 is 2 batches 1+2=3

Answer: C

Step-by-step explanation:

Since you are multiplying the two scientific notations, you would multiply 8.1 and 2.2. After, you would multiply the 10³ and 10^6. When you multiply 2 exponents with the same base, you add the exponents. Therefore, C is your correct answer.

Answer:

(8.1*2.2)*10^3+6

Step-by-step explanation:

The equation = 1.782*10^10=17820000000

The top equation = 10.3*1001000

The second equation = 17.82*10^18=17820000000000000000

The third equation = 17.82* 1000000000= 17820000000

Answer: (a) 4

(b) 5

(c) 14

(d)

Class interval       Class mark

30 - 35                       [tex]\dfrac{35+30}{2}=32.5[/tex]

35 - 40                       [tex]\dfrac{35+40}{2}=37.5[/tex]

40 - 45                        [tex]\dfrac{40+45}{2}=42.5[/tex]

45 - 50                        [tex]\dfrac{45+50}{2}=47.5[/tex]

50 - 55                        [tex]\dfrac{50+55}{2}=52.5[/tex]

Step-by-step explanation:

The data of 40 persons is given as :

Weights (in kg)    Frequency

30 - 35                  6

35 - 40                   13

40 - 45                   14

45 - 50                   4

50 - 55                  3

(a)

Lower limit is the lowest number in a class interval .

So, is the lower limit of fourth-class interval (45 - 50) is 4.

(b)

Class size = Upper limit - lower limit

So, Class size of first class interval = 35-30=5

Thus , class size of each interval is 5. [ class size remains same]

(c)

Highest frequency in table = 14 which is corresponding to 40 - 45   .

Thus , 40 - 45  is the class interval has the highest frequency.

(d)

Class mark is the mid value of each class interval.

Class interval = [tex]\dfrac{(\text{Upper limit+Lower limit})}{2}[/tex]

Class interval       Class mark

30 - 35                       [tex]\dfrac{35+30}{2}=32.5[/tex]

35 - 40                       [tex]\dfrac{35+40}{2}=37.5[/tex]

40 - 45                        [tex]\dfrac{40+45}{2}=42.5[/tex]

45 - 50                        [tex]\dfrac{45+50}{2}=47.5[/tex]

50 - 55                        [tex]\dfrac{50+55}{2}=52.5[/tex]

Answer:

x^3 -10x + 57

Step-by-step explanation:

Answer:

B. 588 inches cubed.

Step-by-step explanation:

the pyramid base with 2inch height = 392 - 14 x 14 = 196 = 392-196 = 196

the pyramid with 9 inch height = 588.25 = 14 x 14 = 196 the adjoined upper base.

= 588.25 - 196 = 392.25 + 196 = 588^3  (inches cubed ) we only needed one base structure

We check the slant = (1/2)base = 7 then divide 392.25/7 = 56.0357142857/4

Then divide by 4 = 56.0357142857/4 = 14 and we know the slant is also 14.

We can find the isosceles central height and know it will be the smaller measure as it always is, using 14^2 - 7^2 = a^2

= 196sr - 49sr = 47sr

a^2 = √47 = 6.8556546004

So we know the diagram isn't to scale.

The equation of a rectangle pyramid =

A=lw+√l (w2)

2+√ 2+w

(l2)2+√ h2

The base is l*w*h - l*l = 392-196

or l*w + 4* h*w =196

The total volume of air inside the skylight is 980 inches cubed. Option D is correct.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

The volume of the rectangular pyramid is (1/3) × base area × height = (1/3) × 14² × 9 = 588 cubic inches.

The volume of the rectangular prism is length × width × height = 14 × 14 × 2 = 392 cubic inches.

The total volume of air inside the skylight is the sum of the volumes of the pyramid and prism, which is 588 + 392 = 980 cubic inches.

Therefore, the answer is (D) 588 inches cubed.

Learn more about Volume here:
https://brainly.com/question/1578538

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Answer:

40 boxes

Step-by-step explanation:

box = 24 x 15 x 10 = 3600 cm

1 paper clip box = 6 x 3 x 5 = 90 cm

3600/90 = 40

so 40 boxes of paper clips will fit

Answer:

40 boxes

box = 24 x 15 x 10 = 3600 cm

A paper clip box = 6 x 3 x 5 = 90 cm

3600/90 = 40

so 40 boxes of paper clips

Answer to the question : 17 units

Answer:

17

Step-by-step explanation:

all you do is add -12 and 5 and pretend the - isnt there, and now you have 17.

Answer:

The final answer is [tex]n > -1[/tex], which would be the first choice.

Step-by-step explanation:

-Solve the inequality:

[tex]-6n + 5 < 11[/tex]

-Subtract both sides by [tex]5[/tex]:

[tex]-6n + 5 - 5 < 11 - 5[/tex]

[tex]-6n < 6[/tex]

-When you are dividing by a negative number, which is [tex]-6[/tex], the inequality sign would change:

[tex]\frac{-6n}{-6} < \frac{6}{-6}[/tex]

[tex]n > -1[/tex]

So, the final answer would be [tex]n > -1[/tex].

Answer:

[tex] x^{33} [/tex]

Step-by-step explanation:

[tex] \dfrac{x^8y^{-26}}{x^{14}y^{-5} \times x^{-39}y^{-21}} = [/tex]

A negative exponent in the numerator is a positive exponent in the denominator.

A negative exponent in the denominator is a positive exponent in the numerator.

[tex] = \dfrac{x^8y^{5}x^{39}y^{21}}{x^{14}y^{26}} [/tex]

[tex] = \dfrac{x^{8 + 39} y^{5 + 21}}{x^{14}y^{26}} [/tex]

[tex] = \dfrac{x^{47} y^{26}}{x^{14}y^{26}} [/tex]

[tex] = x^{47 - 14} y^{26 - 26} [/tex]

[tex] = x^{33} y^{1} [/tex]

[tex] = x^{33} [/tex]

Answer:

1. $1650

2. $1415.52

3. $5540

4. No

5. 145

6. No

Step-by-step explanation:

1. 2230 - 580

2. 157.28 x 9

3. 6630 - 1090

4.

5. 725 - 580

Hope this helps!

Answer:

f(6) = 4

Step-by-step explanation:

We want the value of the function when x =6

Go to where x=6 then go up to when you hit the blue line then find the y value

f(6) = 4

Answer:

r=12.5

Step-by-step explanation:

V=2/3πr³

V=1300π m³

r=?

r=3√(3*1300π/2)

r=12.49

Answer:

x = 2

Step-by-step explanation:

[tex]14x = 28\\\mathrm{Divide\:both\:sides\:by\:}14\\\frac{14x}{14}=\frac{28}{14}\\Simplify\\x=2[/tex]

You could do this with two weighings assuming its a two pan balance - (1) place three balls on each side - if they balance out then its the remaining three that has abnormal ball (2) out of that group, place one ball on each side - if balances it out, the abnormal ball is the remaining one.

If the weighing in step (1) does not balance out, grab the group of three balls that is light or heavy and repeat step (2) described above.

Answer: 2.5

Step-by-step explanation:

y = rx

substitute numbers in and solve for r

if

y = 10

x = 4

then

10 = r4

r = 10/4 = 2.5

this works for all the other numbers and always gives r = 2.5

Answer:

0

Step-by-step explanation:

2(a+3)/b

Let a=-3 and b=2

2(-3+3) / 2

2(0)/2

0/2

0

Answer:

0

Step-by-step explanation:

We are given the expression:

2(a+3)/b

We know that a= -3 and b=2. Therefore, we can substitute -3 in for a and 2 in for b.

2(-3+3)/2

Now, solve according to PEMDAS: Parentheses, Exponents, Multiplication, Addition, Subtraction.

Solve inside the parentheses first. Add -3 and 3.

2(0)/2

Multiply 2 and 0.

0/2

Divide 0 by 2

0

Answer:

8

Step-by-step explanation: