A small bank vault is being designed in the shape of a rectangular prism. The vault’s sides and top should all be 3 feet thick. The outer length of the vault should be twice the outer width. The outer height should be the same as the outer width. What should the outer dimensions of the vault be if is to have 972 cubic feet of space?

(^ incase the words got cut off in the pic) ​

Answer:

x = 4

Step-by-step explanation:

Length = (4x + 3) feet

Width = (4x - 5 )feet  

Area = Length x Breadth

209 = (4x + 3)(4x - 5)

209 = 4x( 4x -5) + 3 (4x -5)

[tex]209 = 16x^2 -20x +12x -15\\\\0 = 16x^2 -8x -15 -209\\\\16x^2 -8x -224 = 0[/tex]

[tex]Quadratic \ Equation \ with a = 16, b = -8, c = -224 \\\\x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}\\\\Substitute \ a, b, c \ in \ the \ equation.\\\\x = \frac{-b + \sqrt{b^2 -4ac}}{2a}, x =\frac{-b \ - \sqrt{b^2 -4ac}}{2a}\\\\x = \frac{8+ \sqrt{64 +14336}}{32}, x = \frac{8- \sqrt{64 +14336}}{32}\\\\x = \frac{8+ \sqrt{14400}}{32}, x = \frac{8-\sqrt{14400}}{32}\\\\x = \frac{8+120 }{32}, x= \frac{8-120}{32}\\\\x = \frac{128}{32} , x = \frac{-112}{32}\\\\x = 4 , x = \frac{-7}{2}[/tex]

Since measure of length or width cannot be negative, we take x = 4

Answer:

35 is the 'is' and 40 is the 'of'

Step-by-step explanation:

is/of = %/100

35/40 = x/100

cross-multiply to get:

40x = 3500

x = 3500/40

x = 87.5

Volume of Cube = a³

side a = 5 Cm

Volume = 5³ = 125 Cm³

Answer:

125m³

Step-by-step explanation:

GIVEN :-

TO FIND :-

GENERAL FORMULAE TO BE USED IN THIS QUESTION :-

Volume of a cube = a³ (where a = length of each side of a cube)

SOLUTION :-

Volume of the cube = 5³ = 125 m³

Answer:

The cofunction of [tex]\tan \frac{2\pi}{11}[/tex] is [tex]\cot \frac{7\pi}{22}[/tex].

Step-by-step explanation:

In trigonometry, a function is a cofunction of another if and only if [tex]f(A) = g(B)[/tex], where A and B are complementary angles. In this case, the complementary function of a tangent function must be a cotangent function, this is:

[tex]\tan \frac{2\pi}{11} = \cot \left(\frac{\pi}{2} - \frac{2\pi}{11} \right)[/tex]

[tex]\tan \frac{2\pi}{11} = \cot \frac{7\pi}{22}[/tex]

[tex]\tan \frac{2\pi}{11} = \frac{1}{\tan \frac{7\pi}{22} }[/tex]

[tex]0.642 = \frac{1}{1.556}[/tex]

[tex]0.642 = 0.642[/tex]

Answer:

okay depending on the question

Answer:

I can try

Step-by-step explanation:

Answer:

A regular dog has 4 legs so it has 4 paws. If each paw needs one wipe Jen will need 4 wipes.

Jen will need 4 wipes for each paw

Answer:

1.   a = 32.96    m∠B = 21°   b = 12.74

2.   x = 24.99

Step-by-step explanation:

1.   Use the law of sines:

a/sin 112 = 26/sin 47

a = 26 sin 112/sin 47

a = 32.96

m∠B = 180 - 47 - 112 = 21°

b/sin 21 = 26/sin 47

b = 26 sin 21/sin 47

b = 12.74

2.   Use the law of cosines

[tex]x^{2} = 17^{2} + 11^{2} - 2(17)(11) cos 125[/tex]

    =  289 + 121 - 374 cos 125

    =  624.5175....

x =  [tex]\sqrt{624.5175...}[/tex]

 = 24.99

Answer:

They only add up to 128.2, so if they are asking for the final angle to equal 180, then it would equal 51.8.

Hope that this helps!

Answer:

6/5

Step-by-step explanation:

-3/5-(-2/15)+5/6

-3/5+2/15+5/6

=-3+2×5/15 + 5/6. (taking lcm)

=-3+6/15+5/6

=3/15+5/6

=3+5×3/15 (taking lcm)

=18/15

=6/5

Answer:

Step-by-step explanation:

-3/5-(-2/15)+5/6

=-3/3+2/15(take lcm of 3 and 15)+5/6

=-3*3+2*1/15+5/6

=-9+2/15+5/6

=-7/15+5/6(take lcm of 15 and 6)

=-7*2+5*5/30

=-14+25/30

=11/30

=11/30

Answer:

Answer is D

Step-by-step explanation:

Answer:

C/4

Step-by-step explanation:

The amount divided by the amount of people will show how much each person owes

Answer:

Step-by-step explanation:

pN = 64/100 = 0,64 = 64%

pW = 80/100 = 0,8 = 80%

The planes of Waxwing airlines are more punctual

Answer:

B also have a great day today

Answer:

D, Between 5.4 and 6.5

Step-by-step explanation:

anything less than .5 gets rounded down and anything higher gets rounded up so it'll end up with 6

Answer:

D

Step-by-step explanation:

Answer:

dα /dt  = -  0.028 rad /sec     or  dα /dt  = - 1.59 °

El signo menos significa que el angulo va decresiendo

Step-by-step explanation:

La escalera, la pared vertical y el pié de la escalera y la pared forman un triangulo rectangulo. En ese triangulo

cos α   (  α  angulo que forma la escalera con el piso )

cos α =   x / L

Tomando derivadas con respecto al tiempo (L es constante ) se tiene:

- sen α  *  dα / dt   =  dx/ dt / L

Cuando  el extremo superior de la escalera está a 18 pies del piso, entonces  sen α  =  18 / 30  =  0.6

dx/dt = 1/2 pie/sec

dα/dt  = - (1/2)/ L* 0.6

dα /dt  = -  0.5 / 18

dα /dt  = -  0.028 rad /sec     or  dα /dt  = - 1.59 °

El signo menos significa que el angulo va decresiendo

Answer:

From 10 a.m. to 2 p.m., the temperature at Sam's house increased by 8 degrees Fahrenheit.

Step-by-step explanation:

Write as a number equation ---->  2 - (-6) = 8

Answer:

The true statements are :

A. A random variable is a numerical description of the outcome of a statistical experiment.

B. In most​ applications, discrete random variables represent counted​ data.

C. In most applications, continuous random variables represent measured data.

Step-by-step explanation:

It is true statement that,

A. A random variable is a numerical description of the outcome of a statistical experiment.

B. In most​ applications, discrete random variables represent counted​ data.

C. In most applications, continuous random variables represent measured data.

The false statement is -

D. The expected value of a discrete random variable is equal to the standard deviation of the random variable.

Reason -

The mean value, or expected value, of a discrete random variable X is given by the following equation:

μ = E(x) = ∑ x p(x)

And

The variance of a discrete random variable is given by the following formula:

σ²=∑ (x−μ)² P(x)

And

The square root of the variance, or, in other words, the square root of σ², is the standard deviation of a discrete random variable :

σ = √σ²

Step-by-step explanation:

============================================================

Explanation:

For now, let's focus on the probability of getting one "5".

There are 4 of these cards (one of each suit) and 52 total. The probability of getting the card we're after is 4/52 = 1/13.

We can think of it like saying "if we focus on one suit only, then there's a 1 in 13 chance of getting a '5' from this pile".

The probability of getting two "5"s in a row is (1/13)*(1/13) = 1/169 assuming we put the first card back. If the first card is not put back, then we would compute it like so: (4/52)*(3/51). I'll leave it unevaluated for you to try out as practice.

Side note: 1/169 = 0.0059 = 0.59% approximately

Answer:

c

Step-by-step explanation:

Answer:

D, a sentence that includes only one independent clause

Step-by-step explanation:

A compound-complex sentence has two independent clauses, and 1 or more dependent clauses. A compound sentence has two independent clauses, and is connected by a conjunction.

This isn't a math question but idrc

Answer:

[tex]1.\:2^x=64, x=\boxed{6},\\2.\:x=\left(\frac{2}{3}\right)^3,x=\boxed{\frac{8}{125}}\\3.\:3\cdot (3^4)=3^x, x=\boxed{5}\\4.\:\frac{16}{25}=x^2,x=\boxed{\frac{4}{5}},[/tex]

Step-by-step explanation:

[tex]1.\\\\2^x=64,\\\log 2^x=\log64,\\x\log 2=\log 64,\\x=\frac{\log 64}{\log 2}=\boxed{6}[/tex]

[tex]2.\\x=\left(\frac{2}{5}\right)^3=\frac{2^3}{5^3}=\boxed{\frac{8}{125}}[/tex]

3. This problem incorporates an exponent property.

Exponent property used: [tex]a^b\cdot a^c=a^{(b+c)}[/tex], yielding an answer of [tex]\boxed{5}[/tex]

[tex]4.\\\\\frac{16}{25}=x^2,\\x=\sqrt{\frac{16}{25}}=\frac{\sqrt{16}}{\sqrt{25}}=\boxed{\frac{4}{5}}[/tex]

Answer:

1. 6

2. 8/25

3. 5

4. 4/5

Step-by-step explanation:

Answer:

As seen on the picture, all the steps A to D are correct.

Note:

Answer:

0.25 pints

Step-by-step explanation:

Hehe, i used goo. gle

Answer:

4

Step-by-step explanation:

h + h

h=2

2+2

4