A diagonal of a cube measures 30 inches. The diagonal of a face measures StartRoot 600 EndRoot inches.


In inches, what is the length of an edge of the cube? Round the answer to the nearest tenth.

Answer:

  3.84 units

Step-by-step explanation:

By the properties of angle bisectors, ...

  WZ/ZX = WY/YX

Solving for WY, we have ...

  WY = (YX)(WZ)/(ZX) = (6.5/6)(WZ)

The length YZ is ...

  YZ = 8 = WY +WZ

  8 = (6.5/6)(WZ) +WZ = 12.5/6(WZ) . . . . substitute for WY

  WZ = 8(6/12.5) . . . . multiply by 6/12.5

  WZ = 3.84

Answer:

The correct answer is indeed 3.84 units

Step-by-step explanation:

I just took the test and got it correct hope this helps ☺

Answer:

5.5 hours

Step-by-step explanation:

We have that the distance is given by:

d = v * t = 50 mph * 1/2 h = 25 miles

The relative speed is given by:

 vr = 55 mph - 50 mph = 5 mph

Now the time required to reach

 would come being:

t = t '+ d / vr

we know that t '= 1/2 h, replacing:

t = 1/2 h + 25 mi / 5 mph

t = 1/2 h + 5 h

t = 5.5 h

Therefore, the required time is 5.5 hours.

Answer:

“It is a binomial with a degree of 3”

Step-by-step explanation:

Since it has just two different coefficients, it would be considered “binomial” for that reason. As you can notice, the highest degree is 3. So match those up and the correct answer would be the second choice “It is a binomial with a degree of 3”

Answer:

B

Step-by-step explanation:

[tex]answer \\ = 5 \sqrt{3} \\ please \: see \: the \: attached \: picture \: for \: \: full \: solution \\ hope \: it \: helps[/tex]

Answer:

[tex]5 \sqrt{3} [/tex]

First answer is correct

Step-by-step explanation:

[tex] \frac{5}{x} = \cos(60) \\ \frac{5}{x} = \frac{1}{2} \\ x = 10 \\ \frac{y}{x} = \sin(60 ) \\ \frac{y}{10} = \frac{ \sqrt{3} }{2} \\ 2y = 10 \sqrt{3} \\ y = \frac{10 \sqrt{3} }{2} \\ y = 5 \sqrt{3} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

The answer for log(ab²) is x + 2y.

Step-by-step explanation:

You have to apply Logarithm Law,

[tex] log(a) + log(b) \: ⇒ \: log(a \times b) [/tex]

[tex] log( {a}^{n} ) \: ⇒ \: n log(a) [/tex]

In this question, you have to seperate it out :

[tex] log(a {b}^{2} ) = log(a) + log( {b}^{2} ) [/tex]

[tex] log( {b}^{2} ) = 2 log(b) [/tex]

[tex]let \: log(a) = x[/tex]

[tex]let log(b) = y[/tex]

[tex] log(a {b}^{2} ) = log(a) + 2 log(b) [/tex]

[tex] log(a {b}^{2} ) = x + 2y[/tex]

Answer:

The median value in this set is -4.5

Step-by-step explanation:

Reorder the numbers from least to greatest

-28,-17,-8,-1,24,32

Then, since there is 6 digits in this data set there is no defined median value. In the numbers 1 to 8 there are 8 different numbers, the middle of 1 to 8 is 4.5. Then since were using the numbers -8,-1 the middle is -4.5

Answer:

y^6/x^2

Step-by-step explanation:

(y^3/2x^-1/2)^4= y^(4*3/2)x^(-1/2*4)=y^6x^-2= y^6/x^2

ANSWER: "There is not enough information to determine the answer". Option D is correct.

Step-by-step explanation:

For a case that was ruled by a court to be reversed by a higher court, they must be conditions in the ruling of the lower court that has been reconsidered by the higher court. This is regardless of the jurisdiction of the court or judge that ruled the case.

A case from all the courts in the options can be reversed by a higher court if the courts judgement lacks merit by the higher court, at any given times, irrespective of the court.

The volume of the solid (call it S) in Cartesian coordinates is

[tex]\displaystyle\iiint_S\mathrm dV=\int_{-1}^1\int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\int_{(x^2+y^2)^2-1}^{4-4(x^2+y^2)}\mathrm dz\,\mathrm dy\,\mathrm dx[/tex]

but I suspect converting to cylindrical coordinates would make the integral much more tractable.

Take

[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=z\end{cases}\implies\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz[/tex]

Then

[tex]4-4(x^2+y^2)=4-4r^2=4(1-r^2)[/tex]

[tex](x^2+y^2)^2-1=(r^2)^2-1=r^4-1[/tex]

and the integral becomes

[tex]\displaystyle\iiint_S\mathrm dV=\int_0^{2\pi}\int_0^1\int_{r^4-1}^{4(1-r^2)}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]

[tex]=\displaystyle2\pi\int_0^1r(4(1-r^2)-(r^4-1))\,\mathrm dr[/tex]

[tex]=\displaystyle2\pi\int_0^1r(5-4r^2-r^4)\,\mathrm dr[/tex]

[tex]=\displaystyle2\pi\int_0^15r-4r^3-r^5\,\mathrm dr[/tex]

[tex]=2\pi\left(\dfrac52-1-\dfrac16\right)=\boxed{\dfrac{8\pi}3}[/tex]

Answer:

Ratio 4 is for Caroline, ratio 5 is for krutika, ratio 1 is for Natasha

Answer:

X ≤ 13

Step-by-step explanation:

Part A: X ≤ 13

Part B:  Draw a closed circle from 13 and up on the number line.

Make the arrow look like this >.

The inequality will be x ≥ 13. The age of the person should be greater than or equal to 13.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

“Children under the age of 13 are not allowed to operate a boat.”

Let x be the age of the person.

The inequality to show the age of children who are allowed to operate a boat will be

x ≥ 13

The age of the person should be greater than or equal to 13.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ2

Answer:

2/8 or 1/4

Step-by-step explanation:

There are 4 sections so if you spin it twice, we would double it so we have 2/8 and simplified to 1/4

I hope it helps you!

Answer:

A-8

Step-by-step explanation:

Any other higher number plugged in makes the equation false

Answer:

y = 5x + 20

Step-by-step explanation:

The initial percent is 20.

Every minute, the percent goes up 5%, so the slope is 5.

So the equation of the line is y = 5x + 20.

Pass = $21 , Souvenir = 2x/3 = $14 , Burger = x/6 =$3.5 .

Answer:

There should be no pattern in the residual plot.

Step-by-step explanation

Remember a residual plot is calculating if a linear model is appropriate or not and since the engineer is trying to find a linear relationship with his air filters then he should be looking for no pattern.

Here, we are required to determine what should be apparent in the residual plot.

The residual plot will have a negative slope, i.e the residual plot descends from the top left to the bottom right.

According to the Engineer's believe, the thicker the air filter, the less pollution that gets through it.

By plotting each of the quantities on either of x and y axis on the residual plot, The residual plot therefore, has a negative slope.

Read more:

https://brainly.com/question/7412322

Answer:

1.5 meters

Step-by-step explanation:

The formula for the area of a trapezoid is h * (a+b)/2, where a is the first base and b is the second base. Now, we can work backwards to determine the height of the trapezoid:

3.75=h*(1.7+3.3)/2

3.75=h*2.5

h=3.75/2.5=1.5

Hope this helps!

Answer:

Step-by-step explanation:

use the formula and rearrange for h.

1/2 x h x  (a + b) = A

1/2 x (1.7 + 3.3) x h = 3.75

2.5 x h = 3.75

h = 1.5

hope this helps! :)

Answer:

14, 32

Step-by-step explanation:

45,15,44,17,40,20,31,25

this is combination of 2 series:

In the first series we can see the pattern as:

In the second series we can see the pattern as:

The series will continue as:

Answer:

14, 32

Step-by-step explanation:

lol :D

Answer:

y = -x + 2

Step-by-step explanation:

The slope intercept form equation of this line can be written like this :

y = my + p ; where m is the slope and p is the y intercept.

[tex]m = \frac{-1-4}{3-(-2)} = \frac{-5}{5} =-1[/tex]

then the equation becomes y = -x + p

(-2,4) is a point of the line means 4 = -(-2) + p

then p = 4 - 2 = 2

finally, y = -x + 2

Answer:

n +10 =20

Step-by-step explanation:

answer =20 . thank God

Answer:

Step-by-step explanation:

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean of type A paint

x2 = sample mean of type B paint

s1 = sample standard deviation type A paint

s2 = sample standard for type B paint

n1 = number of samples of type A paint

n2 = number of samples of type B paint

From the information given,

x1 = 75.7

s1 = 4.5

n1 = 11

x2 = 64.3

s2 = 5.1

n2 = 9

x1 - x2 = 75.7 - 64.3 = 11.4

√(s1²/n1 + s2²/n2) = √(4.5²/11 + 5.1²/9) = √4.709

Degree of freedom = (n1 - 1) + (n2 - 1)

df = (11 - 1) + (9 - 1) = 18

For the 98% confidence interval, the z score from the t distribution table is 2.552

Margin of error = 2.552√4.709 = 5.55

The upper boundary for the confidence interval is

11.4 + 5.55 = 16.95 hours

The lower boundary for the confidence interval is

11.4 - 5.55 = 5.85 hours

The correct option is

B. 5.85 hrs < μ1 - μ2 < 16.95 hrs

Answer:

Rounding to the nearest hour, the times at which the population was 600,000 was at 9 hours and at 39 hours.

Step-by-step explanation:

Determine the time(s) at which the population was 600,000.

This is t for which P(t) = 600000. To do this, we solve a quadratic equation.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]P(t) = -1718t^{2} + 82000t + 10000[/tex]

We have to find t for which P(t) = 600000. Then

[tex]600000 = -1718t^{2} + 82000t + 10000[/tex]

[tex]-1718t^{2} + 82000t - 590000 = 0[/tex]

So [tex]a = -1718, b = 82000, c = -590000[/tex]

Then

[tex]\bigtriangleup = 82000^{2} - 4*(-1718)*(-590000) = 2669520000[/tex]

[tex]t_{1} = \frac{-82000 + \sqrt{2669520000}}{2*(-1718)} = 8.8[/tex]

[tex]t_{2} = \frac{-82000 - \sqrt{2669520000}}{2*(-1718)} = 38.9[/tex]

Rounding to the nearest hour, the times at which the population was 600,000 was at 9 hours and at 39 hours.

Answer:

answer is 2/3

Step-by-step explanation:

probability it is an eclair is 1/15=3/(3+2x+6+x)= 1/(x+3)

so x+3=15 and then x = 12

so the probability it is a humbug is (2*12+6)/(3*12+9) = 30/45 = 2/3

(a)

[tex] \sqrt[5]{ {x}^{3} } [/tex]

(b)

[tex] \sqrt[8]{x} [/tex]

(c)

[tex] \sqrt[3]{ {x}^{5} } [/tex]

(d)

[tex] \sqrt{ {x}^{3} } [/tex]

Answer:

sorry i meant c

Step-by-step explanation:

Answer:50%

Step-by-step explanation:670/1340 = 1/2 = 50%

Answer: 1/4+3/8+1/2+5/8+7/8

= 21/8

Hope this helps :)))

Answer:

21/8

Step-by-step explanation:

Answer:

The tank will contain 202 Ib of salt when it's full.

Step-by-step explanation

To find the amount of salt in the tank at time t= x(t)

If x(0)= 90Ib

To find the volume of the tank at time t

V(t)= 90+(4-3)t=90+t gal

Other solutions are found attached

Answer

g(x) moves 4 spaces to the left compared to f(x),  

when g(4)=0  when f(0)=0

when g(3)=1   when f(-1)=1

...

and so on