(08.01 MC)
The volume of a pyramid that fits exactly inside a cube is 9 cubic feet. What is the volume of the cube? (5 points)
Select one:
a. 3 cubic feet
b. 6 cubic feet
c. 18 cubic feet
d. 27 cubic feet

Answer:

The value of x is 30°

Step-by-step explanation:

We are given that the outer angle of the parallelogram is 60 degrees. Therefore it's respective inner angle will be 180 - 60 = 120 degrees. And, by properties of a parallelogram, the angle opposite to this angle will be 120 degrees as well.

If we draw extend the line creating angle 2x, then we will make ( 1 ) a vertical angle to 2x, ( 2 ) a 90 degree angle, and ( 3 ) and angle that we can let be y. Therefore, 2x + y = 90, and 3x + y = 120.

[tex]\begin{bmatrix}2x+y=90\\ 3x+y=120\end{bmatrix}[/tex] ,

[tex]\begin{bmatrix}6x+3y=270\\ 6x+2y=240\end{bmatrix}[/tex] ,

[tex]6x+2y=240\\-\\\underline{6x+3y=270}\\y=30[/tex],  

[tex]2x + (30) = 90,\\2x = 60,\\x = 30[/tex]

Solution : x = 30°

Answer:

x = 30

Step-by-step explanation:

a+ 60 = 180

a = 120

3x+b = 120  because opposite angles in a parallelogram are equal

2x+90+b = 180 since it forms a line

2x+b = 90

We have 2 equations and 2 unknowns

3x+b = 120

2x+b = 90

Subtracting

3x+b = 120

-2x-b = -90

---------------------

x = 30

Answer:

The probability mass function  that you never win [tex]^xC_o[/tex] = [tex](\dfrac{999999}{1000000})^x[/tex]

Step-by-step explanation:

Given that;

the winning chance of a weekly local lottery = [tex]\dfrac{1}{10^6}[/tex]

= [tex]\dfrac{1}{1000000}[/tex]

The probability of losing = 1 - probability of winning (winning chance)

The probability of losing = [tex]1- \dfrac{1}{1000000}[/tex]

The probability of losing =[tex]\dfrac{999999}{1000000}[/tex]

The probability mass function  that you never win [tex]^xC_o[/tex] = [tex](\dfrac{1}{10^6} )^0 ( \dfrac{999999}{1000000})^x[/tex]

The probability mass function  that you never win [tex]^xC_o[/tex] = [tex](\dfrac{999999}{1000000})^x[/tex]

Answer:

[tex]\sin \left(\theta \right)-\frac{1}{2}\cos \left(2\theta \rightt)+C[/tex]

Step-by-step explanation:

We are given the graph of r = cos( θ ) + sin( 2θ ) so that we are being asked to determine the integral. Remember that [tex]\:r=cos\left(\theta \right)+sin\left(2\theta \right)[/tex] can also be rewritten as [tex]\int \cos \left(\theta \right)+\sin \left(2\theta \right)d\theta \right[/tex].

Let's apply the functional rule [tex]\int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx[/tex],

[tex]\int \cos \left(\theta \right)+\sin \left(2\theta \right)d\theta \right[/tex] = [tex]\int \cos \left(\theta \right)d\theta \right+\int \sin \left(2\theta \right)d\theta \right[/tex]

At the same time [tex]\int \cos \left(\theta \right)d\theta \right=\sin \left(\theta \right)[/tex] = [tex]sin( \theta \right ))[/tex], and [tex]\int \sin \left(2\theta \right)d\theta \right[/tex] = [tex]-\frac{1}{2}\cos \left(2\theta \right)[/tex]. Let's substitute,

[tex]\int \cos \left(\theta \right)d\theta \right+\int \sin \left(2\theta \right)d\theta \right[/tex] = [tex]\sin \left(\theta \right)-\frac{1}{2}\cos \left(2\theta \right)[/tex]

And adding a constant C, we receive our final solution.

[tex]\sin \left(\theta \right)-\frac{1}{2}\cos \left(2\theta \rightt)+C[/tex] - this is our integral

Answer:

1.

d. (-14) + (-8)

2.

a. (-14) + 8

Step-by-step explanation:

(-14) - 8 is equal to (-14) + (-8) because we still add two negative values so the result wouldn't change.

(-14) - (-8) is equal to (-14) + 8 because there's two negative sign in front of 8 and two negative values multiplied makes a positive result.

Answer:

1. D  

2. A

Step-by-step explanation:

1.  It asks you what expression has the same value as (-14)-8.  All you need to do is find other equations that have the same value as that.  So the equation is -14-8.  IF a negative is outside a parenthesis with a positive number inside like -(+5), it is going to be -5.  If it's both negative: -(-5), it will be +5.  If it is both positive: +(+5), it is going to be +5.  

IMPORTANT!

- and + = -

- and - = +

+ and + = +

What we are looking for: -14-8

So choice A is (-14)+8 which is simplified to -14+8.  So, this one isn't right.

Choice B: 14-(-8)= 14+8.  So, it's incorrect.

Choice C: 14+(-8)= 14-8.  Again, it's not -14-8 so it's not right.

Choice D: (-14)+(-8)= -14-8.  This equation matches the one we are looking for!  So it's correct!

2. Same thing as number 1.  Let's simplify the equation it wants us to find first.  

(-14)-(-8)= -14+8

So -14+8 is what we are looking for.

Choice A: (-14)+8= -14+8.  It matches!  So it is correct.  Let's look at the other options anyway.

Choice B: 14-(-8)= 14+8.  Nope.  Not right.

Choice C: 14+(-8)= 14-8 because - always beats +.  So, this one is also incorrect.

Choice D: (-14)+(-8)= -14-8.  Oops, this is also wrong.  So choice A is the right answer.

Keep in mind, when you start getting questions like this with numbers inside the parenthesis as well, you want to remember the same rules for positive and negative, but also multiply the numbers together:

(When there is a number outside and inside a parentheses, multiply them.)

2(5)=10, CORRECT!    2+(5) is not 2 times 5.  It's whatever is closest to the parentheses, in this case being the positive sign.  So + and 5 is just 5!

IMPORTANT!

-2(-5)= - and - is positive, so positive (2 times 5).  Positive 10.

-2(+5)= - and + is negative, so negative (2 times 5). Negative 10.

+2(+5)= + and + is positive, so positive (2 times 5).  Positive 10.

Answer:

F /T = Z

Step-by-step explanation:

F/Z=T

Multiply each side by Z

F/Z *Z=T*Z

F = ZT

Divide each side by T

F /T = ZT/T

F /T = Z

Answer:

[tex]\boxed{\red{ z = \frac{f}{t} }}[/tex]

Step-by-step explanation:

[tex] \frac{f}{z} = t \\ \frac{f}{z} = \frac{t}{1} \\ zt = f \\ \frac{zt}{t} = \frac{f}{t} \\ z = \frac{f}{t} [/tex]

Answer:

d. The graph of g(x) is the graph of f(x) reflected over the x-axis.

Step-by-step explanation:

The standard transformation

g(x) = - f(x)

is a simple reflection about the x-axis.

So the answer is the last option.

Answer:

Last one

Step-by-step explanation:

The function we are interested in are g(x) and f(x).

● g(x)= (-1/x)

● f(x)= 1/x

Notice what happens when we input the same values in both functions.

● g(1) = -1/1 = -1

● f(x) = 1/1 = 1

●g(2) = -1/2 = -0.5

● f(2) = 1/2 = 0.5

Notice that we get opposite values by imputing the same number.

Wich means:

●f(x) = -g(x)

So the graph of g(x) is the graph of f(x) reflected over the x axis.

[tex] \Large{ \boxed{ \bold{ \color{lightgreen}{Solution:}}}}[/tex]

So, Let's solve this question by using cartesian plane.

Well, What is cartesian plane?

A - A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a set of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. 

━━━━━━━━━━━━━━━━━━━━

The required value of the tanФ is given as -3/4. C option is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.

here,
Tan(180 - Ф) = -tanФ = perpendicular / base

From figure,  perpendicular= 12 and  base = 16
-tanФ = 12 / 16
tanФ = -3/4

Thus, the required value of the tanФ is given as -3/4. C option is correct.

Learn more about trigonometry equations here:

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Answer:

It looks like 6 and one eighth of an inch.

Answer:

No

Step-by-step explanation:

The square root of 65 is irrational.

It is not a rational number because 65 is not a perfect square.

The square root of 65 is 8.06225775...

The square root of 65 is not a rational number.

65 is not a perfect square which means it's impossible to

find a whole number times itself to give us 65.

On a calculator if you type in the square root of 65,

you will get an infinite decimal number.

The decimal values never end and never have same repeated pattern.

Answer:

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find GV

To find GV we use cosine

cos∅ = adjacent / hypotenuse

From the question

GV is the adjacent

GC is the hypotenuse

So we have

GC = 55°

GV = 55 cos 37

GV = 43.92495

We have the final answer as

Hope this helps you

Answer:

r = 19

Step-by-step explanation:

( r-5) /2 = ( r+2) /3

The least common denominator is 6

3/3 *( r-5) /2 = ( r+2) /3 * 2/2

3( r-5) /6 = 2( r+2) /6

Since the denominators are the same, the numerators are the same

3( r-5) = 2(r+2)

Distribute

3r -15 = 2r+4

Subtract 2r from each side

3r-2r -15 = 2r+4-2r

r-15 =4

Add 15 to each side

r-15+15 = 4+15

r = 19

Since they are multiples if 12

The possibilities are

12, 12, 156

12,24,144

12,36,132

12,48,120

12,60,108

12,72,96

12,84,84

24,24,132

24,36,120

24,48,108

24,60,96

24,72,84

36,36,108

36,48,96

36,60,84

36,72,72

48,48,84

48,60,72

60,60,60

Hence the probability is 1/19 or 0.0526

Hey  There!

Answer:

Step-by-step explanation:

HCF

If HCF is  ''9'' that means that ''9'' is the divisible of two numbers.

So 18 and 19 can be divided by 9 and that's the highest divisible for both factors.

And always remeber the answer is a ''Prime factor.''

LCM

If LCM is ''3'' that means ''3'' is the lowest common multiple out of  two numbers.

Hope this helps!

Have a nice Day!:)

Answer:

5

Step-by-step explanation:

This shape is formed by two right triangles.

Let's start by the little one.

Let y be the third side.

Using the Pythagorian theorem we get:

y^2 = 6^2 + 3^2

y^2 = 36 + 9

y^2 = 45

y = 3√(5)

●●●●●●●●●●●●●●●●●●●●●●●●

Now let's focus on the second triangle. Let z be the third side.

The Pythagorian theorem:

6^2 + x^2 = z^2

Using the Pythagorian theorem on the big triangle :

[3√(5)]^2 + z^2 = (3+x)^2

45 + z^2 = 3x^2 + 6x + 9

36 +z^2 = 3x^2 +6x

So we have a system of equations.

36+ x^2 = z^2

36 +z^2 = 3x^2 +6x

We want to khow the value of x so we will eliminate z .

Add (36+x^2 -z^2 =0) to the second one.

36 + x^2-z^2+36+z^2 = 3x^2+6x

72 + x^2 = 3x^2 +6x

72 - 2x^2 -6x = 0

Multipy it by -1 to reduce the number of - signs

2x^2 + 6x -72 = 0

This is a quadratic equation

Let A be the discriminant

● a = 2

● b = 6

● c = -72

A = b^2-4ac

A = 36 -4*2*(-72) = 36 + 8*72 =612

So this equation has two solutions

The root square of 612 is approximatively 25.

● (-6-25)/4 = -31/4 = -7.75

● (-6+25)/4 = 19/4 = 4.75 wich is approximatively 5

A distance cannot be negative so x = 5

Answer:

A typical example would be when a statistician wishes to estimate the ... by the standard deviation ó) is known, then the standard error of the sample mean is given by the formula: ... The central limit theorem is a significant result which depends on sample size. ... So, the sample mean X/n has maximum variance 0.25/ n.

Step-by-step explanation:

Answer:

-36

Step-by-step explanation:

3*12=36

she is going down (negative) so, it is -36

not sure if this is what you are asking for, if not try this

0-12-12-12=-36

Answer:

(A) 37.5 miles

Step-by-step explanation:

The trains x and y are travelling on tracks starting simultaneously from a from opposite ends of 100 miles roads.

Translate these information into a simple represention to visualize the problem. (Picture below)

■■■■■■■■■■■■■■■■■■■■■■■■■■

First let's calculate the velocity of both trains.

The velocity formula is:

● V = d/t

d is the distance travelled and t is the tile needed to do it.

● V(x) = 100/5 = 20 miles per hour

● V(y) = 100/3 = 33.33.. wich is approximatively 33 after rounding to the nearest unit.

■■■■■■■■■■■■■■■■■■■■■■■■■■

After calculateingboth velocities, Let's find when the trains meet.

First understand what does it mean matematically when both trains meet.

Go back to the representation and notice what happens when the trains meet.

Let t be that moment.

When x and y reches the meeting point at t, the sum of the distances they have travelled is equal to the total distance wich is 100 miles .

We khow that V = d/t so d = V×t

Let's find the expression of the distances both trains travelled when they have met each other.

● d = V(x) × t

● d' = V(y) × t

■■■■■■■■■■■■■■■■■■■■■■■■■■

So the equation will be:

● V(x) × t + V(y) × t = 100

Factor using t

● t (V(x) + V(y) ) = 100

Replace V(x) and V(y) by their values

● t (20+33) = 100

● 53 t = 100

Divide both sides by 53

● 53t /53 = 100/53

● t = 1.88

■■■■■■■■■■■■■■■■■■■■■■■■■

Replace t in the expression of the distance that train x has travelled when meeting y.

● d = V(x) × t

● d = 20 × 1.88

● d = 37.6 wich is approximatively 37.5 miles

Answer:

1) the domain is all real numbers

2) the range is

[tex]y \geqslant 3[/tex]

Answer:

Step-by-step explanation:

[tex] \frac{2}{5} + p = \frac{4}{5} + \frac{3}{5} p[/tex]

Multiply through by the LCM

The LCM for the equation is 5

That's

[tex]5 \times \frac{2}{5} + 5p = 5 \times \frac{4}{5} + \frac{3}{5}p \times 5[/tex]

We have

2 + 5p = 4 + 3p

Group like terms

5p - 3p = 4 - 2

2p = 2

Divide both sides by 2

We have the final answer as

Hope this helps you

Answer:

C. x = 2, y = -2

Step-by-step explanation:

y = -3x + 4

x + 4y = -6

x + 4(-3x + 4) = -6

x - 12x + 16 = -6

-11x = -22

x = 2

y = -3(2) + 4 = -2

Answer:

Exoected age is 15.49 years

Step-by-step explanation:

Expected age

= E(x)

= sum (p(i)*i)

= 13*0.01+14*0.23+15*0.26+16*0.28+17*0.20+18*0.02

= 15.49

Answer:

Step-by-step explanation:

Given the inequality [tex]|z+4|>15[/tex], we are to find the solution set of the inequality. Since the the function is an absolute value, this means that the function will be positive and negative.

For the positive value of the function;

[tex]z+4>15\\\\subtract\ 4\ from \ both \ sides\\z+4-4 > 15 -4\\\\z>11[/tex]

For the negative value of the function we have;

[tex]-(z+4) > 15\\\\-z-4> 15\\add\ 4 \ to\ both \ sides\\\\-z-4+4> 15+4\\\\-z> 19\\\\[/tex]

Multiplying both sides of the inequality by -1 will change the sense of the inequality sign;'

[tex]-(-z)< -19\\\\z<-19[/tex]

Hence the solution sets are [tex]z> 11 \ and \ z< -19 \\[/tex] OR z less-than negative 19 or z greater-than 11

Answer:

z less-than negative 19 or z greater-than 11

Step-by-step explanation:

Answer:

The area of the pyramid is 360 unit²

Step-by-step explanation:

Given

Base Edge, a = 10

Height, h = 12

Required

Determine the surface area

The surface area of a regular pyramid is calculated as thus;

[tex]A = a^2 + 2a\sqrt{\frac{a^2}{4} + h^2}[/tex]

Substitute values for a and h

[tex]A = 10^2 + 2 * 10 * \sqrt{\frac{10^2}{4} + 12^2}[/tex]

Evaluate all squares

[tex]A = 100 + 2 * 10 * \sqrt{\frac{100}{4} + 144}[/tex]

[tex]A = 100 + 2 * 10 * \sqrt{25 + 144}[/tex]

[tex]A = 100 + 2 * 10 * \sqrt{169}[/tex]

Take positive square root of 169

[tex]A = 100 + 2 * 10 * 13[/tex]

[tex]A = 100 + 260[/tex]

[tex]A = 360[/tex]

Hence, the area of the pyramid is 360 unit²

Answer:

B.) 360 units2

Step-by-step explanation:

I got it correct on founders education

Answer:

R: {y∈R | -1 ≤ y ≤ 5}

Step-by-step explanation:

the lowest point is -1 and the highest point is 5.

Answer:

Step-by-step explanation:

x + 30 + 25 = 180

x + 55 = 180

x = 125

y + 125 = 180

y = 55

Answer:

  C)  549 km²

Step-by-step explanation:

The area of the regular pentagon is given by ...

  A = (1/2)Pa

where P represents the perimeter, and 'a' represents the apothem (6.2 km). Of course, the perimeter is 5 times the side length.

The lateral area is the product of the perimeter and the height:

  LA = Ph

Using these formulas, and recognizing the total area includes two (2) pentagons, we have ...

  total area = (LA) +2(A) = Ph +2(1/2)Pa = P(h +a)

  = (45 km)(6 km +6.2 km) = 549 km^2

Answer:

y = 700x - 400

Step-by-step explanation:

A negative number represents an altitude below sea level.

Beginning: -400

y = mx + b

y = mx - 400

In 2 hours the altitude was now 1000 m.

1000 m - (400 m) = 1400 m

The altitude went up 1400 m in 2 hours. The rate of change is

1400/2 m/h = 700 m/h

The rate of change is the slope.

y = 700x - 400

Answer:

The graph answer is below :)

Step-by-step explanation:

Answer:

W = 9 * g

Step-by-step explanation:

W/9 = g

W = 9 * g

The expression W/9 = g can be written as W = 9g after cross multiplication.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

W/9 = g

To solve for W

Make subject as W:

W = 9g

By cross multiplication.

Thus, the expression W/9 = g can be written as W = 9g after cross multiplication.

Learn more about the expression here:

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Answer:

x = 17/5

y = -2/5

Step-by-step explanation:

2x + 2y = 6

3x - 2y = 11

sum both equations results

5x + 0 = 17

x = 17/5

2x + 2y = 6

2*17/5 + 2y = 6

34/5 + 2y = 6

2y = 6 - 34/5

2y = 30/5 - 34/5

2y = -4/5

y = (-4/5)/2

y = -2/5

verify:

3x - 2y = 11

3*17/5 - 2*-2/5 = 11

51/5 + 4/5 = 55/5

51 + 4 = 55