A company ships coffee mugs using boxes in the shape of cubes. The function g(x) = gives the side length, in inches, for a cube with a volume of x cubic inches. Suppose the company decides to double the volume of the box. Which graph represents the new function?

Answer:

C. 33.

Step-by-step explanation:

The sides of a 45-45-90 triangle are in the ratio 1:1:√2 so the side opposite to 45 degrees = 11√6 / √2.

Consider the larger triangle containing the 60 degree angle:

tan 60 = x / (11√6 / √2).

x = tan 60 * 11√6 / √2

x = 33.

The value of the variable x will be 33 units. Then the correct option is C.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The diagram is shown below.

Let h be the height of the triangle.

The value of h is given by the sine of angle 45°. Then the value of the height h will be

sin 45° = h / 11√6

h = 11√6 × 1/√2

h = 11√3 units

The value of h is given by the tangent of angle 60°. Then the value of the height h will be

tan 60° = x / h

x = 11√3 × √3

x = 11 × 3

x = 33 units

Thus, the value of the variable x will be 33 units.

Then the correct option is C.

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Answer:

Option C is correct

Step-by-step explanation:

[tex]y−6=−4(x+1) \\ [/tex]

[tex]y−6=−4x−4 \times 1[/tex]

[tex] y−6=−4x−4 [/tex]

[tex]y=−4x−4+6 [/tex]

[tex]y=−4x+2[/tex]

Answer:

2x+10=4b

Step-by-step explanation:

If you look at the previous equation, you will notice that

x*2 = 2x and

5*2 = 10.

So now all you need to do is also multiply the right side of the equation with b by 2, just like you did to the left side, and you'll get

2x+10 = 4b.

I hope this helped! :D

Answer:

2x + 10 = 4b

Step-by-step explanation:

Given

x + 5 = 2b ( multiply through by 2 )

2x + 10 = 4b

Answer:

Step-by-step explanation:

I got 12 so not sure.

3x-3=x+3

2x=6

X=3

So 3x3 =9. +3. =12

Answer:

increasing

Step-by-step explanation:

a function is increasing when y increases as x increases

Since the graph goes up as x increases, the function f(x) is increases between -2 and -1

Answer:

Kameron is 50 years old.

Step-by-step explanation:

We can make equations and start filling in what we already know, assuming [tex]n[/tex] is Niko's age, [tex]L[/tex] is Lila's age, [tex]a[/tex] is Amber's age, and [tex]k[/tex] is Kamerons age.

Our first equation:

n = 3L

We know that Niko is 45, so

45 = 3L

Divide both sides by 3:

L = 15

So, Lila is 15 years old.

Another equation:

n = L + 3a

We already know Niko and Lila's age:

45 = 15 + 3a

Subtract 15 from both sides:

30 = 3a

Divide both sides by 3:

a = 10

So Amber is 10 years old.

Another equation:

k = 2(a + L)

We know Amber and Lila's age:

k = 2(10 + 15)

k = 2(25)

k = 50

So Kameron is 50 years old.

Hope this helped!

Answer:

jsjuuusjus??dujj??uu?jw?wuw?jjdj

Step-by-step explanation:

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Answer:

585 is the answer of your question.

Step-by-step explanation:

because formula is

Mp _ d% of mp

Answer:

12

Step-by-step explanation:

Since it's a equilateral triangal all sides are equal.

First you double 6 since that is a right angle in the triangle the other side will have the same length. 6x2=12.

Answer: Linear model

The fact the height increases the same amount each time indicates we have a linear model. The slope is the rate of growth, so it is 2.5 feet per season.

Keep in mind that the linear model only works for a specific interval and doesn't work forever (the tree can't grow forever and at the same rate). A more realistic scenario is that the tree's height grows quickly at first and then slows down over time. For this type of scenario we would use a logarithmic model.

The linear model best fits the given situation option (B) linear is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

The height of a tree increases by 2.5 feet each growing season.

Let h is the height and s be the number of seasons.

The relation between h and s:

h = 2.5s

Thus, the linear model best fits the given situation option (B) linear is correct.

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Answer:

7.834 × 10^-8

Step-by-step explanation:

= 7.834 × 10^-8

(scientific notation)

= 7.834e-8

(scientific e notation)

= 78.34 × 10^-9

(engineering notation)

(billionth; prefix nano- (n))

= 0.00000007834

(real number)

^ means the number after is exponent.

Answer:

The end balance is $910.62 and the total interest $660.62. (That is without tax or inflation rate) I hope this helps.

Step-by-step explanation:

Answer:

without tax: interest total=$660.62

Step-by-step explanation:

I multiplied...

Answer:

1.0625

Step-by-step explanation:

Answer:

21.4 m²

Step-by-step explanation:

To find the surface area of this whole triangular prism, we have to look at the bases (the triangles), find their surface area, then look at the sides (the rectangles) and find theirs.

Let's start with the triangles. The area of any triangle is [tex]\frac{bh}{2}[/tex]. The base of this triangle is 2m (because there are 2 one meters) and the height is 1.7m.

[tex]\frac{2\cdot1.7}{2} = \frac{3.4}{2} = 1.7[/tex]

So the area of one of these triangles is 1.7m. Multiplying this by two, because there are two triangles in this prism:

[tex]1.7\cdot2=3.4[/tex]

Now let's find the area of the sides.

The side lengths are 2 and 3, so

[tex]2\cdot3=6[/tex], and there are 3 sides (including the bottom/floor) so [tex]6\cdot3=18[/tex].

Now we add.

[tex]18+3.4=21.4[/tex] m².

Hope this helped!

Answer: 21.4 square meters^2

Step-by-step explanation:

Answer:

24 inches

Step-by-step explanation:

So, 1 inch = 5 feet

then, x inch = 120 feet

Let's represent this as a ratio.

1 inch / x inch = 5 feet / 120 feet

1 inch / x inch = 1 feet /24 feet

x = 24 inches

Answer:

The 6th term is 3072.

Step-by-step explanation:

Answer:

48 km/h

Step-by-step explanation:

80/50*30=48 km/h

Answer:

[tex] \boxed{12 \sqrt{2} }[/tex]

Step-by-step explanation:

Isosceles triangle are those triangle which have two equal sides.

Perpendicular ( p ) = 12 inches

Base ( b ) = 12 inches

Hypotenuse ( h ) = ?

Now,Using Pythagoras theorem,

[tex] \mathsf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

Plug the values

[tex] \mathsf{ {h}^{2} = {12}^{2} + {12}^{2} }[/tex]

Evaluate the power

[tex] \mathsf{ {h}^{2} = 144 + 144}[/tex]

Calculate the sum

[tex] \mathsf{ {h}^{2} = 288}[/tex]

Squaring on both sides

[tex] \mathsf{h = 12 \sqrt{2} }[/tex]

Hope I helped!

Best regards!

Answer:

well just do area, and since it's the same in each side 12×4= 144

Answer:

Graph B

Step-by-step explanation:

Look at the first part of the function: 2-x , -7 ≤ x ≤ 5

If you put -7 in place of x you'll have:

2 - (-7) = 2 + 7 = 9

In the graph A, the point x = -7 have a y = 8, so cannot be the graph A. and it have to be graph B

Answer:

1

Step-by-step explanation:

Anything real number (except 0) to the zeroth power would be 1.

Therefore, 12 to the zeroth power would also be 1.

[tex]12^0=1[/tex]

Answer:

As you know everynumber raised to 0 is always 1 even if its x or infinity so the answer will be 12^0 will be 1

Step-by-step explanation:

any and every number raised to 0 is 1

Answer:

Step-by-step explanation:

B ----> Base Area

Base is triangle

base = b = 10 in

height = h = 6 in

Area of base B = [tex]\frac{1}{2}bh[/tex]

                         [tex]=\frac{1}{2}*10*6\\\\= 5* 6\\\\= 30 \ in^{2}[/tex]

B = 30 in²

H = 15 in

Volume of triangular prism = BH

                                            = 30 * 15

                                            = 450 in³

Answer:

Step-by-step explanation:

[tex]\displaystyle f(x)=\sin(3x)\\\\\\f'(x)=\lim_{h\to0}\dfrac{\sin(3(x+h))-\sin(3x)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{\sin(3x+3h)-\sin(3x)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{3x+3h+3x}{2}\right)\sin\left(\dfrac{3x+3h-3x}{2}\right)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{6x+3h}{2}\right)\sin\left(\dfrac{3h}{2}\right)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{6x+3h}{2}\right)\sin\left(\dfrac{3h}{2}\right)}{\dfrac{3h}{2}}\cdot\dfrac{3}{2}[/tex]

[tex]\displaystyle f'(x)=\lim_{h\to0}2\cos\left(\dfrac{6x+3h}{2}\right)\cdot\dfrac{3}{2}\\\\f'(x)=\lim_{h\to0}3\cos\left(\dfrac{6x+3h}{2}\right)\\\\f'(x)=3\cos\left(\dfrac{6x+3\cdot 0}{2}\right)\\\\f'(x)=3\cos\left(\dfrac{6x}{2}\right)\\\\f'(x)=3\cos(3x)[/tex]

The derivative of sin 3x using first principles is; 3cos(3x)

We want to find the derivative of sin 3x using first principles.

Step 1;

f'(x) = [tex]\lim_{h \to \ 0} \frac{(sin3(x + h)) - sin(3x)}{h}[/tex]

Step 2; Expand the bracket to get;

f'(x) = [tex]\lim_{h \to \ 0} \frac{(sin(3x + 3h)) - sin(3x)}{h}[/tex]

Step 3: According to trigonometric identities, we know that;

sin A - sin B = [tex]2cos\frac{A + B}{2} sin\frac{A - B}{2}[/tex]

Applying that to the answer in step 2 gives;

f'(x) = [tex]\lim_{h \to \ 0} \frac{2(cos\frac{(3x + 3h + 3x)}{2}) sin\frac{(3x + 3h - 3x)}{2})}{h}[/tex]

Step 4; Simplify the brackets to obtain;

f'(x) = [tex]\lim_{h \to \ 0} \frac{2(cos\frac{(6x + 3h)}{2}) sin\frac{(3h)}{2})}{h}[/tex]

Step 5; Rewrite the denominator to get;

f'(x) = [tex]\lim_{h \to \ 0} \frac{2(cos\frac{(6x + 3h)}{2}) sin\frac{(3h)}{2})}{\frac{3h}{2}*\frac{2}{3}}[/tex]

Step 6; Input the limit of 0 for h to get;

f'(x) = [tex]\frac{2(cos\frac{(6x)}{2}) sin\frac{(0)}{2})}{\frac{0}{2}*\frac{2}{3}}[/tex]

⇒ f'(x) = [tex]\frac{2(cos3x)}{2/3} \frac{ 0}{{0}}[/tex]

0/0 = 1. Thus;

f'(x) = 3cos(3x)

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Answer:

1) 120

2) E (Z) = 12 and Variance of Z = 90

a) 5 liters

Step-by-step explanation:

1. We can find this by suing combinations.

Here n= 10 and r= 3 so n C r

= 10 C 3= 120

2. E(X) = 8 and E(Y) = 3

Z = 2X - 3Y +5

E(Z ) = 2 E (X) - 3(E)(Y) +5   ( applying property for mean)

       = 2(8) - 3(3)+ 5 = 16+5-9= 21-9= 12

V(X) = 9 and V(Y) = 6.

V(Z) = E(Z )²-  V(X) *V(Y)   (applying property for Variance for two variables )

        = 144- 54= 90

3. 55 liters contain adulterated milk in 7: 4.

So it contains 4/ 11*55= 20 liters of water

But we want to make it a ratio of 7:6

the water will be 6/13 *55= 25.38 when rounded gives 25 liters of water

So 25- 20 = 5 liters must be added to make it a ratio of 7:6

Answer:

T(H) = -3H + 50.

Step-by-step explanation:

The constant will be 50 degrees Celsius. The surface temperature at the location will not change. The temperature decreases by 3 degrees Celsius for every kilometer going up, so the slope will be -3 degrees.

You are trying to find the temperature on the planet, and you are changing the kilometers of altitude to find the temperature. The x-variable is your independent variable, which means that you will be changing the x-variable. So, H is your x-variable while T is your y-variable.

T = -3H + 50.

To graph, we can use the Math is Fun Function Grapher and Calculator. The graph is seen below.

Hope this helps!

Answer:

0.036

Step-by-step explanation:

We can find the probability by dividing the number of people with type A blood by the total amount of people.

There are 900 people in total and 323 of them have type A blood.

323/900

= approximately 0.036

Answer: Choice B)  0.36

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

Work Shown:

323 people have blood type A

900 people are being sampled

323/900 = 0.35888888888889 approximately

This rounds to 0.36, which is the probability of picking someone with type A blood.

We don't use any other values given, so they are probably put in there as a distraction.

Answer:

4.44

Step-by-step explanation:

The tangent of B is the relation of the opposite cathetus to the lying cathetus

tg B= AC/CB= 40/9= 4.44

The value of the tangent of angle B is 4.4.

In trigonometry, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

In other words, it is the ratio of sine and cosine function of an acute angle such that the value of cosine function should not equal to zero.

Given that, a right triangle Δ ABC, the measure of ∠C = 90°, AC = 40, BA = 41, and CB = 9. We need to find the value of the tangent of ∠B,

So, here,

The opposite side = AC and the adjacent side = CB

So, tan B = AC / CB = 40/9 = 4.4

Hence, the value of the tangent of angle B is 4.4.

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