(Q4) Solver the inequality.
6^x < 3^x

Answer:

The total surface area of this square pyramid is [tex]297\ mm^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of a square pyramid is equal to

[tex]SA=b^{2} +4[\frac{1}{2}(b)(h)][/tex]

we have

[tex]b=9\ mm[/tex] ----> the length side of the square base

[tex]h=12\ mm[/tex] ----> the height of the triangular faces

substitute the values

[tex]SA=9^{2} +4[\frac{1}{2}(9)(12)]=297\ mm^{2}[/tex]

Answer:

Set of all real numbers

Step-by-step explanation:

Given in the question the equation:

f(x) = ∛(x)

The domain of a cube root function is the set of all real numbers.

The interval notation (-∞ , ∞)

Cube Root of negative numbers exists:

Negative numbers can't have real number square roots, but negative numbers can have real number cube roots because when you are multiplying an odd number of negative numbers, the result is negative.

Example

(-2)³ = (-2)(-2)(-2) = -8

Answer:

The answer is Ф = 1.82 or 4.46 ⇒ answer (c)

Step-by-step explanation:

* The domain of the function is 0 ≤ Ф ≤ 2π

- Lets revise the ASTC rule to solve the problem

# In the 1st quadrant all trigonometry functions are +ve

# In the 2nd quadrant sinФ and cscФ only are +ve

# In the 3nd quadrant tanФ and cotФ only are +ve

# In the 4th quadrant cosФ and secФ only are +ve

* Lets solve the problem

∵ secФ = -4.0545 ⇒ negative value

∴ Angle Ф is in the 2nd or 3rd quadrant

- In the 2nd quadrant Ф = π - α ⇒ (1)

- In the 3rd quadrant Ф = π + α ⇒ (2)

where α is an acute angle

* Now use the calculator to find α with radiant mode

- Let secα = 4.0545

∴ cosα = 1/4.0545

∴ α = cos^-1(1/4.0545) = 1.321585

* Substitute the value of α in (1) and (2)

∴ Ф = π - 1.321585 = 1.82

∴ Ф = π + 1.321585 = 4.46

* The answer is Ф = 1.82 or 4.46

X=1/2

Explanation

Multiple both sides times 5

Then the 5 just cancels out on the left side and you’re left with 1/2

Answer:

The pyramid's volume is [tex]125\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the pyramid is equal to

[tex]V=(1/3)Bh[/tex]

where

B is the area of  base of pyramid

h is the height of the pyramid

Find the area of the base B

[tex]B=5^{2}=25\ in^{2}[/tex] -----> is a square

[tex]h=15\ in[/tex]

substitute the values

[tex]V=(1/3)(25)(15)=125\ in^{3}[/tex]

Answer: 45 in²

Step-by-step explanation:

3 stamps by 4 stamps = 12 stamps

9 in / 12 stamps = 0.75 in/stamp

6 stamps by 10 stamps = 60 stamps

60 stamps * 0.75 in/stamp = 45 in²

Answer:

Step-by-step explanation:

Total Number of Rolls = 10

Number of Defective Rolls = 3

Probability = Number of Defective Rolls / Total Number of Rolls

Probability = 3 / 10

Now there is one less defective roll.

Total Number of Rolls = 10 - 1

Number of Defective Rolls = 3 - 1

Total Number of Rolls = 9

Number of Defective Rolls = 2

Probability = Number of Defective Rolls / Total Number of Rolls

Probability = 2 / 9

Multiply the two probabilities together to find the overall probability.

3 / 10 * 2 / 9

3 * 2  = 6

10 * 9 = 90

6 / 90

Simplify

6 / 90 = 3 / 45 = 1 / 15 = 0.06666666666....

To find the probability of selecting two defective rolls of film in a row from a box of 10 rolls where 3 are defective, you multiply the probability of each selection. The result is a 1/15 chance of selecting two defective rolls consecutively.

The question deals with the concept of probability without replacement. In this scenario, we calculate the probability by considering each step independently. Initially, there are 10 rolls of film, and 3 are defective. The probability of selecting a defective roll first is 3 out of 10, or 3/10. Once a defective roll has been selected, there are now 9 rolls left with 2 being defective. The probability of selecting another defective roll is then 2 out of 9, or 2/9. To find the overall probability of both events happening in sequence ('and' probability), we multiply the probabilities of each step:

P(First defective and second defective) = P(First defective) * P(Second defective | First defective) = (3/10) * (2/9) = 6/90 = 1/15.

Therefore, the probability of selecting two defective rolls in a row is 1/15.

Answer:

The length of the container is [tex]14\ in[/tex]

Step-by-step explanation:

we know that

The surface area of a triangular prism (a mailing container) is equal to

[tex]SA=2B+PL[/tex]

where

B is the area of the triangular base

P is the perimeter of the triangular base

L is the length of the container

step 1

Find the area of the base B

[tex]B=\frac{1}{2}(2)(1.7)=1.7\ in^{2}[/tex]

step 2

Find the perimeter of the base P

[tex]P=3(2)=6\ in[/tex]

step 3

Find the length L of the container

we have

[tex]SA=87.4\ in^{2}[/tex]

[tex]B=1.7\ in^{2}[/tex]

[tex]P=6\ in[/tex]

substitute and solve for L

[tex]87.4=2(1.7)+(6)L[/tex]

[tex]L=[87.4-2(1.7)]/(6)[/tex]

[tex]L=14\ in[/tex]

Answer:

The answer is $6

Step-by-step explanation:

20 divided by 30% is 6! So it’s therefore 6$

Answer:

  5/9

Step-by-step explanation:

The scale factor by which T was dilated is ...

   (side of T')/(corresponding side of T)

   = 20/36 = 10/18 = 5/9 . . . (reduced form)

Answer:

C) the answer is 5/9 or C

Step-by-step explanation:

i got it roght on the edgen quiz.

Answer:

[tex]7.30\ mi[/tex]

Step-by-step explanation:

Let

b-----> the base of the missing measurement of the parallelogram

we know that

The area of the parallelogram is equal to

[tex]A=bh[/tex]

we have

[tex]A=27\ mi^{2}[/tex]

so

[tex]27=bh[/tex] ------> equation A

In this problem

[tex]h=3.7\ mi[/tex]

substitute the value in the equation A and solve for b

[tex]27=b(3.7)[/tex]

[tex]b=27/3.7=7.30\ mi[/tex]

Answer:

45 units ^2

Step-by-step explanation:

make sure to divide the triangle and sqaure up when finding the area of this polygon..

hope this helps!!

Answer:

[tex]\large\boxed{D.\ 12x^2-29x+14}[/tex]

Step-by-step explanation:

Use FOIL: (a + b)(c + d) = ac + ad + bc + bd

[tex](3x-2)(4x-7)=(3x)(4x)+(3x)(-7)+(-2)(4x)+(-2)(-7)\\\\=12x^2-21x-8x+14\qquad\qquad\text{combine like terms}\\\\=12x^2+(-21x-8x)+14=12x^2-29x+14[/tex]

Looks like the temperature is given by

[tex]t(x,y,z)=200e^{-x^2-3y^2-7z^2}[/tex]

We have gradient at any point [tex](x,y,z)[/tex]

[tex]\nabla t(x,y,z)=200e^{-x^2-3y^2-7z^2}(-2x,-6y,-14z)[/tex]

Then the rate of change of [tex]t[/tex] at [tex]p[/tex] in the direction of (5, -5, 6) is given by

[tex]\nabla t(4,-1,4)\cdot\dfrac{(5,-5,6)}{\|(5,-5,6)\|}=\left(-\dfrac{400}{e^{131}}(4,-3,28)\right)\cdot\dfrac{(5,-5,6)}{\sqrt{86}}=-\dfrac{40600}{e^{131}}\sqrt{\dfrac2{43}}[/tex]

which is very nearly 0.

The rate of change of temperature at the point p(4, -1, 4) in the direction towards the point (5, -5, 6) can be found by computing the gradient vector at p, obtaining a unit direction vector towards the other point, and calculating their dot product.

To find the rate of change in the direction towards the point (5, -5, 6), we need to compute the gradient vector of the temperature at point p(4, -1, 4), and then calculate the directional derivative in the direction towards the other point.

First, we calculate the partial derivative of t with respect to x, y, and z. These derivatives give us the gradient vector ∇t at point p. The gradient vector represents the direction of the steepest incline at p and its magnitude gives the rate of increase of t.

Next, we need to find the unit vector in the direction towards point (5,-5,6) from p. Subtracting the coordinates of p from the other point gives us the direction vector. Normalizing this vector gives us the unit direction vector.

Finally, the rate of change of temperature at p in the direction towards the other point is given by the dot product of ∇t at p and the unit direction vector. This is known as the directional derivative of t at p in the mentioned direction.

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Hence zeros of function are
,x=-9, x=-8

Value of x that makes function value 0.

[tex]x^{2[/tex] +17x+72=0

[tex]x^{2}[/tex]+ 8x+9x+72=0

x(x+8)+9(x+8)=0

(x+9)(x+8)=0

x=-9,-8

Hence ,x=-9, x=-8

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Final answer:

The zeros of the function f(x) = x² + 17x + 72 are -9 and -8, found by factoring the quadratic equation.

Explanation:

To find the zeros of the function f(x) = x² + 17x + 72, we need to solve the equation for x when f(x) = 0. This can be done by factoring the quadratic equation if possible.

The quadratic factors as (x + 9)(x + 8) = 0. So the solutions to the equation x² + 17x + 72 = 0 are:

x = -9

x = -8

Therefore, the zeros of the function are -9 and -8.

Answer:

[tex]\large\boxed{d_2=15\ cm}[/tex]

Step-by-step explanation:

The formula of an area of a kite:

[tex]A=\dfrac{d_1d_2}{2}[/tex]

d₁, d₂ - diagonals

We have A = 120 cm² and d₁ = 16 cm. Substitute:

[tex]\dfrac{16d_2}{2}=120[/tex]

[tex]8d_2=120[/tex]           divide both sides by 8

[tex]d_2=15\ cm[/tex]

Step-by-step explanation:

We transform the system of equations to the form:

[tex]\left\{\begin{array}{ccc}ax+by=c\\dx+ey=f\end{array}\right[/tex]

Where a & b and d & e are relatively prime number.

If a ≠ d or b ≠ e then the system of equations has one solution.

Example:

[tex]\left\{\begin{array}{ccc}2x-3y=-4\\3x+3y=9\end{array}\right[/tex]

Add both sides of equations:

[tex]5x=5[/tex]     divide both sides by 5

[tex]x=1[/tex]

Substitute it to the second equation:

[tex]3(1)+3y=9[/tex]

[tex]3+3y=9[/tex]           subtract 3 from both sides

[tex]3y=6[/tex]       divide both sides by 3

[tex]y=2[/tex]

[tex]\boxed{x=1,\ y=2\to(1,\ 2)}[/tex]

If a = d and b = e and c = f then the system of equations has infinitely many solutions.

Example:

[tex]\left\{\begin{array}{ccc}2x+3y=5\\2x+3y=5\end{array}\right[/tex]

Change the signs in the second equation. Next add both sides of equations:

[tex]\underline{+\left\{\begin{array}{ccc}2x+3y=5\\-2x-3y=-5\end{array}\right}\\.\qquad0=0\qquad\bold{TRUE}[/tex]

[tex]\boxed{x\in\mathbb{R},\ y=\dfrac{5-2x}{3}}[/tex]

If  a = d and b = e and c ≠ f then the system of equations has no solution.

Example:

[tex]\left\{\begin{array}{ccc}3x+2y=6\\3x+2y=1\end{array}\right[/tex]

Change the signs in the second equation. Next add both sides of equations:

[tex]\underline{+\left\{\begin{array}{ccc}3x+2y=6\\-3x-2y=-1\end{array}\right}\\.\qquad0=5\qquad\bold{FALSE}[/tex]

Answer:

a) There is a 66.7% chance that you were given box 1

b) There is a 80% chance that you were given box 1

Step-by-step explanation:

To find this, we need to note that there is a 1/10 chance of getting a defective bulb with box 1 and a 1/20 chance in box 2.

a) To find the answer to this, find the probability of getting a defective bulb for each box. Since there is only one bulb pulled in this example, we just use the base numbers given.

Box 1 = 1/10

Box 2 = 1/2

From this we can see that Box 1 is twice as likely that you get a defective bulb. As a result, the percentage chance would be 2/3 or 66.7%

b) For this answer, we need to square each of the probabilities in order to get the probability of getting a defective one twice.

Box 1 = 1/10^2 = 1/100

Box 2 = 1/20^2 = 1/400

As a result, Box 1 is four times more likely. This means that it would be a 4/5 chance and have a probability of 80%

The solution involves using conditional probability and Bayes' theorem to find the chance of picking a defective lightbulb from a specific box. In part (b), the problem is slightly more complex, assuming the lightbulbs are selected independently.

This problem involves conditional probability. We're given two scenarios (a box is selected randomly, a lightbulb picked is defective, and two lightbulbs chosen are wrong). Let's use the following symbols: B1 (Box 1), B2 (Box 2), D (faulty lightbulb).

(a) The probability of a lightbulb being defective, given it came from Box 1 (P(D|B1)), is 0.10. The total likelihood of a lightbulb being inferior (P(D)) can be worked out from the total of defective lightbulbs divided by the total number of lightbulbs. The probability we're after, according to Bayes' theorem, is P(B1|D) = [P(D|B1)*P(B1)] / P(D).

(b) This question is more complex but can be solved similarly. Assuming the lightbulbs are selected independently, the probability of picking two defective lights from a given box is simply the square of picking one defective lightbulb from that box. Thus, we calculate P(2D|B1) = [P(D|B1)]^2 = (0.10)^2 = 0.01 (or 1%). Then, we use Bayes' theorem in part (a) to find P(B1|2D).

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Answer:

The length of 30 inches is longer

Step-by-step explanation:

we know that

[tex]1\ ft=12\ in[/tex]

Convert the length to inches

[tex]2\ ft=2(12)=24\ in[/tex]

therefore

[tex]30\ in>24\ in[/tex] ------> [tex]30\ in>2\ ft[/tex]

The length of 30 inches is longer

Step-by-step explanation:

x^2 - 8x = 20

1. Subtract 20 from both sides

x^2 - 8x - 20 = 20 - 20

2. Simplify

x^2 - 8x - 20 = 0

3. Factor the equation out by grouping

(x - 10)(x + 2) = 0

4. Change signs:

x = 10, x = -2

Hope This Helped!!

~Shane

Answer:{-2,10}

Step-by-step explanation:

trust

Answer:

95%.

Step-by-step explanation:

That would be about 95% of the observations.

The percentage within 1 standard deviation is about 68%.

[tex] \cot(x) \sin(x) = \frac{ \cos(x) }{ \sin(x) } \sin(x) = \cos(x) \\ \Rightarrow b. \cot(x) = \frac{ \cos(x) }{ \sin(x) } [/tex]

Answer:

B

Step-by-step explanation:

The dot product is a scalar product, so you can eliminate the first two choices right away.

We have

[tex]v\cdot w=\langle3,4,7\rangle\cdot\langle6,-9,7\rangle=3\cdot6+4\cdot(-9)+7\cdot7=31[/tex]

Answer:

31

Step-by-step explanation:

v ⋅ w = (3)(6) + (4)(-9) + (7)(7)

v ⋅ w = 18 - 36 + 49

v ⋅ w = 31

Answer:

44 years old

Step-by-step explanation:

The deifference between their ages is always the same. So 23x2=46

but that is in 2 years so we -2 from 46 =44

Answer:

44

Step-by-step explanation:

Answer:

the answer is D according to what i got

~batmans wife

Answer:

E. b/3 + 3

Step-by-step explanation:

For all real number b and c, if the product of c and 3 is b,

mathematically; 3c = b...(1)

To find the sum of c and 3 in terms of b;

Mathematically, the sum of c and 3 gives c+3...(2)

From equation 1, c = b/3

Substituting c = b/3 into equation 2, we will have;

(b/3) + 3 option E

= (b+9)/3

Answer:

k(qq)/r^2 times the length of the distnace

Step-by-step explanation:

Force times distance. The Electrical force is the only thing you have to find first.

The work required to move a particle with charge q from the other vertex to the center of the line joining the fixed particles is -kq^2/a.

To find the work required to move a particle with charge q from the other vertex to the center of the line joining the fixed particles, we need to calculate the electrostatic potential energy. The potential energy is given by the equation:

U = kqQ/r

where U is the potential energy, k is the electrostatic constant, q and Q are the charges, and r is the distance between the charges.

In this case, we have two charges of magnitude q and -q at the vertices of an equilateral triangle. The distance from the center of the triangle to each charge is a/2, where a is the length of the side of the triangle. Therefore, the potential energy is:

U = (1/4πε0)q(-q)/a

where ε0 is the permittivity of free space. Simplifying the expression, we get:

U = -kq2/a

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Answer:

[tex]\$20[/tex]

Step-by-step explanation:

Let

x-----> the cost of his lunch

y----> the cost of his dinner

we know that

[tex]x+y=872-136-210-500[/tex]

[tex]x+y=26[/tex] -----> equation A

[tex]x=0.3y[/tex] ---> equation B

substitute equation B in equation A

[tex]0.3y+y=26[/tex]

[tex]1.3y=26[/tex]

[tex]y=\$20[/tex] -----> the cost of the dinner

Answer:

549

Step-by-step explanation:

The next larger whole number, 550, will round up to 600.

The largest whole number that rounds to 500 is 549 when rounding to hundreds.