Which of the following is an equivalent form of the compound inequality-33 > -3x - 6 > -6

Answer:

1. y² = 169

taking a square root of both sides

y = √169

we know that 13 * 13 = 169

since when squaring a number, the signs on the numbers do not matter

(i.e - 2* 2 = 4 and (-2)*(-2) = 4)

So (-13) * (-13) = 169 as well

Hence we can say that √169 = ±13      OR      √169 = +13   and   -13

2. Volume of a cube-shaped crate = side*side*side

Volume = side³

(We are given that volume = 27)

27 = side³

side = ∛27

Since 3*3*3 = 27     and (-3)*(-3)*(-3) = 27

So, we can say that ∛27  = ± 3

BUT

the side of a crate cannot be negative, so the side will NOT be -3 and hence,

side = 3

3. b³ = 1000

we know that 10*10*10 = 1000    and     (-10)*(-10)*(-10) = 1000

So, ∛1000 =  ∛(10*10*10)= ±10

4. Area of a square(Patio)  = Side²

Area = Side²

196 = Side² (Since we are given the area of the patio)

Side = √196 = √(14*14) or √(-14*-14)

Hence,

Side = + 14 or -14

but the side of a patio cannot be negative

Side = +14 ft

Answer:

it should be C

Step-by-step explanation:

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

The expected amount to be lost is  0.5263 cents per game

b

The expected amount to be lost is  

     [tex]P = \$ 526 .3 [/tex]

Step-by-step explanation:

From the question we are told that

   The probability of winning is  [tex]p = \frac{1}{38} = 0.0263[/tex]

Generally the probability of losing is mathematically evaluated as

            [tex]q =  1-p [/tex]

=>        [tex]q = 1-0.0263 [/tex]

=>        [tex]q = 0.9737[/tex]

Generally the expected value is mathematically represented as

      [tex]E(X) =  \sum x_i *  P(x_i)[/tex]

Here [tex]x_i[/tex] is a discrete variable (i.e it is a countable )  are outcomes of the player winning and the player losing

So

     [tex]E(X) =   x_1 *  P(x_1) + x_2 *  P(x_2)  [/tex]

Now the outcome of winning is  making $350  so

       [tex]x_1 = \$ 350[/tex]

        the outcome of losing is losing $10  so  

        [tex]x_2 = - \$10[/tex]

So

     [tex]E(X) =  350* 0.0263 -10 *  0.9737  [/tex]

       [tex]E(X) = -0.5263 [/tex]

hence the expected amount to be lost is  0.5263 cents per game

If you played the game 1000​ times, the amount that is expected to be lost is  

    [tex]P =  1000 * -0.5263[/tex]

=> [tex]P = -\$ 526 .3 [/tex]

Hence the expected amount to be lost is  

     [tex]P = \$ 526 .3 [/tex]

Answer:

he total time is 4 seconds. The elevator descends 10 feet each second so the total is:

4seconds x -10 feet/sec = -40 feet

The total change in elevation is -40 feet. You need the negative sign because the elevator is moving downward. Hope this helps!

Answer:

The sample size n will be "52".

Step-by-step explanation:

The given values are:

c = 0.98​

σ = 8.7

Margin of error

E = 2

[tex]Z_{\frac{\alpha}{2} }=Z_{\frac{0.1}{2} }=1.65[/tex]

For 90% confidence level:

⇒  [tex]n=[\frac{Z_{\frac{\alpha}{2}}\times \sigma}{E} ]^2[/tex]

⇒     [tex]=[\frac{1.65\times 8.7}{2} ]^2[/tex]

⇒     [tex]=51.5165[/tex]

i.e.,

⇒  [tex]n=52[/tex]

Solutions: x=1.

Hope this helps!

First, isolate the variable:

x>-33

The answers would be 25, 14, -25.

I am not sure if that is a more than sign or a more than or equals sign; if it is a more than sign the answers mentioned above are the only answers, but if it a more than or equals sign, the answers are 25, 14, -25, -33.

If it helped please consider giving be brainliest :)

Answer:

Step-by-step explanation:

Solving in steps

Correct answer choices:

Answer: 3/9 or 1/3

Step-by-step explanation:

3, 6 and 9 are all multiples of 3 equal or below 9.

Step-by-step explanation:

Let the smaller number be x.

So, according to Question,

the larger number will be 1+4x.

Now, sum of the numbers is 61, like this:-

[tex]1 + 4x + x = 61[/tex]

[tex]5x = 61 - 1[/tex]

[tex]5x = 60[/tex]

[tex]\tt{x = \dfrac{60}{5}}[/tex]

[tex]\boxed{\tt{x = 12}}[/tex] is the required Answer.

Hope it helps :)

Answer:

7.2

Step-by-step explanation:

Answer:

7 2/9; estimate is about 7

Step-by-step explanation:

convert mixed numbers to improper fractions

(whole number × denominator + numerator)

104/3 ÷ 24/5

copy dot flip

104/3 × 5/24

multiply numerators

520

multiply numerators

72

520/72

convert back to mixed numbers

7 16/72

simplify

7 2/9

Answer:

34 quarters.

6 nickles.

Step-by-step explanation:

Answer:

C. 8,034

Step-by-step explanation:

26 x 309 = 8,034

Answer:

Step-by-step explanation:

You can easily find the slope by using two points. Let’s use (13, 11) and (14, 6)

We look at the slope equation as: y2 - y1 divided by x2 and x1.

13 = x1 11= y1 and 14= x2 6=y2

Plug in: 6-11/14-13 and solve

Answer: -5

Hope I made sense :)

Answer:

Slope (m) = -5

Step-by-step explanation:

*If all the given four points are on a straight line then; the slope derived from first two points should be equal to the slope derived from the next to points.

Let's verify this ...

For the first two points:

Slope (m) = change in y ÷ change in x = [tex]\frac{6 - 11}{14 - 13} = \frac{-5}{1} = -5[/tex]

For the next two points:

m = [tex]\frac{-4 - 1}{16 - 15} = -5[/tex]

*Proved ∴ points (13,11) , (14,6) , (15, 1) and (16,-4) are on the same line.

Taking another point (x,y) on the line and point (13,11);

m = [tex]\frac{y - 11}{x - 13} = -5[/tex]

y = -5x + 65 + 11

y = -5x + 76

Answer:

[tex]\frac{x-4}{(x+3)(x-5)}[/tex]

Step-by-step explanation:

Since the rational function has vertical asymptotes at -3, and 5, the denominator must equal 0 when x is -3 or 5. Therefore, the denominator must be:

(x+3)(x-5)

Now, to make the x-intercept at (4, 0), the numerator must be equal to 0 when x is 4. Therefore, the numerator must be:

x-4

Therefore, that rational function is:

[tex]\frac{x-4}{(x+3)(x-5_}[/tex]

Answer:

y+7 = -3 ( x-4)

Step-by-step explanation:

First find two points on the graph to find the slope

( 1,2) and ( 3,-4)

The slope is given by

m = ( y2-y1)/(x2-x1)

m = ( -4-2)/(3-1)

    = -6/2

    =-3

We can use the point slope form

y - y1 = m(x-x1)  where m is the slope and x1,y1 is a point on the line

We have two choices with a slope of -3

We can either use and x coordinate of -2 or 4

for  -2, the y coordinate is not shown

for 4 , the y coordinate is -7

Using ( 4, -7) and m = -3

y--7 = -3( x- 4)

y+7 = -3 ( x-4)

Answer:

A

Step-by-step explanation:

We want to write the equation of the line as shown in the graph.

First and foremost, we should find the slope of the line. To do so, we will pick two points that the line crosses.

We see that the line crosses the points (0, 5) and (2, -1). Now, we can use the slope formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let (0, 5) be (x₁, y₁) and let (2, -1) be (x₂, y₂). Substitute:

[tex]m=\frac{-1-5}{2-0}[/tex]

Subtract and reduce. So, our slope is:

[tex]m=-6/2=-3[/tex]

Therefore, our slope is -3.

Now, we can use the point-slope form to find the equation. Point-slope form is:

[tex]y-y_1=m(x-x_1)[/tex]

Where m is our slope and (x₁, y₁) is any point the line crosses.

First, since we already know that our slope is -3, let's substitute -3 for m:

[tex]y-y_1=-3(x-x_1)[/tex]

So, we can eliminate choices C and D since the slope of those equations is 3 and not -3.

Now, we need to pick our (x₁, y₁). Let's go through the answer choices A and B to see which one is correct.

For A, we have:

[tex]y+7=-3(x-4)[/tex]

We can rewrite this as:

[tex]y-(-7)=-3(x-(4))[/tex]

Therefore, in A, our point is (4, -7).

Now, check. Does our line actually pass through (4, -7).

From the graph, we can see that it does. Therefore, A is our correct answer!

However, let's do B just to confirm. For B, we have:

[tex]y+1=-3(x+2)[/tex]

We can rewrite this as:

[tex]y-(-1)=-3(x-(-2))[/tex]

So, our point is (-2, -1).

Does our line pass through (-2, -1)?

Upon inspection, our line does not pass through (-2, -1). So, B is not correct.

So, our answer is A.

And we're done!

Answer:

y=-1/10 x - 41/10

Step-by-step explanation:

slope: y2-y1 / x2-x1 = -5-(-4) /  9-(-1) = -1/10

y= -1/10 x +b, substitute (-1,-4) to solve b

-4=-1/10 (-1) +b

b=-41/10

Answer:

the triangle is 10 the rest are 3

Answer:

B. 11 MPH

Step-by-step explanation:

60/4=15

15-11=4

Answer:

10

Step-by-step explanation:

At first, (goh)(x)= g{h(x)}

= g{2x-2}

={2x-2}^2 +3x

[tex] = 4 {x}^{2} - 8x + 4 + 3x \\ = 4 {x}^{2} - 5x + 4 \\ then \: \:(goh)(2) = 4 \times {2}^{2} - 5 \times 2 + 4 \\ = 16 - 10 + 4 \\ = 10[/tex]

hope u got it.....

Answer:

0.46

Step-by-step explanation:

Answer:

0.4667

Step-by-step explanation:

First off, we'll interpret the fraction bar to mean "divided by." This means that 7/15 is the same as 7 divided by 15.

Second, you have requested to see 3 decimal places in your answer, so we'll write the 7 as 7.000 instead (a 7 with 3 zeros after the decimal point).

Now, we'll just do what the fraction bar says: divide 7.000 by 15:

And that's about it! 7/15 written as a decimal to 3 decimal places is 0.467

Answer:

117/125

Step-by-step explanation:

Answer:

117/125

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer and Step-by-step explanation:

SOLUTION:

Given function:

h (x, y, z) = ln (x2 + y2 – 1) + y +6z,  p0(1, 1, 0)

Derivatives of the function:

∂h / ∂x = (1 / x2 + y2 -1). (2x)

          = 2x / x2 + y2 -1

∂h/∂y = (1 / x2 + y2 – 1) (2y + 1)

          = (2y / x2 + y2 -1) + 1

∂h / ∂z = 6

Now compute the partial derivatives:

∂h (1, 1, 0) / ∂x = 2(1) / 1 +1 -1

                            = 2

∂h(1, 1, 0) / ∂y =( 2(1) / 1 +1 -1) + 1

                           = 3

∂h (1, 1, 0) / ∂z = 6

Δh (1,1,0) = ( 2, 3, 6)

The definition of gradient is:

Δf (x, y, z) = (∂f / ∂x , ∂f / ∂y)

Put the coordinate values to arrive at solution:

Umax = Δh (1,1,0) / | Δh (1,1,0) |

      = (2, 3, 6) / |2, 3, 6|

     = (2, 3, 6) / √(22+33+62)

   = (2, 3, 6) / √49

    = (2, 3, 6) / 7

= (2/7 , 3/7, 6/7)

Umin = - U max = ( -2/7, -3/7, -6/7)

Compute direction by finding unit vector:

Du h max = Δh (1,1,0)  . u max

                 = (2, 3, 6) . (2/7, 3/7, 6/7)

                 = 2(2/7) + 3(3/7) + 6(6/7)

                 = 4/7 +  9/7 +36/ 7

                  = 49 / 7

                  = 7

Du h min = -Du h max

                = -7

Answer: 1/2 and 3/2

Step-by-step explanation:

Like fractions have the same denominator