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4 years ago

Explain the difference between (-5)2 and -52.

Mathematics

2 answers:

Tpy6a [65]4 years ago

7 0

Answer:

the parentheses say that you have to multiply -5 and 2

where as -52 is just a number.

Volgvan4 years ago

5 0

Answer:

(-5)2 = -10 (you multiply because of the parenthesis)

Step-by-step explanation:

(-5)2 = -5 × 2 = -10

-52 is just a negative intenger.

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A board game contains a cube withone of the letters A, G, E, I, K, and W on each of its faces. With each roll, what is the proba

LenKa [72]

The probability that a vowel will land face up on the cube would be 1/2. This is because there are six total letters; three vowels and three consonants, so there is a 3/6 chance of it being a vowel and you simplify it down to 1/2. I hope this helped :)

3 0

3 years ago

An open top rectangular box is to be made from a rectangular piece of metal that is 3cm wide and 8cm long by cutting a square fr

Tanzania [10]

Answer:

x = 0.67 cm

Step-by-step explanation:

Let call " x " the length of the side of the square to cut from each corner

then the sides of the future box would be

L = 8 - 2x and D = 3 - 2x

The volume of the box is:

V = L*D*x

And such volume as function of x is

V(x) = ( 8 - 2x ) * ( 3 - 2x ) * x ⇒ V(x) = ( 24 - 16x - 6x + 4x²) * x

V(x) = 4x³ - 22x² + 24x

Taking derivatives on both sides of the equation we get:

V´(x) = 12x² - 44x + 24

Then V´(x) = 0 ⇒ 12x² - 44x + 24 = 0 ⇒ 3x² - 11x + 6 = 0

We got a second degree equation solving for x

x₁,₂ = [11 ± √ 121 - 72 ] / 6

x₁ = ( 11 + 7 ) / 6 x₁ = 3 we dismiss this solution since according to problem statement one side would become negative

Then

x₂ = ( 11 - 7 ) / 6 ⇒ x₂ = 4/6 ⇒ x₂ = 0.67 cm

As the second drivative is smaller than 0 then there is a maximun in that point

V´´(x) = 12x - 44 < 0

Sides of the box

L = 8 - 2x ⇒ L = 8 - 2*(0.67) ⇒ L = 8 - 1.34 ⇒ L = 6.66 cm

D = 3 - 2x ⇒ D = 3 - 2* (0.67) ⇒ D = 3 - 1.34 ⇒ D = 1.66 cm

Heigh = x = 0.67 cm

V(max) = 6.66*1.66*0.67

V(max) = 7.41 cm³

5 0

3 years ago

What is 6 x blank = 36

Elenna [48]

Answer:6

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Suppose that the pH of soil samples taken from a certain geographic region is normally distributed with a mean pH of 7 and a sta

Otrada [13]

Answer:

a) P=0

b) P=1

c) P=0

d) X=7.1645

Step-by-step explanation:

We have the pH of soil for some region being normally distributed, with mean = 7 and standard deviation of 0.10.

a) What is the probability that the resulting pH is between 5.90 and 6.15?

We calculate the z-score for this 2 values, and then compute the probability.

$z_1=(X_1-\mu)/\sigma=(5.9-7.0)/0.1=-11\\\\z_2=(X_2-\mu)/\sigma=(6.15-7)/0.1=-8.5$

Then the probability is

$P(5.90$

b) What is the probability that the resulting pH exceeds 6.10?

We repeat the previous procedure.

$z=(6.10-7)/0.1=-9\\\\P(x>6.1)=P(z>-9)=1$

c) What is the probability that the resulting pH is at most 5.95?

$z=(5.95-7)/0.1=-10.5\\\\P(x$

d. What value will be exceeded by only 5% of all such pH values?

We have to calculate the value of pH for which only 5% is expected to be higher. This can be represented as P(X>x)=0.05.

In the standard normal distribution, it happens for a z=1.645.

$P(z>1.645)=0.05$

Then, we can calculate the pH as:

$x=\mu+z\sigma=7.0+1.645*0.1=7.0+0.1645=7.1645$

4 0

3 years ago

PLS HELP ME 30 POINTS

Setler [38]

Answer:

I think its. -9tt/8

-25tt/8

23tt/8

3 0

3 years ago