Truth tables I need help solving each row

Answer:

E(X)=3.125

Step-by-step explanation:

We are given that two four sided dice.

Then , the sample space

{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}

Total number of outcomes=16

Let the random variable X represent the maximum value of the two dice

Outcomes                            X                                 P(X)

(1,1)                                          1                                 1/16

(1,2),(2,1),(2,2)                                   2                        3/16

(1,3),(2,3),(3,1),(3,2),(3,3)                    3                           5/16  

(1,4),(3,4) ,(2,4),(4,1),(4,2),(4,3),(4,4)    4                            7/16

Using the probability formula

[tex]P(E)=\frac{Favorable\;outcomes}{Total\;number\;of\;outcomes}[/tex]

Now,

[tex]E(X)=\sum_{i=1}^{n}x_iP(x_i)[/tex]

[tex]E(x)=1(1/16)+2(3/16)+3(5/16)+4(7/16)[/tex]

[tex]E(x)=\frac{1+6+15+28}{16}[/tex]

[tex]E(x)=\frac{50}{16}=3.125[/tex]

This is because the given expression factors to (x+4)(x+4), which condenses to (x+4)^2.

To factor, think of two numbers that A) multiply to 16, and B) add to 8. Those values would be 4 and 4

4+4 = 8

4*4 = 16

So that's how we end up with (x+4)(x+4). You can use the FOIL rule to expand that out and get x^2+8x+16 again to help verify you have the correct factorization.

Answer:

✎There will be 30 Chocolate-Covered raisins in each bag.

✎ And 5 Remaining.

Step-by-step explanation:

Take 185 and divide it by 6 and you should get 30 per bag with a remainder of 5 :)

Answer:

30 miles

Step-by-step explanation:

Given that :

Scale = 2 inches represents 5 miles

This means that 2 inches in the map equals to 5 miles on ground ;

Hence, if the trail measures 12 inches on the map, the length on ground will be ; x

2 inches = 5 miles

12 inches = x miles

Cross multiply :

2x = (12 * 5)

2x = 60

x = 60 / 2

x = 30 miles

Answer:

Step-by-step explanation:

Slope of line through (5,4) and (3,7) = (7-4)/(3-5) = -1.5

Point-slope equation of line:

y-4 = -1.5(x-5)

Convert equation to standard form:

y-4 = -1.5x + 7.5

1.5x + y = 11.5

3x +2y = 23

9514 1404 393

Answer:

Step-by-step explanation:

When the same problem is repeated, I like to solve it using a spreadsheet. That way, the formulas only need to be entered once, and the arithmetic is (almost) guaranteed to be done correctly.

A "form factor" computed from side lengths can be used to determine the type of triangle. Where 'c' is the long side, that factor can be computed as ...

  f = a² +b² -c²

and interpreted as follows:

(The sign of f matches the sign of the cosine of the largest angle computed using the law of cosines.)

Of course, a right triangle can also be identified by looking at the slopes of the sides of the triangle. If any pair of slopes has a product that is -1, or if any pair is 0 and "undefined", then the triangle will be a right triangle.

__

The attached spreadsheet is designed to accommodate a number of different problem requirements. It shows both side lengths and slopes, and it shows the "form factor" as described above. The final classification is shown at far right.

Answer:

S/100r

Step-by-step explanation:

S% of 1/r = (1/r x S) : 100

(1/r x S) : 100

S/r : 100

S/100r

Answer:

1=2p+3

2=

Step-by-step explanation:

Answer:

Option (3)

Step-by-step explanation:

Given function is,

f(x) = 3x² - 2x

     = [tex]3(x^{2} -\frac{2}{3}x)[/tex]

     = [tex]3(x^{2} -\frac{2}{3}x+\frac{1}{9}-\frac{1}{9})[/tex]

     = [tex]3(x^{2}-\frac{2}{3}x+\frac{1}{9})-\frac{1}{3}[/tex]

     = [tex]3(x-\frac{1}{3})^2-\frac{1}{3}[/tex]

Vertex of the parabola → [tex](\frac{1}{3},-\frac{1}{3})[/tex]

Here, leading coefficient is positive (+3),

Therefore, parabola will open upwards.

In a parabola opening upwards function decreases from negative infinity to the x value of the vertex.

Function will decrease in the interval (-∞, [tex]\frac{1}{3}[/tex]).

Option (3) will be the answer.

Answer:

it should be 8.333333%

Step-by-step explanation:

Answer:

The probability that at least 7 employees were over 50 is 0.0073%.

Step-by-step explanation:

Given that a town recently dismissed 8 employees in order to meet their new budget reductions, and the town had 9 employees over 50 years of age and 16 under 50, if the dismissed employees were selected at random, to determine what is the probability that at least 7 employees were over 50, the following calculation must be performed:

9/25 x 8/24 x 7/23 x 6/22 x 5/21 x 4/20 x 3/19 = X

0.36 x 0.33 x 0.304 x 0.272 x 0.238 x 0.2 x 0.157 = X

0.000073 = X

100X = 0.0073

Therefore, the probability that at least 7 employees were over 50 is 0.0073%.

Answer:

11

Step-by-step explanation:

3p²q+pq²=3×1/4×4+1/2×16=3+8=11

Answer:

15

Step-by-step explanation:

3/8 = 9

9÷3= 3

the remainder of 3/8 is 5/8 so

5x3=15

Answer:

B is the right statement

Answer:

add the answer choices

Step-by-step explanation:

Answer:

Start with the formula for Z:

Z = (x-µ)/(σ/√n)

We want the sample mean to be within one-half year of the population mean, so we set x-µ=0.5. We are looking for a 99% confidence interval, so we set Z=2.7578. We are told to use σ=18.1. Plugging those values into the formula, we get:

2.5758 = 0.5(18.1/√n)

We can rearrange to solve for n:

((2.5758-18.1)/0.5)2 = n

Plugging that into our calculator, we get n = 964.003. Since we can't have a fraction of a person in our sample, it would be safest to round up to n=965. (But since .003 is so small, I'd also accept 964 as an answer.)Step-by-step explanation:

The required sample size for the given population distribution is; n = 8696 female ages

We are given;

Standard deviation; σ = 18.1

Confidence level; CL = 99%

Now, formula to find the margin of error is;

E = z(σ/√n)

Where;

E is margin of error

z is critical value at confidence level

σ is standard deviation

n is required sample size

Now we are told that the sample mean is within one-half year of the population mean.

Thus;

E = 0.5

z value at 99% Confidence level is;

z = 2.576

Thus, Making n the subject of the formula is;

n = (zσ/E)²

n = (2.576 × 18.1/0.5)²

n = 8695.78

Approximating to a whole number gives;

n = 8696 female ages

Read more about margin of error at; https://brainly.com/question/6650225

The base of the solid - call it B - is the set of points

B = {(x, y) : 0 ≤ x ≤ 1 and x ⁴ ≤ y ≤ 1}

Recall the area of a circle with radius r is πr ²; in terms of the diameter d = 2r, the area is π (d/2)² = π/4 d ². Then the area of a semicircle with the same diamater is half of this, π/8 d ².

Cross sections of the solid in question are semicircles arranged perpendicular to the x-axis, which means the diameters of each cross section corresponds to the vertical distance between y = x ⁴ and y = 1 for any given values of x between 0 and 1. So d = 1 - x ⁴, which makes the area of each cross section come out to π/8 (1 - x ⁴)².

Split up the solid into very thin cross sections with "base" area π/8 (1 - x ⁴)² and thickness ∆x. Take the sum of these half-cylinders' volumes, then let ∆x converge to 0. In short, we get the total volume by integrating,

[tex]\displaystyle \int_0^1\frac\pi8(1-x^4)^2\,\mathrm dx = \frac\pi8\int_0^1(1-2x^4+x^8)\,\mathrm dx = \boxed{\frac{4\pi}{45}}[/tex]

Answer:

What is the diferentes between and red bolos celos ?

Step-by-step explanation:

so basically after doing all the algebra, you will have to use the log function to solve. rearranging things and you will get the log expression that I obtained, then solve it using the change of base formula.

Answer: -3/8

Step-by-step explanation:

Expanding z we get  

z = 4x^2 - 4xy + y^2 - 2y^2 - 3y

  = -y^2 - (4x + 3) y + 4x^2.

After Archimedes chooses x, Brahmagupta will choose

y=-(4x+3/2) in order to maximize z

Then  

z=-((-4x+3)/2)^2 -(4x+3)(-4x+3)/2)^2)+4x^2

z=8x^2+6x+9/4

To minimize this expression, Archimedes should choose x=-3/8

Answer:

5

Step-by-step explanation:

The scale factor is 5. Answered by Gauthmath

The length and the width of rectangle a are expanded 5 times respectively.

The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.

According to the question

Rectangle a is dilated to form rectangle b.

By division operation, the ratio

[tex]\frac{20}{4} =\frac{30}{6} =5[/tex]

The length and the width of rectangle a are expanded 5 times respectively.

Find out more information about scale factor here

brainly.com/question/2839518

#SPJ2

Answer:  200 miles

Work Shown:

(1.25 inches)/(250 miles) = (1 inch)/(x miles)

(1.25)/(250) = 1/x

1.25x = 250*1 ..... cross multiplication

1.25x = 250

x = 250/(1.25)

x = 200 miles

It doesn't change because to add fractions, you need a common denominator. To find it, they multiplied 1/3 by 2 to make 2/6, to add to the 3/6.

Answer:

96cm3

Step-by-step explanation:

formula is

v=1/3×area of the base×height

area of base which is a square=l×l

which is equal to 6×6=36

therefore

v=1/3×(6×6)×8

=96cm3

I hope it helps

Answer:

The answer would be D

Step-by-step explanation:

This is a piecewise function, meaning that it is split into two parts. The right side is an exponential and that part is greater than one, the left side is a line less than or equal to one. The only equation that matches the criteria for that is D.

Answer:

[tex]\lim_{x \to \infty} \frac{ln(5x)}{5x} = \lim_{x \to \infty} \frac{1/x}{5} = \lim_{x \to \infty} \frac{1}{5x} = 0[/tex]

Step-by-step explanation:

L'Hopital's rule says that, if both numerator and denominator diverge, then we can look at the limit of the derivates.

Here we have:

[tex]\lim_{x \to \infty} \frac{ln(5x)}{5x}[/tex]

The numerator is ln(5x) and when x tends to infinity, this goes to infinity

the denominator is 5x, and when x tends to infinity, this goes to inifinity

So both numerator and denominator diverge to infinity when x tends to infinity.

Then we can use L'Hopithal's rule.

The numerator is:

f(x) = Ln(5x)

then:

f'(x) = df(x)/dx = 1/x

and the denominator is:

g(x) = 5*x

then:

g'(x) = 5

So, if we use L'Hopithal's rule we get:

[tex]\lim_{x \to \infty} \frac{ln(5x)}{5x} = \lim_{x \to \infty} \frac{1/x}{5} = \lim_{x \to \infty} \frac{1}{5x} = 0[/tex]

Answer:

[tex]4\sqrt{5}[/tex] units

Step-by-step explanation:

The distance between any two points on the x y plane (a,b) and (c,d) has one of two formulas.  [tex]\sqrt{(a-c)^2+(b-d)^2}[/tex] or [tex]\sqrt{(c-a)^2+(d-b)^2}[/tex]  if you use c-a you have to also use d-b, and the other way around for a-c and b-d.  You can rearrange which order you add though.    So with (-1,5) and (3,3) here is the math

[tex]\sqrt{(3-(-1))^2+((-3)-5)^2} \\\sqrt{4^2+(-8)^2} \\\sqrt{16+64}\\\sqrt{80}[/tex]

You could simplify this to [tex]4\sqrt{5}[/tex]

Let me know if there was anything you didn't understand.

Answer:

10,-4

Step-by-step explanation:

not sure where the options are but if you were to solve this equation first bring everything to one side.

x^2 - 6x - 40 = 0

factor it

(x-10)(x+4) = 0

set each part to 0

x-10 = 0 and x+4 = 0

solutions are 10 and -4

Answer:

56

Step-by-step explanation:

clearly, the sequence is built by adding 5 for every new term.

so, an = an-1 + 5

a1 = 25 (the starting value)

a2 = a1 + 5 = 25 + 5 = 30

a3 = a2 + 5 = a1 + 5 + 5 = a1 + 2×5 = 25 + 10 = 35

...

an = an-1 + 5 = a1 + (n-1)×5

now, we know, the last term is 300.

when we determine for which n we get an = 300, we know that n is the number of terms in the sequence.

so,

300 = a1 + (n-1)×5 = 25 + 5n - 5 = 20 + 5n

280 = 5n

n = 56

a56 = 300

so, we have 56 terms in this sequence

Answer:

56

Step-by-step explanation:

nth term = a+d(n-1) =25+5(n-1) = 25+5n-5 = 20+5n

300 = 20 + 5n

5n = 280

n = 56

since 300 is the last term in the sequence, the total number would be 36