Put the following equation of a line into slope-intercept form, simplifying all fractions.


Thanks In advance

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]

Answer:

x=2    x=-1

Step-by-step explanation:

f(x) = x^2 - X - 2

0= x^2 -x-2

Factor

0 =(x-2)(x+1)

Using the zero product property

x-2 =0   x+1 =0

x=2    x=-1

Answer:

x=2, -1

Step-by-step explanation:

Hi there!

We want to find the zeros of this function: f(x)=x²-x-2

The zeros are the values of x that will make f(x)=0

So that means in order to find the zeros, set f(x) as 0

In that case,

x²-x-2=0

Now let's solve the quadratic equation

We can do it by factoring

-x is the sum of two numbers, while -2 is the product of those two same numbers

Now think: which two numbers add up to -1, but multiply to get -2?

Those numbers are -2 and 1

Now factor the polynomial by FOIL:

(x-2)(x+1)=0

Split and solve

x-2=0

x=2

x+1=0

x=-1

The zeros are x=2, -1

Hope this helps!

Answer:

5 ft

Step-by-step explanation:

The formula for Volume is V=lwh, or Volume = length x width x height.

The equation would be:

[tex]180=l(4)(9)[/tex]

or

[tex]180=36l[/tex]

To find the answer, divide by 36.

[tex]\frac{180}{36} =\frac{36l}{36}[/tex]

[tex]5=l[/tex]

Answer:

[tex]\frac{2}{5}^{-3}[/tex]×[tex]x=\frac{1}{2}^{4}[/tex]

[tex]x=\frac{2}{5} ^{3} \\[/tex]×[tex]\frac{1}{2}^{4}[/tex]

(negative in the exponent means reciprocal of the fraction)

x= [tex]\frac{1}{250}[/tex]

Brainliest please

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]

That's a question about exponentiation.

Answer:

Kenji is wrong because he does not aply the porperty correctly.

Step-by-step explanation:

A exponetiation has this form:

[tex]\boxed{a^b}[/tex]

a is the base

b is the power or exponent

To understand that situation it's important to know a property about exponentiation. When we have a multiplication with the same exponent and diferent bases, the result is the multiplication of the bases with the same exponent. Let's see this above, in mathematical language:

[tex]\boxed{a^b \cdot c^b = (a\cdot c) ^b}[/tex]

Examples:

Now, we can say why Kenji is wrong. It's easy simplify [tex]3^5 \cdot 4^5[/tex]! We know that the result is [tex](3 \cdot 4) ^5 = 12^5[/tex], but Kenji multiplied the bases and added the exponents, that's why he is wrong.

I hope I've helped. ^^

Enjoy your studies! \o/

Answer:

it should be 8.333333%

Step-by-step explanation:

Answer:

B. 3.39 m

Step-by-step explanation:

r² = A/π

= 36/3.14

= 11.465

r = √11.465 = 3.39

Answer:

The point at the bottom has to move over 2 to the left to be aligned with the point at the top however they will have a 3 space in between the 2 same for the point at the top, the top point moves over 2 to the right to be aligned with the bottom point, then they will have a 3 square space between each other.

Answer:Around 3 spaces between?

Step-by-step explanation:

Answer:

B is the right statement

Answer:

add the answer choices

Step-by-step explanation:

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:  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

Answer:

15

Step-by-step explanation:

3/8 = 9

9÷3= 3

the remainder of 3/8 is 5/8 so

5x3=15

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:

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:

B. 11.5

Step-by-step explanation:

That missing length can be solved via the equation a^2+b^2=c^2, where the hypotenuse is c. We know A and B, which is 7 and 9.

7^2+9^2=130

sqrt 130 is 11.4017543

Here, you kinda have to break the rules of rounding to say that it is B.

There could be a more efficient route for resolving this answer, but this is the method that I was taught.

Answer:

The endpoints of the latus rectum are [tex](12, -7)[/tex] and [tex](-8, -7)[/tex].

Step-by-step explanation:

A parabola with vertex at point [tex]C(x, y) = (h,k)[/tex] and whose axis of symmetry is parallel to the y-axis is defined by the following formula:

[tex](x-h)^{2} = 4\cdot p \cdot (y-k)[/tex] (1)

Where:

[tex]y[/tex] - Independent variable.

[tex]x[/tex] - Dependent variable.

[tex]p[/tex] - Distance from vertex to the focus.

[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex.

The coordinates of the focus are represented by:

[tex]F(x,y) = (h, k+p)[/tex] (2)

The latus rectum is a line segment parallel to the x-axis which contains the focus. If we know that [tex]h = 2[/tex], [tex]k = -2[/tex] and [tex]p = -5[/tex], then the latus rectum is between the following endpoints:

By (2):

[tex]F(x,y) = (2, -2-5)[/tex]

[tex]F(x,y) = (2,-7)[/tex]

By (1):

[tex](x-2)^{2} = -20\cdot (-7+2)[/tex]

[tex](x-2)^{2} = 100[/tex]

[tex]x - 2 = \pm 10[/tex]

There are two solutions:

[tex]x_{1} = 2 + 10[/tex]

[tex]x_{1} = 12[/tex]

[tex]x_{2} = 2-10[/tex]

[tex]x_{2} = -8[/tex]

Hence, the endpoints of the latus rectum are [tex](12, -7)[/tex] and [tex](-8, -7)[/tex].

Answer:

Hello,

Answer A (-4,0) and (0,0)

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y&=&x^2+4x\\y+x^2&=&-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\y&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\x^2+4x&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}2*x^2+8*x&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}x(x+4)&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\[/tex]

[tex]\left\{\begin{array}{ccc}x&=&0 \\y&=&0\\\end{array} \right. \ or\ \left\{\begin{array}{ccc}x&=&-4 \\y&=&0\\\end{array} \right.[/tex]

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: x = 2

Step-by-step explanation:

P-----------------------T----------------------Q

         (3x-3)                   (5x-7)

Since T is the midpoint we know that PT and TQ are equal

Just solve the equation: 3x-3 = 5x-7

[tex]3x-3 = 5x-7[/tex]

now move the x to one side

[tex]-3 = 2x-7[/tex] (I subtracted the 3x)

then get the 2x by itself

[tex]4=2x[/tex]

lastly, divide by 2 to get x by itself

[tex]x=2\\[/tex]

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:

In 2025, t=30. so D=418*30+6000 = 18540

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:

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

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:

The population is the population of 3521 people who made credit card purchases.

The sample is the 172 people who returned the survey form.

Step-by-step explanation:

Department mails customers satisfactions forms to those who make credit cards purchase at the store, totaling 3521 people. Thus, the population is the population of 3521 people who made credit card purchases.

Surveys are mailed to 278 of these people, chosen at random, and 172 people return the survey form.

Thus the sample, that is, those from whom the data will be taken and expanded to the rest of the population, is the 172 people who returned the survey form.

The population is all 3521 people who made credit card purchases.

The sample is the 172 people who returned the survey form.

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: -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