Alex has a collection of cards: 4 are black, 2 are blue, 3 are white, and 1 is brown. What is the probability that he will pick a black card twice without replacement?

Answer:

The visiting team had a greater fraction of strikeouts

Step-by-step explanation:

Ratios

The ratios are useful to compare rates of change or average values. In our case, we need to compare the average of strikeouts from two teams.

The home team had 12 strikeouts for 32 batters. This gives an average of:

[tex]\frac{12}{32}=0.38[/tex]

The visiting team had 15 strikeouts for 35 batters for an average of:

[tex]\frac{15}{35}=0.43[/tex]

The visiting team had a greater fraction of strikeouts

Answer:

The answer is A.

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

√[tex]80k^3[/tex] expressed in simplest radical form is 4√[tex](5k^2)[/tex].

To simplify the expression √[tex]80k^3[/tex] (square root of [tex]80k^3[/tex]) in its simplest radical form, you can break down [tex]80k^3[/tex] into its prime factors:

[tex]80k^3 = 2^4 * 5 * k^3[/tex]

Now, take the square root of each factor:

√[tex]80k^3[/tex] = √[tex](2^4 * 5 * k^3)[/tex]

Since square roots of perfect squares simplify to whole numbers, and the square root of [tex]k^3[/tex] is [tex]k^{3/2}[/tex], the simplified radical form is:

√[tex]80k^3[/tex] = [tex]2^2[/tex] * √[tex](5k^2)[/tex] = 4√[tex](5k^2)[/tex]

Therefore, √[tex]80k^3[/tex] expressed in its simplest radical form is 4√[tex](5k^2)[/tex].

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Answer:

[tex]m=\frac{2}{3}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (40, 10)

Point (70, 30)

Step 2: Find slope m

Answer:

m=0

Step-by-step explanation:

We simplify the equation to the form, which is simple to understand  

93+12m=3(4m-1)+96

Reorder the terms in parentheses

93+12m=+(+12m-3)+96

Remove unnecessary parentheses

+93+12m=+12m-3+96

We move all terms containing m to the left and all other terms to the right.  

+12m-12m=-3+96-93

We simplify left and right side of the equation.  

m=0

Hope this helps!

Brain-List?

Answer:

infinite solutions

Step-by-step explanation:

First, you do the property of distribution

93+12m=3(4m-1) +96

93+12m=12m-3+96

then you combine like terms

93+12m=12m+93

0=0 is the answer if you were to continue.

Answer:

30 birthday cakes

Step-by-step explanation:

42÷7=6

6×5=30

Step-by-step explanation:

here,

x^2 -3xy-18xy^2

=x^2-(6-3)xy-18xy^2

=x^2-6xy+3xy-18y^2

=x(x-6y)+3y(x-6y)

=(x-6y)(x-3y)

Answer:

0.75x = y

Step-by-step explanation:

The required expression represents the relationship between the number Tyler ate (x) and the number Han ate (y) is y = x/4.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
Tyler ate x fruit snacks, and Han ate 3/4 less than that
Let the snacks eaten by Han be y,
According to the question,
y = x - 3/4x
y = x/4

Thus, the required expression represents the relationship between the number Tyler ate (x) and the number Han ate (y) is y = x/4.

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Answer:

a = 3

Step-by-step explanation:

The vertex form of a quadratic is

y = a(x-h) ^2 +k  where ( h,k) is the vertex

the vertex is (-2,2)

y = a(x- -2) ^2 +2

y = a(x+2) ^2 +2

Pick another point on the graph to determine a

(-1,5) and substitute into the equation

5 = a( -1+2) ^2 +2

5 = a(1)^2 +2

5 = a(1) +2

Subtract 2 from each side

5-2 = a+2-2

3 = a

Answer:

A=3

Step-by-step explanation:

I got it right on the test

=Answer:

Step-by-step explanation:

f(-7) = -(-7)^2 - 10(-7) = -49 +70 = 21

Answer:

(5 / 6) / 2 1/6 = 0.384615385

Step-by-step explanation:

Answer:0.2587 hope this helps you out. have a good day!

Step-by-step explanation:

Answer:

decimal=0.8

percentage=80%

Answer:

D. a pencil can not have thoughts like a person, so it is personification.

Answer:

The answer is D.

12 : 48 : 24

thats the answer

12 passion fruit

48 grapefruit

24 grape juice

Answer:

1 hour 12minutes

Step-by-step explanation:

Answer: (4,12) or (1/3) simplified

Answer:

2/6

Step-by-step explanation:

so do rise of run but you would move down on the rising. So you go down 2 and run 6

Answer:

Solve one of the equations for one of the variables. Let's solve the first equation for y: ...

Step 2: Substitute that equation into the other equation, and solve for x. ...

Step 3: Substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

Answer:

wdym? .................

Answer:

-9-9x=27+9

-9x=36÷(-9)

x=-4

Step-by-step explanation:

prove me wrong

Answer:

Undefined

Step-by-step explanation:

If the slope was a horizontal line, then we could say y=2, however, it is only going through the x-axis so it would be x=2, but in terms of y it is undefined.

Answer:

70°

Step-by-step explanation:

1. the rule is: m(∠1)+m(∠2)+m(∠3)=180°.

2. the substitution according to the rule above:

b+2b-90+b-10=180;

4b=280;

b=70°

Answer:

8.5 cm

Step-by-step explanation:

We know that the square has side lengths of 6cm. To calculate the distance from one corner of the square to the opposite corner, we are calculating the diagonal of the square.

Along the diagonal is where the square gets split in half into two right triangles. The Pythagorean theorem states that [tex]a^2+b^2=c^2[/tex] where c is the longest side of a right triangle and a and b are the other two sides.

To find the length of the square's diagonal, we essentially need to calculate c, the longest side of the triangles. We can do this by plugging 6 into the equation as a and b.

[tex]a^2+b^2=c^2\\6^2+6^2=c^2\\36+36=c^2\\72=c^2\\\sqrt{72} =c[/tex]

[tex]8.5[/tex] ≈ [tex]c[/tex]

Therefore, it will be approximately 8.5cm from one corner of the square to the opposite corner.

I hope this helps!

Answer:

option 1 is correct

Step-by-step explanation:

yes makes me brain list

Answer:

the lowest common multiple is 60

Step-by-step explanation:

The multiples of 12 are : 12, 24, 36, 48, 60, 72, 84,

The multiples of 15 are : 15, 30, 45, 60, 75, 90, ....

60 is a common multiple (a multiple of both 12 and 15), and there are no lower common multiples.

Therefore, the lowest common multiple of 12 and 15 is 60.

Answer:

[tex]60[/tex]

Step-by-step explanation:

Least Common Multiplier (LCM)

The LCM of [tex]a,b[/tex] is the smallest positive number that is divisible by both [tex]a[/tex] and [tex]b[/tex]

Prime factorization of [tex]12[/tex]

[tex]12[/tex]

[tex]12[/tex] divides by [tex]2[/tex]     [tex]12=6*2[/tex]

[tex]=2*6[/tex]

[tex]6[/tex] divides by [tex]2[/tex]     [tex]6=3*2[/tex]

[tex]2,3[/tex] are both prime numbers, therefore no further factorization is possible

[tex]=2*2*3[/tex]

Prime factorization of [tex]15[/tex]

[tex]15[/tex]

[tex]15[/tex] divides by [tex]3[/tex]    [tex]15=5*3[/tex]

[tex]3,5[/tex] are both prime numbers, therefore no further factorization is possible

Multiply each factor the greatest number of times it occurred in either [tex]12[/tex] or [tex]15[/tex]

[tex]=2*2*3*5[/tex]

Multiply the numbers: [tex]2*2*3*5=60[/tex]

[tex]=60[/tex]

Answer:

4960?

Step-by-step explanation:

31 times 160 = 4960

Answer:

X² =4.75

Step-by-step explanation:

The formula for calculating the chi square value is expressed as

X² = [ (O - E)²/ E ].

O is the observed frequency

E is the expected frequency

Given

O = 9.5

E = 19

Substitute into the formula:

X² = (9.5-19)²/19

X² = 9.5²/19

X² = 90.25/19

X² = 4.75

Hence the chi square value will be 4.75

Answer:

4x - 7

Step-by-step explanation:

Answer:

[tex]\dfrac{-8^3}{6}[/tex]

Step-by-step explanation:

According to the divergence theorem;

The flux through the surface S is given by the formula:

[tex]\iint _S F.dS = \iiint_E \ div (F) \ dV[/tex]

where the vector field is:

F = [tex]\langle y,z-y,x \rangle[/tex]

Then the divergence of the vector field is:

[tex]div (F) = \bigtriangledown.F = \Bigg [ \dfrac{\partial (y)}{\partial x} + \dfrac{\partial (z-y)}{\partial (y)}+ \dfrac{\partial (x)}{\partial (z)} \Bigg ][/tex]

= 0 - 1 + 0

= -1

Thus, the flux through the surface of the tetrahedron is:

[tex]\iint_S . FdS = \iiint _E(-1) \ dV \\ \\ = - \iiint_E \ dV[/tex]

To determine the  volume of the tetrahedron with vertices O(0,0,0), A(8,0,0), B (0,8,0) & C(0,0,6)

The equation of the plane P moving through the vertices A, B and C is:

[tex]P = \dfrac{x}{8}+ \dfrac{y}{8}+ \dfrac{z}{8} = 1[/tex]

x + y + z = 8

Range:

For z: 0 ≤ z ≤ 8 - x - y

For y: 0 ≤ y ≤ 8 - x

For x; 0 ≤ x ≤ 8

Thus;

[tex]\iiint_E \ dV = \int ^8_0 \int ^{8-x}_{0} \int ^{8-x-y}_{0}[/tex]

[tex]\int ^8_0 \int ^{8-x}_{0} [z] ^{8-x-y}_{0} \ dydx = \int ^8_0 \int ^{8-x}_{0} \ (8 -x-y) \ dy dx[/tex]

[tex]\int ^8_0 [ (8-x)^2 - \dfrac{(8-x)^2}{2} ] dx = \dfrac{1}{2} \int ^8_0 (8-x)^2 \ dx[/tex]

i.e.

[tex]= \dfrac{1}{2} [ \dfrac{(8-x)^3}{(-1)^3}]^8_0[/tex]

[tex]= \dfrac{-1}{6}[(8-8)^3-(0-8)^3][/tex]

[tex]= \dfrac{-8^3}{6}[/tex]

This question is based on the Gauss Divergence theorem. Therefore, the surface integral  [tex]\int\limits {F.dS}[/tex] is  -85.33.

Given:

F(x, y, z) = y i + (z − y) j + x k S in outward orientation.

Tetrahedron with vertices (0, 0, 0), (8, 0, 0), (0, 8, 0), and (0, 0, 8).

We have to evaluate the surface integral  [tex]\int\limits {F.dS}[/tex] .

According to the Gauss divergence theorem ,

The flux through the surface S is given by the formula:

[tex]\int\int _s F.dS = \int \int \int_e div (F)\; dV[/tex]

Where the vector field is:

F  = ( y, z-y, x )

Therefore,  the divergence of the vector field is:

[tex]div(F) = \bigtriangledown .F = ( \dfrac{\partial( y)}{\partial (x)} + \dfrac{\partial(z-y)}{\partial(y)} + \dfrac{\partial(x)}{\partial(z)} )\\\\div(F) = \bigtriangledown .F = 0-1+0=-1[/tex]

Thus, the flux through the surface of the tetrahedron is:

[tex]\int\int _s F.dS = \int \int \int_e (-1)\; dV = -\int \int \int_e \; dV[/tex]

Now, determine the  volume of the tetrahedron with vertices O(0,0,0), A(8,0,0), B (0,8,0) & C(0,0,6).

The equation of the plane P moving through the vertices A, B and C is:

[tex]P = \dfrac{x}{8} +\dfrac{y}{8} +\dfrac{z}{8} = 1[/tex]

x + y + z = 8

Range:

For z: 0 ≤ z ≤ 8 - x - y

For y: 0 ≤ y ≤ 8 - x

For x; 0 ≤ x ≤ 8

Thus,

[tex]\int\int\int_e dV = \int\limits^8_0\int\limits^{8-x} _ 0 \int\limits^{8-x-y}_0 \; dzdxdy\\= \int\limits^8_0\int\limits^{8-x} _ 0 [z]\limits^{8-x-y}_0 dx \\= \int\limits^8_0\int\limits^{8-x} _ 0 (8-x-y) dy dx\\= \int\limits^8_0 [ 8y-xy-\dfrac{y^{2} }{2} ]\limits^{8-x}_ 0 dx\\= \int\limits^8_0 ([ 8-x]^{2} - \dfrac{ [ 8-x]^{2}}{2} ) dx\\= \dfrac{1}{2} [\dfrac{(8-x)^{3} }{(-1)^{3} } ] \limits^8_0\\=\dfrac{-8^{3} }{6} \\\\= -85.33[/tex]

Therefore, the surface integral  [tex]\int\limits {F.dS}[/tex] is  -85.33.

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