7. Sarah draws a card from a standard deck, throws the card away, and then draws another card.
Are these events independent or dependent?

Complete question :

Birth Month Frequency

January-March 67

April-June 56

July-September 30

October-December 37

Answer:

Yes, There is significant evidence to conclude that hockey​ players' birthdates are not uniformly distributed throughout the​ year.

Step-by-step explanation:

Observed value, O

Mean value, E

The test statistic :

χ² = (O - E)² / E

E = Σx / n = (67+56+30+37)/4 = 47.5

χ² = ((67-47.5)^2 /47.5) + ((56-47.5)^2 /47.5) + ((30-47.5)^2/47.5) + ((37-47.5)^2/47.5) = 18.295

Degree of freedom = (Number of categories - 1) = 4 - 1 = 3

Using the Pvalue from Chisquare calculator :

χ² (18.295 ; df = 3) = 0.00038

Since the obtained Pvalue is so small ;

P < α ; We reject H0 and conclude that there is significant evidence to suggest that hockey​ players' birthdates are not uniformly distributed throughout the​ year.

Answer:

about 75.36

Step-by-step explanation:

we know the radius of the base (circle) is 2 since 4/2 is 2.

Area of cylinder is height times area of base

6*4π=24π

You round π as 3.14

so 3.14*24= 75.36

Answer:

[tex] 75.4 \: {cm}^{3} [/tex]

Step-by-step explanation:

Height of the cylinder h = 6 cm

Diameter d = 4 cm

Radius r = 4/2 = 2 cm

[tex]V_{cylinder} = \pi {r}^{2} h \\ \\ = 3.14 \times {(2)}^{2} \times 6 \\ \\ = 3.14 \times 4 \times 6 \\ \\ = 3.14 \times 24 \\ \\ = 75.36 \\ \\ = 75.4 \: {cm}^{3} [/tex]

Answer:

The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step-by-step explanation:

Zeros of the given equation are {-2, 3, (-1±i√3)/2}

As the last term is -6 then, ± 2 , ±3 are possible zeroes.

Try 2:-

[tex]2^4-6*(2)^2-7*2-6=-28[/tex] so  2 is not a zero.

Try 3:-

[tex]3^4-6*(3)^2-7*3-6=0[/tex]  so 3 is a zero.

[tex](-2)^4-6*(-2)^2-7*(-2)-6=0[/tex]  so -2 is also a zero.

Divide the function by (x +2)(x - 3),  that is  [tex]x^2 - x - 6[/tex]

gives  [tex]x^2 + x + 1[/tex]

[tex]x^2 + x + 1[/tex]

So we have [tex]x^2 + x + 1 = 0[/tex]

[tex]x = [-1 +\sqrt{1^1 - 4*1*1}] / 2[/tex]

= -1 + √(-3) / 2 , - 1 - √(-3)  / 2.

= -0.5 + 0.866i, -0.5 - 0.866i

In mathematics, the number that results in the original number when multiplied by itself is called the root.

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Answer:

24 patterns

Step-by-step explanation:

Given that four lettered patterns are to be formed using the three alphabets. Since letters may be repeated, then;

4[tex]P_{3}[/tex] = [tex]\frac{4!}{(4 - 3)!}[/tex]

      = [tex]\frac{4 x 3 x 2!}{1!}[/tex]

     = 4 x 3 x 2

     = 24

4[tex]P_{3}[/tex] = 24

Therefore, 24 four letter patterns can be formed when the given letters are repeated.

Given:

The fractions are:

[tex]\dfrac{6}{5},\dfrac{11}{7},\dfrac{21}{4}[/tex]

To find:

The each fraction as the sum of a whole number and a fraction less than 1.

Solution:

The given fraction is [tex]\dfrac{6}{5}[/tex].

[tex]\dfrac{6}{5}=\dfrac{5+1}{5}[/tex]

[tex]\dfrac{6}{5}=\dfrac{5}{5}+\dfrac{1}{5}[/tex]

[tex]\dfrac{6}{5}=1+\dfrac{1}{5}[/tex]

Therefore, the given fraction [tex]\dfrac{6}{5}[/tex] can be written as [tex]1+\dfrac{1}{5}[/tex].

The given fraction is [tex]\dfrac{11}{7}[/tex].

[tex]\dfrac{11}{7}=\dfrac{7+4}{7}[/tex]

[tex]\dfrac{11}{7}=\dfrac{7}{7}+\dfrac{4}{7}[/tex]

[tex]\dfrac{11}{7}=1+\dfrac{4}{7}[/tex]

Therefore, the given fraction [tex]\dfrac{11}{7}[/tex] can be written as [tex]1+\dfrac{4}{7}[/tex].

The given fraction is [tex]\dfrac{21}{4}[/tex].

[tex]\dfrac{21}{4}=\dfrac{20+1}{4}[/tex]

[tex]\dfrac{21}{4}=\dfrac{20}{4}+\dfrac{1}{4}[/tex]

[tex]\dfrac{21}{4}=5+\dfrac{1}{4}[/tex]

Therefore, the given fraction [tex]\dfrac{21}{4}[/tex] can be written as [tex]5+\dfrac{1}{4}[/tex].

Answer:

x = 45

Step-by-step explanation:

2x + 6 and 96 are vertically opposite angles and are congruent , then equation is

2x + 6 = 96 ( subtract 6 from both sides )

2x = 90 ( divide both sides by 2 )

x = 45

Answer:

False

Step-by-step explanation:

right!!

Answer:

J is the answer ............

Answer:

The answer is G.

Step-by-step explanation:

The MIRR statistic for the project I given the cost of capital and the reinvestment rate, is 7. 43 %.

A monetary indicator of an investment's allure is the modified internal rate of return or MIRR. Ranking equivalent alternative investments is done in capital budgeting.

You can use a spreadsheet to find the MIRR by first ordering the cash flows as shown in the attached image. Then use the = MIRR function.

The cost of capital is the finance charge which is 11 %. The reivestment rate will be the same as the finance charge if not given so it will be 11 % as well.

The MIRR is therefore 7 .43 %.

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Answer:

0 1 2 3

Step-by-step explanation:

Since n is an integer

We have n = { 0 1 2 3 }

Answer:

40.5

I hope u get a good mark glll

Step-by-step explanation:

Answer:

y -7 = -4(x + 2)   (Answer D)

Step-by-step explanation:

The general point-slope equation is y - k = m(x - h)

If the slope, m, is -4, and the point is (h, k) with h = -2 and k = 7), then we have in this case

y -7 = -4(x + 2)   (Answer D)

Answer:

A

Step-by-step explanation:

If the dice are fair and 6 sided then you can roll a 4 in three ways

2    2

1     3

3    1

The total number of ways you can throw two 6 sided dice is 6 * 6 or 36

So P(4) = 3/36 = 1/12

Answer:

0.135%

Step-by-step explanation:

Given :

Mean, m = 60

Standard deviation, σ = 5

x = 45

The Zscore = (x - m) / σ

Z = (45 - 60) / 5 = - 15 / 5 = - 3

P(Z < - 3) = 0.0013499

0.0013499 * 100%

= 0.13499%

Only about 0.135% scored below 45

the formula for volume of sphere is 4/3||r^3

diameter=2radius

in the formula we need to have radius but we have been given diameter so we convert diameter to radius

d=2r

r=d/2

9.5÷2

4.75

Answer:

The expression 56 with a variable of -1 is not well defined. The term 56 is a constant number, and the variable of -1 is also a constant. Therefore there is nothing to evaluate.

Step-by-step explanation:

If you want to evaluate the expression 56*(-1) it would give -56 as output because -1 is a scalar and multiplying with a scalar will change the sign of the constant 56 but it won't change its value.

In other words, to evaluate an expression, it needs to have a mathematical operation or function, operands, and/or variables that can be replaced with values or expressions. Without any operation, there's nothing to evaluate.

Answer:

The domain is the set of numbers that the x value can be.

In an equation like  the domain is all real numbers because x can be any number.

In the case of , any x value that is less than or equal to -4 will not work because you would be taking the square root of a negative number, which doesn't work unless you're graphing on a complex plane, which I assume you aren't.

Thus, the domain is

I hope that helps!

Step-by-step explanation:

The equation system is appropriately described by the formula 4x - y=6.A mathematical formula known as an equation combines two assertions .

A mathematical formula known as an equation combines two assertions using the equal sign (=) to denote equivalence. The terms 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14, for example. Mathematical equations are used to express the relationship between two phrases on either side of a letter. In most cases, the symbol serves as the sole variable. a good example is 2x - 4 = 2.

given

Graphing, substitution, and elimination are the three techniques used to solve systems of equations.

By graphing the given equations, you can easily solve a system by finding the point(s) where they all cross.

The values of the variables you are solving for will be provided by the coordinate of this point.

The equation system is appropriately described by the formula 4x - y=6.

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Answer:

(1, -4), (4, -1)

Step-by-step explanation:

A solution to a system of equations is when the two lines intersect. In this case, we have two intersections, which means two solutions.

From left to right, we first see an intersection at (1, -4).

Continuing to the right, we see another intersection at (4, -1)

These are our two solutions.

(1, -4), (4, -1)

Hope this helps!

Answer:

50.24=4squared times pie

Step-by-step explanation:

Answer:

The area of a circle with a diameter of 0.8 meters is approximately 0.50 [tex]m^2[/tex].

Step-by-step explanation:

Since the diameter of the circle is 0.8 meters, that means the radius of the circle would be 0.4 meters. The area of a circle can be found by the formula [tex]\pi r^2[/tex], where [tex]r[/tex] represents the radius of the circle. In this case, the area would be [tex]0.4^2*\pi[/tex] = [tex]0.16 * \pi[/tex] ≈ 0.50 [tex]m^2[/tex].

The blank spaces of the statement coefficient: The number in BLANK of the variable within the BLANK BLANK are, front, addition, subtraction.

A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it.

Terms that have the same variables raised to the same power are referred to as like terms. The only difference is in the numerical coefficients.

We know a coefficient is a constant value combined with a variable.

For example, In 7x the coefficient of x is 7.

Given, A fill-in-the-blank statement,

coefficient: The number in BLANK of the variable within the BLANK BLANK.

Therefore,

coefficient: The number in front of the variable within the addition subtraction.

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Answer:

the value of x that will make A||B is 4

Answer:

  See attached

Step-by-step explanation:

You want various combinations of the functions g(a) = -3a+1 and h(a) = 3a³ +4a.

The functions have no common factors, so their ratio leaves the function expressions unchanged:

  [tex]\dfrac{g(a)}{h(a)}=\boxed{\dfrac{-3a+1}{3a^3+4a}}[/tex]

The like terms are combined when the functions are added.

  [tex]h(a)+g(a)=(3a^3+4a)+(-3a+1)=3a^3+(4-3)a+1\\\\=\boxed{3a^3+a+1}[/tex]

Similarly, the like terms are combined when the functions are subtracted.

  [tex]g(a)-h(a)=(-3a+1)-(3a^3+4a)=-3a^3+(-3-4)a+1\\\\=\boxed{-3a^3-7a+1}[/tex]

The product is found the way products are usually found. Each term of one of the factors is multiplied by each term of the other factor, and these products are summed. You can think of it as repeated application of the distributive property.

  [tex]g(a)\cdot h(a)=(-3a+1)(3a^3+4a)=-3a(3a^3+4a)+1(3a^3+4a)\\\\=-9a^4-12a^2+3a^3+4a\\\\=\boxed{-9a^4+3a^3-12a^2+4a}[/tex]