Put the events in order of what is most likely to happen, to least likely to happen. If you were to win a million dollars for winning one of these events, which would you pick to play? Use probability to explain your answers.

Winning the Lottery: If the six numbers on the lottery ticket match the six numbers drawn, then you win. The numbers can range from 1-49.
Rolling a 7: Roll two dice numbered 1-6 then add the numbers that are face up to get 7.
Drawing the Ace of Spades: In a deck of 52 cards, what is the likelihood of drawing the Ace of Spades in one try.
2 Heads in a Row: Using a coin with a heads-side and tails-side, what is the likelihood of flipping a heads twice in a row?
Marbles: You have a bag with 3 red marbles, 4 blue marbles, and 5 green marbles. What is the probability of pulling out a red marble 3 times in a row, assuming you put each marble back into the bag before drawing another?

The number of solutions to the system is 1

A linear equation is a equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

y = 4x + 8

4y = 4x - 8

Substitute y = 4x + 8 in 4y = 4x - 8

4(4x + 8) = 4x - 8

Expand the equation

16x + 32 = 4x - 8

Evaluate the like terms

12x = - 40

Divide by 12

x = -10/3

The above means that the number of solutions to the system is 1

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The factor of such equation described as having the number 3 as a root can be determined as; (x-3).

It follows from the task content that; we are required to determine a possible factor of a polynomial in the event that such polynomial has a root of 3.

The implication of a polynomial having a root of 3 is that; such a polynomial has 3 to be one of it's zeros.

Hence, a linear equation which holds for such polynomial is that; x = 3 and when expressed as a linear factor, the linear factor is; (x-3).

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Hello,

The triangle be right only if : 18² = 8² + 12²

We have : 18² = 18 × 18 = 324

and 8² + 12² = 8 × 8 + 12 × 12 = 208

324 ≠ 208 → the triangle can not be a right triangle

Answer:

  x = 3

Step-by-step explanation:

Maybe you want the value of x such that ...

  4(6^x) = 864

Dividing by 4 gives ...

  6^x = 216

You may know that 216 = 6^3. Using that, we can equate exponents:

  6^x = 6^3

  x = 3

Alternatively, we can use logarithms to find x. Taking logs gives ...

  x·log(6) = log(216)

  x = log(216)/log(6) = 3

Step-by-step explanation:

First thing first, let find the x value of where P and Q both meet y=5, we know that y=5, and y=2x^2+7x-4, so using transitive law,

[tex]5 = 2 {x}^{2} + 7x - 4[/tex]

[tex]2 {x}^{2} + 7x - 9[/tex]

[tex]2 {x}^{2} - 2x + 9x - 9[/tex]

[tex]2x(x - 1) + 9(x - 1)[/tex]

[tex](2x + 9)(x - 1) = 0[/tex]

[tex]x = 1[/tex]

[tex]2x + 9 = 0[/tex]

[tex]x = - \frac{9}{2} [/tex]

Now, to find the gradient of the curve let take the derivative of both sides

[tex]5 = 2 {x}^{2} + 7x - 4[/tex]

[tex]0 = 4x + 7[/tex]

[tex]4x + 7[/tex]

Plug in -9/2, let call that point P

[tex]4( \frac{ - 9}{2} ) + 7 = - 11[/tex]

Plug in 1, let call that point Q

[tex]4(1) + 7 = 11[/tex]

So the gradient of the curve at point P (-9/2,5) is -11

The gradient of the curve at point Q (1,5) is 11.

Answer:

21

Step-by-step explanation:

(-4)(-2)+2(6+5)

(8)+2(11)

10+11

21

Hope this helps! :)

Answer:32

Step-by-step explanation: First, we do parentheses. 6+5 = 11. Next, we have to do multiplication (-4)(-2) is positive 8 because there are two negatives. 8+2 is 10 + 2(11) is 10+22 which is 32

The angles in degrees to radian is as follows:

-54 degrees = -3π / 10 radian

The measurement is in degrees. Let's convert it to radian with respect to π.

Therefore,

180 degrees = π radian

-54 degrees = ?

cross multiply

Hence,

angle in radian = -54 × π / 180

angle in radian = - 54π / 180

angle in radian = - 6π / 20

angle in radian = -3π / 10 radian

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Hello and Good morning/afternoon:

Let's take this problem step-by-step:

What does the problem want:

 ⇒ unit rate ⇒ price per gallon

What does the problem give us:

  ⇒ price of all three milk

  ⇒ number of gallons of milk bought

Therefore

   [tex]\hookrightarrow \text {unit rate} = \text{total amount of money spent} / \text {total amount of milk bought}\\\\\hookrightarrow\text{unit rate} = 9.75 / 3 = 3.25 _. \text {dollar per gallon}[/tex]

Answer: 3.25 dollars per gallon

Hope that helps!

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The cost of goods sold using LIFO is $99.

Using this formula

Cost of goods sold=(March 3 Purchased units × March 3 Purchase price)+ [(March 3 Purchased units -March 9 sold units)×March 1 Beginning inventory cost]

Let plug in the formula

Cost of goods sold=(15 units×$3.90)+[(22 units-15 units)×$5.80]

Cost of goods sold=$58.5+(7 units×$5.80)

Cost of goods sold=$58.5+$40.6

Cost of goods sold=$99.1

Cost of goods sold=$99 (Approximately)

Therefore the cost of goods sold using LIFO is $99.

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The factor of given expression is 6(5-v-3w) and 2(15-3v-9w). correct option is c and d.

Given that factor 30-6v-18w.

Equivalent expressions are expressions that work the same way, even if they look different. If two algebraic expressions are equivalent, the two expressions have the same value if we enter the same values ​​for the variables.

For option A

Factor the expression:

2(15-2v)≠6(5-v-3w)

get the result: False

Answer: False

For option B

Factor the expression:

3(10-3v+6w)≠6(5-v-3w)

get the result: False

For option C

Factor the expression:

6(5-v-3w)=6(5-v-3w)

get the result: True

For option D

Factor the expression:

6(5-v-3w)=2(15-3v-9w)

get the result: True

Hence, the equivalent expression of the factor 30-6v-18w is 6(5-v-3w) and 2(15-3v-9w).

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Answer:

38°

Step-by-step explanation:

EFGH is an isosceles trapezoid (a trapezoid with two congruent legs is isosceles)

∠HGF=70° (base angles of an isosceles trapezoid are congruent)

∠EGH=32° (angles in a triangle add to 180°)

∠FGE=38° (angle subtraction postulate)

Answer:

x=3/2 y=1/2

Step-by-step explanation:

there are two expressions that can represent the length of the rectangle, these two expressions are:

L = x

or

L = (4x + 12)

Remember that for a rectangle of length L and width W, the area is given by:

A = L*W

In this case, we know that the area is:

[tex]A = 4x^2 + 12x[/tex]

We can factorize that expression into:

[tex]A = x*(4x + 12)[/tex]

So there are two expressions that can represent the length of the rectangle, these two expressions are:

L = x

or

L = (4x + 12)

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Answer:

36

Step-by-step explanation:

[tex]\sqrt{24a}=12\sqrt{6} \\ \\ 24a=864 \\ \\ a=36[/tex]

Answer 1:

1.23456789 × (10-6) = 4.93827156

Answer 2:

(1.23456789 × 10) - 6 = 6.3456789

Answer 3:

1.23456789 × [tex]10^{-6}[/tex] = 0.000000123456789

Hope this helped! :)

The probability of obtaining a success is 0.010935.

Given that the probability of obtaining success is P(X>=5),n=6,p=0.3.

We are required to find the probability of obtaining a success if the probability is P(X>=5).

Probability is basically likeliness of happening an event among all the events possible.

Binomial distribution is basically the discrete probability distribution of the number of successes in a sequence of n independent experiments.

[tex](a+b)^{n} =nC_{0}p^{0} (1-p)^{n-0}+-----------nC_{n} p^{n} (1-p)^{0}[/tex]

We have to just put n=6 anr r=6 and 5 one by one to get the probability.

P(X>=5)=[tex]6C_{5}(0.3)^{5} (0.7)^{1} +6C_{6}(0.3)^{6} (0.7)^{0}[/tex]

=6!/5!1!8*0.00243*0.7+0.000729

=6*0.00243*0.7+0.000729

=0.010206+0.000729

=0.010935

Hence the probability of obtaining a success if the probability is P(X>=5) is 0.010935.

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Essentially just count the tick marks between the two letters.

JL= 5

JK= 3

KP= 9

NP= 2

JP= 12

LN= 5

The asked lengths are from the number line:

JK = 3, JL = 5, KP = 9, NP = 2, JP = 12 and LN = 5.

Given that is a number line we need to find the asked values,

1. JK =

K = -4 and J = -7

So, JK = -4-(-7)

JK = -4+7

JK = 3

2. JL =

J = -7 and L = -2

So, JL = -2-(-7)

JL = -2+7

JL = 5

3. KP =

K = -4 and P = 5
So, KP = 5-(-4)

KP = 9

4. NP =

N = 3 and P = 5

So, NP = 5-3

NP = 2

5. JP =

J = -7 and P = 5

So, JP = 5-(-7)

JP = 12

6. LN =

L = -2 and N = 3

So, LN = 3-(-2)

LN = 5

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Step-by-step explanation:

x = number of heavy equipment operators

y = number of general laborers

x + y = 37 (37 people were hired)

out if this we get e.g.

x = 37 - y

124x + 82y = 3916 (daily rate for each role, in total 3916)

now we use the first equation in the second :

124(37 - y) + 82y = 3916

4588 - 124y + 82y = 3916

672 - 42y = 0

672 = 42y

y = 16

x = 37 - y = 37 - 16 = 21

21 heavy equipment operators were hired.

16 general laborers were hired.

The constant of proportionality between the cost and the number of pounds is: A. 0.59.

The constant of proportionality of a relationship between two variables X and Y can be defined as the ratio between of X and Y at a constant value. This means that the ratio or product of X and Y will give us a constant if both are in a proportional relationship.

Thus, the constant of proportionality for the  relationship between two variables X and Y would be calculated as:

Constant of proportionality (k) = Y/X. [this is the proportional between the two quantities, X and Y].

Given the table of values, using a pair of points on the table, say, (5, 2.95), we can calculate the constant of proportionality as:

X = 5

Y = 2.95

Constant of proportionality (k) = Y/X = 2.95/5

Constant of proportionality (k) = 0.59 pounds per dollar.

Therefore, the constant of proportionality between the cost and the number of pounds is: A. 0.59.

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The detail  Description on how to create a number line with the above  points is given below:

Note that we were given the following: points 4, 1, 25, and opposite of 2. The step to take  to First draw on Number Line.

Since Numbers with a negative sign are known to be less than zero ( Right of zero is shown by ‘+’ sign and to the left of zero is shown by ‘–’ sign while the + sign numbers can be depicted as simply numbers)

Then:

Therefore, The detail  Description on how to create a number line with the above points given above is correct:

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Answer:

[tex]t = \cfrac{1}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]4(t+\cfrac{1}{4})=3[/tex]

Divide both sides by 4:

[tex]t+\cfrac{1}{4}=\cfrac{3}{4}[/tex]

Subtract 1/4 from both sides:

[tex]t = \cfrac{3}{4}- \cfrac{1}{4}[/tex]

[tex]t = \cfrac{2}{4}[/tex]

Simplify:

[tex]t = \cfrac{1}{2}[/tex]

Answer:

[tex]t = \frac{1}{2} [/tex]

Step-by-step explanation:

[tex]4(t + \frac{1}{4} ) = 3[/tex]

Divid the whole equation by 4.

[tex] \frac{4(t + \frac{1}{4} )}{4} = \frac{3}{4} [/tex]

[tex](t + \frac{1}{4} ) = \frac{3}{4} [/tex]

[tex]t + \frac{1}{4} = \frac{3}{4} [/tex]

Take 1/4 to right side.

[tex]t = \frac{ 3}{4} - \frac{1}{4} [/tex]

[tex]t= \frac{2}{4} [/tex]

To simplify the answer more divide the numerator and denominator by 2.

[tex]t = \frac{1}{2} [/tex]

The total product cost per unit.

TPC= $33

This is further explained below.

Generally, The direct materials cost per unit, the direct labor cost per unit, the variable overhead cost per unit, and the fixed overhead cost per unit make up the total product cost per unit.

The total costs of the product may be calculated by adding up the costs of all of the direct materials, all of the direct labor and all of the overhead expenses of the production process. 1 Information such as the cost of manufacturing on a per-unit basis may assist a company in determining an acceptable selling price for the final product.

Generally, the equation for total product cost per unit. is  mathematically given as

TPC= 20 + 10 + 2 + 1

TPC= $33

In conclusion, the total product cost per unit.

TPC= $33

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Answer:

$33

Step-by-step explanation:

Answer:

  |-3| = 3 and -|-4| = -4

Step-by-step explanation:

The absolute value function changes the sign to positive, if it isn't already. The usual rules of arithmetic and logic apply to these statements.

|-3| = 3 (true) and -|-4| = -4 (true)   ⇒ this statement is true

|-3| = 3 (true) and |-4| = -4 (false)   ⇒ this statement is false

-|3| = 3 (false) and |4| = 4 (true)   ⇒ this statement is false

|-3| = 3 (true) and -|4| = 4 (false)   ⇒ this statement is false

__

Additional comment

A compound "and" statement is only true if all of the parts of it are true.

Answer:

[tex]s=\frac{u}{r} -\frac{t}{r}[/tex]

Step-by-step explanation:

You have to move the variables (r and t) with u to isolate s.

[tex]rs+t=u[/tex]

   [tex]-t[/tex]       [tex]-t[/tex]

------------------------

[tex]rs=u-t[/tex]

÷ [tex]r[/tex]       ÷ [tex]r[/tex]

------------------------

[tex]s=\frac{u}{r} -\frac{t}{r}[/tex]

Divide the interval [3, 5] into [tex]n[/tex] subintervals of equal length [tex]\Delta x=\frac{5-3}n = \frac2n[/tex].

[tex][3,5] = \left[3+\dfrac0n,3+\dfrac2n\right] \cup \left[3+\dfrac2n,3+\dfrac4n\right]\cup\left[3+\dfrac4n,3+\dfrac6n\right]\cup\cdots\cup\left[3+\dfrac{2(n-1)}n, 3+\dfrac{2n}n\right][/tex]

The right endpoint of the [tex]i[/tex]-th subinterval is

[tex]r_i = 3 + \dfrac{2i}n[/tex]

where [tex]1\le i\le n[/tex].

Then the definite integral is given by the Riemann sum

[tex]\displaystyle \int_3^5 \sqrt{8+x^2} \, dx = \lim_{n\to\infty} \sum_{i=1}^n \sqrt{8+{r_i}^2} \Delta x = \boxed{\lim_{n\to\infty} \frac2n \sum_{i=1}^n \sqrt{17 + \frac{12i}n + \frac{4i^2}{n^2}}}[/tex]

The critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881

The scatter plot of the election is added as an attachment

From the scatter plot, we have the following highlights

Start by calculating the degrees of freedom (df) using

df =n - 2

Substitute the known values in the above equation

df = 8 - 2

Evaluate the difference

df = 6

Using the critical value table;

At a degree of freedom of 6 and significance level of 0.01, the critical value is

z = 0.834

From the list of given options, 0.834 is between  -0.881 and 0.881

Hence, the critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881

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