If the probability of drawing an ace from a deck of cards is 0.077 and the probability of rolling a "2" using a fair die is 0.167, then the probability of drawing an ace and rolling a "2" is

663/3 = 21

21 is the middle number,

21+1 = 22

21-1 = 20

20 + 21 + 22 = 63

Our three consecutive integers can be represented as

X → first integer

X + 1 → second integer

X + 2 → third integer

If the sum of our three consecutive integers is 63, our equation will read...

X + X + 1 + X + 2 = 63

Now, we can simplify on the left. Once we simplify, our equation will now read

3x + 3 = 63

      -3    -3  ← subtract 3 on both sides

  3x = 60 ← divide both sides by 3

   X = 20

Our three consecutive integers can be represented as

X → first integer = 20

X + 1 → second integer = 21

X + 2 → third integer = 22

Therefore, the three consecutive integers are 20, 21, and 22.

Answer:

18.2

Step-by-step explanation:

The woman should have paid \$64 for the regular price of the merchandise.

To find out what the woman should have paid for the regular price, we need to reverse engineer the discount. Here's the step-by-step calculation:

Calculate the Discount Amount: Since the sale is 1/4 off, the discount is 1/4 of the regular price. So, the discount is:

[tex]\[ \frac{1}{4} \times \text{Regular Price} \][/tex]

[tex]\[ \text{Discount} = \frac{1}{4} \times \text{Regular Price} \][/tex]

Subtract the Discount from the Regular Price to Get the Sale Price: The sale price is the regular price minus the discount:

[tex]\[ \text{Sale Price} = \text{Regular Price} - \text{Discount} \][/tex]

Calculate the Sale Price: We know the woman bought $48 worth of merchandise at the sale price, so:

[tex]\[ \text{Sale Price} = \$48 \][/tex]

Find the Regular Price: Now we can set up an equation using the information we have:

[tex]\[ \$48 = \text{Regular Price} - \text{Discount} \][/tex]

Substituting the discount calculated earlier:

[tex]\[ \$48 = \text{Regular Price} - \left(\frac{1}{4} \times \text{Regular Price}\right) \][/tex]

Solve for the Regular Price:

[tex]\[ \$48 = \left(\frac{4}{4}\right) \times \text{Regular Price} - \left(\frac{1}{4}\right) \times \text{Regular Price} \][/tex]

[tex]\[ \$48 = \left(\frac{3}{4}\right) \times \text{Regular Price} \][/tex]

To isolate the regular price, multiply both sides by [tex]\( \frac{4}{3} \)[/tex]:

[tex]\[ \text{Regular Price} = \$48 \times \frac{4}{3} \][/tex]

[tex]\[ \text{Regular Price} = \$64 \][/tex]

So, the woman should have paid $64 for the regular price of the merchandise.

Complete Question:

The dress store is having a sale where all merchandise is 1/4 off a woman buys $48 of merchandise at the sale price what should she have paid for the regular price

Option B, spinning "back 2 spaces" on a spinner, describes a simple event as it represents a single outcome from the experiment, in contrast to the other options which describe compound events.

A simple event is an event that consists of a single outcome of an experiment. When tossing a coin 5 times and getting heads twice, we're looking at a compound event because it involves a combination of outcomes. In the options given, option B, spinning "back 2 spaces" on a spinner represents a simple event because it describes a single outcome that can occur from the experiment. The other options involve multiple outcomes or combinations and are therefore not simple events.

Considering the additional information provided:
Coin tosses and the outcomes of 5 coin tosses just give us a set of possible results which help illustrate compound events. The idea of grouping real world observations into outcomes or events shows us that a simple event is a single, specific outcome, such as getting an even number when rolling a die, which can be defined as an event with a single characteristic and has a calculable probability.

The sum of the geometric series is approximately 324.

The sum of a geometric series can be found using the formula:

Sn = a1(1 - rn) / (1 - r)

Where Sn is the sum of the series, a1 is the first term, r is the common ratio, and n is the number of terms.

Plugging in the given values, we have:

Sn = 4(1 - 3n) / (1 - 3)

Now we can solve for n by plugging in the given value of an:

324 = 4(1 - 3n) / (1 - 3)

Cross-multiplying and simplifying:

324(1 - 3) = 4(1 - 3n)

324 - 972 = 4 - 12n

-648 = -8n

Dividing both sides by -8, we get:

81 = 2n

Taking the logarithm base 2 of both sides:

n = log2(81)

Using a calculator, we find that n is approximately 6.3398.

Now we can plug this value back into the formula:

Sn = 4(1 - 36.3398) / (1 - 3)

Simplifying further:

Sn ≈ -648 / -2

Sn ≈  324

Answer:

(x+3)(x-8)

Step-by-step explanation:

To solve the given system of equations using substitution, we'll start by solving the first equation for x in terms of y. We'll substitute this expression for x in the other two equations to find the values of y and z.

To solve the given system of equations using substitution, we'll start by solving the first equation for x in terms of y: x = -2y + 10. We'll substitute this expression for x in the other two equations to find the values of y and z. Substituting -2y + 10 for x in the second equation, we have -6y = 6(-2y + 10) - 6.

Simplifying this equation, we get y = -2. Substituting y = -2 in the first equation, we find x = -2*(-2) + 10 = 14. Finally, substituting x = 14 and y = -2 in the third equation, we find z = -3*14 + 10*(-2) = -52.

The equivalent equation solving for volume is v = mass/density

Data;

The density of an object can be calculated using the formula

[tex]density = \frac{mass}{volume}[/tex]

Making the volume the subject of formula here

[tex]density = \frac{mass}{volume}\\ volume = \frac{mass}{density}[/tex]

The equivalent equation solving for volume is v = mass/density

Learn more on density here;

https://brainly.com/question/25693692

Answer:29.15475947 (not rounded)

Step-by-step explanation:

the men can be arranges in 5! ways

 and the women in 5! ways

so (5*4*3*2) = 120

120 *120 = 14,400 ways

The coordinates of the midpoint M, point A, and point C in the rhombus can be found using formulas. The coordinates of M are (4, 6), the coordinates of A are (0, 0), and the coordinates of C are (4, 2).

To find the coordinates of the midpoint of BD, we can use the midpoint formula:

M = ( (x1+x2)/2, (y1+y2)/2 )

Substituting the coordinates of B and D into the formula, we get:

M = ( (2+6)/2, (10+2)/2 )

Simplifying, we get:

M = (4, 6)

Since A lies on the x-axis, its y-coordinate is 0. Therefore, the coordinates of A are:

A = (0, 0)

To find the coordinates of C, we can use the fact that a rhombus has opposite sides equal in length and parallel. Since B and D have the same y-coordinate, the y-coordinate of C will also be the same. The x-coordinate of C will be the average of the x-coordinates of B and D. Therefore, the coordinates of C are:

C = ( (2+6)/2, 2 )

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