Find a formula for the inverse of the function, f(x)= 8-3/x^2, x>0. Explain if you can.

To guarantee two pairs, a player must pick at least 14 cards from a deck of 52 playing cards without replacement. For three of a kind, a minimum of 16 cards is required. This is an example of sampling without replacement, where each selection affects subsequent draws.

To determine the minimum number of cards one must pick from a standard deck of 52 playing cards to guarantee getting two pairs, consider the worst-case scenario where you pick one card of each rank before getting any pair. Since there are 13 different ranks, picking 13 single cards wouldn't guarantee a pair, but the 14th card will definitely match one of the previously drawn ranks, thus forming a pair. To ensure two pairs, you could go through another 13 cards without getting a match to your first pair, so the 15th card would be the second pair. Therefore, you must pick at least 14 cards to guarantee two pairs.

For three of a kind, you pick sequentially from the different ranks. After picking one card of each of the 13 ranks, the 14th card will form a pair, and the 15th card could potentially be of a new rank. However, the 16th card drawn must either create a pair with another rank or a 'three of a kind' with the rank that already has two. Thus, the minimum number of cards one must pick to guarantee a three of a kind is 16.

In sampling without replacement, drawn cards are not returned to the deck, making each draw dependent on the previous ones. This contrasts with sampling with replacement, where each draw is independent since cards are returned to the deck and reshuffled after each pick.

The probability that fewer than 7 field mice are found in the 5-acre field is 0.0458.

The probability that fewer than 7 field mice are found in the entire 5-acre field is not simply 58.10% multiplied by 5. This is because the mice are not independent on each other. The number of mice on one acre doesn't affect the number found on another.

To find the probability for the entire field, we need to consider all possible combinations of the number of mice on each acre. This can be a complex calculation involving multiple Poisson distributions.

However, if we assume that the distribution of mice across the field is approximately uniform, we can use a simpler approach. We can assume that the probability of finding fewer than 7 mice on each acre is independent of the others and multiply the individual probabilities:

P(total < 7) ≈ (0.5810)^5 ≈ 0.0458

Therefore, under the assumption of approximate uniformity, the probability of finding fewer than 7 field mice in the entire 5-acre field is approximately 0.0458%.

Complete question:

The average number of field mice per acre in a 5-acre wheat field is estimated to be 12. find the probability that fewer than 7 field mice are found on a given acre that is 5.

Mr. Brown should increase the monthly rent by $2.25 to cover the additional annual property tax caused by the tax rate increase from $25 to $28 per $1000 assessed valuation on a $9000 house.

The student is asking for a calculation of how much the monthly rent of a house should be increased to cover the additional property tax imposed when the tax rate was increased from $25 to $28 per $1000 assessed valuation. The house is valued at $9000.

First, we calculate the initial annual tax by multiplying the assessed valuation by the initial tax rate:

Initial annual tax = $9000 / 1000 times $25 = $225

Then we calculate the new annual tax with the increased rate:

New annual tax = $9000 / 1000 times $28 = $252

The increase in the annual tax amount is:

Increased tax amount = New annual tax - Initial annual tax = $252 - $225 = $27

To find the monthly increase, we divide by 12:

Monthly rent increase = Increased tax amount / 12 = $27 / 12 = $2.25

Therefore, the monthly rent should be raised by $2.25 to absorb the increase in that year's taxes.

Answer:

Here you go!

Step-by-step explanation:

estimating wage to nearest dollar would be 22 x 40

 would be 22 x 4 = 88 so 880 per week

estimating 50 weeks

88 x 5 = 440 so 44,000 per year

 exact would be 21.50 x 40 = 860 per week

860 x 52 = 44,720 per year

Answer:

Total length of the biking trail is 14 units

Step-by-step explanation:

The trail starts from point P(-3, 2) and touches points Q(1, 2), R(1, -1) and S(8, -1).

We have to calculate the total length of the biking trail.

Since distance between two points are represented by

d = [tex]\sqrt{(x-x')^{2}+(y-y')^{2}}[/tex]

So length of PQ = [tex]\sqrt{(1+3)^{2}+(2-2)^{2}}[/tex]

PQ = [tex]\sqrt{(4)^{2}}[/tex]

PQ = 4 units

QR = [tex]\sqrt{(1-1)^{2}+(2+1)^{2}}[/tex]

QR = [tex]\sqrt{(3)^{2}}[/tex]

QR = 3 units

RS = [tex]\sqrt{(8-1)^{2}+(-1+1)^{2}}[/tex]

RS = [tex]\sqrt{(7)^{2}}[/tex]

RS = 7 units

Now total biking trail = PQ + QR + RS

= 4 + 3 + 7

= 14 units

Total length of the biking trail is 14 units

Answer:

The answer is 14 units

Step-by-step explanation:

There are 4500 four-digit even numbers possible when the leftmost digit cannot be a zero.

The question is about finding out the number of four-digit even numbers possible given that the first or leftmost digit cannot be a zero. In a four-digit even number, the last digit (rightmost) should be an even number, i.e., 0, 2, 4, 6, or 8. Hence, there are 5 possibilities for the last digit.

Next, since the leftmost digit cannot be a zero, it leaves us with 9 possibilities (1-9). Lastly, the middle two digits can be any digit from 0 to 9, so there are 10 possibilities each for the second and third digits.

Therefore, the total number of four-digit even numbers under the given conditions is found by multiplying these possibilities: 9 (for the first digit) * 10 (for the second digit) * 10 (for the third digit) * 5 (for the last digit) = 4500.

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To find the number of four-digit even numbers where the leftmost digit cannot be zero, there are 9000 possibilities.

To find the number of four-digit even numbers where the leftmost digit cannot be zero, we need to consider the following:

By multiplying the number of choices for each position, we get the total number of four-digit even numbers without leading zeros: 9 * 10 * 10 * 10 = 9000.

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4 * 1.5 = 6 cm <== Because this is the answer.

42/3 = 14

14-1=13

14+1= 15

13+14+15 = 42

 3 numbers = 13, 14 & 15

The relationship of the two of the same digits that are next to each other in a multi-digit number lies in their place value, wherein the digits from the decimal point that is to the left, is 10 times of larger value compared to the digit in their left. And from the decimal point to the right, it is 10 times of small value that the digit in their right.

Let’s see an example:

123.45, wherein 1 is hundreds, two is tens, 3 is ones, and then after the decimal points, is where 4 is the tenths and 5 is the hundredths.

Take note of each place value that is next to each other since each value is 10 times in difference.

1/6 = 1/2 hr

2/6 = 1 hr

6/6-1/6 = 5/6 left of the test

2/6 + 2/6 = 4/6 = 2 hours

4/6 + 1/6  = 2 + 1/2 = 2 1/2

 so 2 1/2 more hours

At the 25,000 salary scale, the options yield will be the same salary the answer is 25,000.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

Your employer offers you a choice of wage scales:

A monthly salary of $2800 plus a commission of 8% of sales or

A salary of $3300 plus a 6% commission.

First choice of wage scale:

= 2800 + 0.08s

Second choice of wage scale:

= 3300 + 0.06s

2800 + 0.08s = 3300 + 0.06s

0.08s - 0.06s = 3300 - 2800

0.02s = 500

s = 25,000

Thus, at the 25,000 salary scale, the options yield will be the same salary the answer is 25,000.

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The given expression [tex]\rm x^3\times x^2[/tex] can be reduced to [tex]\rm x^5[/tex] and this can be determined by using the arithmetic operations.

Given :

Expression  --  [tex]\rm x^3\times x^2[/tex]

The following steps can be used in order to evaluate the given expression:

Step 1 - The arithmetic operations can be used in order to evaluate the given expression.

Step 2 - Write the given expression.

[tex]= \rm x^3\times x^2[/tex]

Step 3 - According to the arithmetic operation if a variable 'a' is multiplied by the same variable 'a' then the expression becomes [tex]\rm a^2[/tex].

Step 4 - Applying the property mentioned in the above step in order to evaluate the given expression.

[tex]x^2\times x^3=x^5[/tex]

Therefore, the correct option is B).

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The hypotenuse of a right triangle formed by dividing a square cake diagonally can be found using the Pythagorean Theorem, with the shortcut that the hypotenuse is the side length of the square multiplied by √2. Examples include a hypotenuse of 10√2 inches for a 10-inch square, 8√2 inches for an 8-inch square, 12√2 inches for a 12-inch square, and 15√2 inches for a 15-inch square.

Finding the Hypotenuse of Right Triangles in Squares

To find the length of the hypotenuse in a right triangle that is formed by dividing a square cake diagonally, we use the Pythagorean Theorem which states that for a right triangle with sides a and b and hypotenuse c, the relation is c = √(a ² + b ²). Since the sides of the square are equal in length, for a square with 10-inch sides, the hypotenuse will be √(10 inches ² + 10 inches ²) = √(100 + 100) = √200 inches = 10√2 inches.

For the other square cakes:

8-inch square: Hypotenuse = √(64 + 64) = 8√2 inches

12-inch square: Hypotenuse = √(144 + 144) = 12√2 inches

15-inch square: Hypotenuse = √(225 + 225) = 15√2 inches

The shortcut discovered is that the length of the hypotenuse is always the side length of the square multiplied by √2, because each side of the square forms a right triangle with equal sides when the square is divided diagonally.