if a child is given cards with a, c, d, g, o, and t on them, what is the probability he or she could spell got by guessing the correct arrangement of 3 cards from the 6? (enter your probability as a fraction.)

Answer:

5

Step-by-step explanation:

To evaluate (g ￮ h)(9), evaluate h(9) , then use this value to evaluate g(x)

h(9) = \(\sqrt{9}\) = 3, then

g(3) = 2(3) - 1 = 6 - 1 = 5

Answer: 1kg = 1,000,000mg

Step-by-step explanation:

You know that 1kg = 1,000g

If you know that 1g = 1,000mg,

then it follows that 1,000g = 1,000,000mg

but since 1,000g = 1kg,

you can substitute: 1kg = 1,000,000mg

And theres your answer :)

Calculating this expression will give us the probability that a random sample of 60 households in the town contains exactly 20 households that have 3 or more vehicles.

To solve this probability problem, we need to use the binomial probability formula.

The binomial probability formula calculates the probability of getting a specific number of successes in a fixed number of independent Bernoulli trials.

In this case, the probability of success is 30% (0.30), which represents the probability that a household owns 3 or more vehicles. The probability of failure is 70% (0.70), which represents the probability that a household does not own 3 or more vehicles.

Let's denote X as the number of households in the sample of 60 that have 3 or more vehicles. We want to find the probability that X = 20.

The formula for the probability mass function (PMF) of a binomial distribution is:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the number of combinations of n items taken k at a time (n choose k),

p is the probability of success,

n is the total number of trials,

k is the number of successes.

In our case:

p = 0.30 (probability of success)

n = 60 (total number of trials)

k = 20 (number of successes)

Now, we can calculate the probability:

P(X = 20) = C(60, 20) * (0.30)^20 * (1 - 0.30)^(60 - 20)

Using the combination formula, C(n, k) = n! / (k! * (n - k)!), we can calculate:

P(X = 20) = (60! / (20! * (60 - 20)!)) * (0.30)^20 * (0.70)^40

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The length of the shortest ladder is 16.64 ft.

In triangle ABC, using Pythagoras theorem

\(AC^{2} = AB^{2} + BC^{2}\)  OR

\(L^{2} = h^{2} + (x+4)^{2}\)       .....(1)

We also have similar triangles if we consider:

△ABC and △DEC

Which gives us the proportional relationship:

AB:DE = BC:EC

or    h/8 = (4+x) / x

h = 8( 4+x) /x      

Substituting this last expression for h into Eq [1] we get:

\(L^{2} = \frac{(8(x+4))^{2} }{x^{2} } + (x+4)^{2}\)

Our aim is to now minimize L wrt x, and this involves looking for critical points of the derivative, so differentiation wrt x we get:

\(2L\frac{dL}{dx} = 2( 8 + \frac{32}{x} ) (-\frac{32}{x^{2} } ) + 2(x+4)\)

At a critical point the derivative is zero and so we have the equation:

         =  \(2 (x + 4) ( 1 - \frac{256}{x^{3} } ) = 0\)

From here we can find the value x :

x + 4 = 0                                                            1 - \(\frac{256}{x^{3} }\)  = 0

x = -4                                                                 x  = \(\sqrt[3]{256}\)

We require x > 0 so we neglect the -ve solution and only take +ve solution

therefore the minimum height of the ladder can be given by putting the value of x in eqn 1.

\(L^{2} = ( 8 + \frac{32}{\sqrt[3]{256} } )^{2} + ( \sqrt[3]{256} +4) ^{2}\)

L² = 277.14

L = 16.64 ft

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Answer:

\(8 \geq x + 3\\5 \geq x\)

Step-by-step explanation:

The following equations both represent the problem, with the top showing the inequality exactly as it is explained in the prompt, and the bottom showing the inequality simplified.

Hope it helps :) and let me know if you want me to elaborate.

Answer:

16-25

Step-by-step explanation:

Answer:

16-25 as looking at the bar graph!!

The number of elements in the sample space for this experiment is 969.

If a person eating at a cafeteria must choose 3 of 19 vegetables on offer, we can calculate the number of elements in the sample space, or the total number of possible outcomes, using the formula for combinations:

nCr = n! / [r!(n - r)!]

where n is the total number of items in the set and r is the number of items being chosen.

In this case, we have 19 vegetables and we want to choose 3 of them, so we can plug in n = 19 and r = 3:

19C3 = 19! / [3!(19 - 3)!]

= 19! / (3!)(16!)

= 969

Therefore, there are 969 possible combinations of 3 vegetables that a person can choose from a selection of 19 vegetables.

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Answer:

8.35,7.94

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

to find the number between you just add the numbers and divide by two , hopefully the image above helps !

let me know if you any more explaining :)

The Cartesian coordinate system is also referred to as a plane because it represents a two-dimensional space.

In mathematics, a plane is a flat surface that extends infinitely in all directions. The Cartesian coordinate system consists of two perpendicular lines, known as the x-axis and y-axis, which intersect at a point called the origin. These axes divide the plane into four quadrants.

The term "plane" in the context of the Cartesian coordinate system originates from the concept of a geometric plane, which is a fundamental concept in Euclidean geometry. In Euclidean geometry, a plane is a flat, two-dimensional surface that extends infinitely in all directions.

The Cartesian coordinate system borrows this concept and applies it to represent points, lines, curves, and shapes in a two-dimensional space.

By using the Cartesian coordinate system, we can assign coordinates (x, y) to any point in the plane, where the x-coordinate represents the horizontal position and the y-coordinate represents the vertical position.

This system allows us to precisely locate and describe objects or phenomena within the two-dimensional space, making it a valuable tool in various fields such as mathematics, physics, engineering, and computer graphics.

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Using linear approximation, we estimate that √65.3 ≈ 47.822, rounded to four decimal places.

To use linear approximation, we need to find the equation of the tangent line to the function f(x) at x=64. Then, we can use this tangent line to approximate the value of f(x) near x=64.

First, let's find the equation of the tangent line to f(x) at x=64. The slope of the tangent line is given by the derivative of f(x) at x=64:

f'(x) = √3/2x^(1/2)

f'(64) = √3/2(64)^(1/2) = √3/2 * 8 = 4√3

Equation of tangent line f(x) at x=64:

y - f(64) = f'(64)(x - 64)

y - 64√3 = 4√3(x - 64)

y = 4√3x - 128√3

Now, we can use this tangent line to approximate f(x) near x=64. We want to estimate √65.3, which is close to x=64. Let's substitute x=65.3 into the equation of the tangent line:

y = 4√3(65.3) - 128√3 ≈ 47.822

Therefore, using linear approximation, we estimate that √65.3 ≈ 47.822, rounded to four decimal places.

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Answer:

Eric is correct; side must be between 4 and 16 inches

Step-by-step explanation:

triangle inequality theorem:

6 + 10 > x;    16 > x

x + 6 > 10;     x > 4

4 < x < 16

Answer:

x≤7

Step-by-step explanation:

Start by solving for x

-12+4x≤16

4x≤28

x≤7

see pic below for the second part

Answer:

Step-by-step explanation:

\( { ({6}^{2} )}^{x} = 1 \\ { ({6}^{2}) }^{x} = {6}^{0} \\ {6}^{2 \times x} = {6}^{0} \\ 2x = 0 \\ x = \frac{0}{2} \\ x = 0 \\ \)

\( {( {6}^{0} )}^{x} = 1 \\ { ({6}^{0} )}^{x} = {6}^{0} \\ {6}^{0 \times x} = {6}^{0} \\ 0 \times x = 0 \\ x = 0\)

Answer:

real part = -302

Imaginary part=19.3i

9514 1404 393

Answer:

  12/11 = 1 1/11 hours

Step-by-step explanation:

The total rate is the sum of the individual rates in rooms per hour.

Tom can paint 1/4 room per hour.

Sam and Victor can each paint 1/3 room per hour.

Their total rate is ...

  1/4 +1/3 +1/3 = 11/12 . . . rooms per hour

The rate in "hours per room" is the inverse of this.

It takes them 12/11 = 1 1/11 hours to paint one room.

Answer:

firstly read the length of the arc then

center angle=l/r

=1/6

=6

Answer:

8 buses

Step-by-step explanation:

Find the total number of people going on the trip by adding the number of students and the number of chaperones:

Total number of people = Number of students + Number of chaperones

= 324 + 32

= 356

Divide the total number of people by the capacity of each bus to find the number of buses needed:

Number of buses needed = Total number of people / Bus capacity

= 356 / 48

≈ 7.42

Since we cannot have a fraction of a bus, we must round up to the nearest whole number, which means we need 8 buses.

The remainder of the division, 0.42, represents the fraction of a bus that would be needed to transport the remaining people if we had more than 8 buses available. In this case, since we do not have a fraction of a bus, we round up to the next whole number.

1. The initial sale to B. Ltd. is recorded by debiting Accounts Receivable and crediting Sales.

2. The return of goods by B. Ltd. is recorded by debiting Sales Returns and Allowances and crediting Accounts Receivable.

3. The payment for freight on the returned merchandise is recorded by debiting Freight Out and crediting Cash.

4. The receipt of payment from B. Ltd. is recorded by debiting Cash, crediting Sales Discount (2% of $10,000), and crediting Accounts Receivable.

5. The sale of goods to Y. Ltd. is recorded by debiting Accounts Receivable and crediting Sales.

6. The receipt of payment from Y. Ltd. is recorded by debiting Cash, crediting Sales Discount (2% of $15,000), and crediting Accounts Receivable.

To prepare journal entries in the books of A Ltd. using the net method, we need to record the relevant transactions. Here are the journal entries for the given transactions:

1. June 3:

Accounts Receivable - B. Ltd.  $10,000

   Sales                          $10,000

   To record the sale of goods to B. Ltd.

2. June 5:

Sales Returns and Allowances $500

   Accounts Receivable - B. Ltd.   $500

   To record the return of goods by B. Ltd.

3. June 7:

Freight Out                          $20

   Cash                                  $20

   To record the payment for freight on returned merchandise.

4. June 10:

Cash                                      $9,780

   Sales Discount                  $200

   Accounts Receivable - B. Ltd.   $10,000

   To record the receipt of payment from B. Ltd. after deducting the sales discount (2% of $10,000).

5. June 13:

Accounts Receivable - Y. Ltd.  $15,000

   Sales                                     $15,000

   To record the sale of goods to Y. Ltd.

6. June 25:

Cash                                      $14,760

   Sales Discount                  $240

   Accounts Receivable - Y. Ltd.  $15,000

   To record the receipt of payment from Y. Ltd. after deducting the sales discount (2% of $15,000).

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The expected return on this stock should be 11.38%

The expected return on a stock can be calculated using the Capital Asset Pricing Model (CAPM) formula:

Expected Return on Stock = Risk-Free Rate + Beta * (Expected Return on Market - Risk-Free Rate)

Given that the beta of the stock is 1.15, the expected return on the market is 10.3 percent, and the risk-free rate is 3.1 percent, we can plug these values into the formula:

Expected Return on Stock = 3.1% + 1.15 * (10.3% - 3.1%)

Expected Return on Stock = 3.1% + 1.15 * 7.2%

Expected Return on Stock = 3.1% + 8.28%

Expected Return on Stock = 11.38%

Therefore, the expected return on this stock should be 11.38%.

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As given the sum of squares of three consecutive integers,  four digits which never occur in the ones place are 1,3,6,8.

As given,

Let x -1 , x , x +1 are three consecutive integers.

Sum of the squares of three consecutive integers

= (x -1)² +x² + (x+1)²

= x² -2x +1 +x² +x² +2x +1

=3x² +2

Now substitute x = 0,1,2,3,4,5,6,7,8,9

Sum = 2, 5,14,29, 50, 77, 110, 149, 194, 245

Four digit never occur at ones place = 1,3,6,8

Therefore, as given the sum of squares of three consecutive integers,  four digits which never occur in the ones place are 1,3,6,8.

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Answer:

The slope would be 4

Step-by-step explanation:

8 is where we started at, so 4x + 8

The mean proportion of samples made with chocolate liquor would be 0.20, which is the same as the population proportion.

The problem states that 20% of all candies produced by the factory are made with chocolate liquor. This means that the population proportion of candies made with chocolate liquor is 0.20.

If we take a random sample of 500 candies, we can calculate the proportion of candies made with chocolate liquor in that sample. This proportion is called the sample proportion.

The central limit theorem states that, as long as the sample size is large enough, the distribution of sample proportions will be approximately normal, with a mean equal to the population proportion.

In this case, the sample size is 500, which is large enough for the central limit theorem to apply. Therefore, the mean of all sample proportions will be equal to the population proportion, which is 0.20. Therefore, the answer is that the mean proportion of samples made with chocolate liquor would be 0.20.

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The measure of angle c is 70 degrees.

If angle a and angle b are complementary, it means that the sum of their measures is equal to 90 degrees.

Given:

Measure of angle a = 10x + 10

Measure of angle b = 20

We can set up the equation:

(10x + 10) + 20 = 90

Simplifying the equation:

10x + 30 = 90

Subtracting 30 from both sides:

10x = 60

Dividing both sides by 10:

x = 6

Now, we have found the value of x to be 6.

To find the measure of angle c, we can substitute the value of x into the equation for angle a:

Measure of angle a = 10x + 10

Measure of angle a = 10(6) + 10

Measure of angle a = 60 + 10

Measure of angle a = 70

As a result, angle c has a measure of 70 degrees.

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Yes, we are 95% confident that more than half are in favor because 0.5 does not fall within the 95% confidence interval (0.5039, 0.6827). Thus, it can be concluded that the proportion of all Yellowstone visitors who favor the restrictions is greater than 0.5.

a) Explanation:The sample proportion of Yellowstone Park visitors who favor restrictions on the number of vehicles allowed to enter the park, `p-hat` = 89/150 = 0.5933. Standard error: SE = `√[(p^)(1 - p^)/n]`SE = `√[(0.5933)(0.4067)/150]` = 0.0456`

Margin of Error` at 95% confidence level = `1.96 × SE` = `1.96 × 0.0456` = 0.0894

Confidence interval = (`p^` – `Margin of Error`, `p^` + `Margin of Error`) = (0.5933 – 0.0894, 0.5933 + 0.0894) = (0.5039, 0.6827)

Therefore, the 95% confidence interval for the proportion of all Yellowstone visitors who favor the restrictions is (0.5039, 0.6827).b)

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The key features of a dyad are its small size, symmetry, instability, interdependence, and intensity.

A dyad refers to a social relationship between two individuals or groups. In sociology, Georg Simmel was the first to identify the unique features of a dyad. Simmel believed that a dyad has distinct characteristics that make it different from other social relationships. In this answer, we will explore the key features of a dyad according to Simmel.

The first key feature of a dyad is that it is the smallest social group, consisting of only two members. Due to the small size of the dyad, each member has a more significant impact on the relationship's outcome than in a larger social group. In a dyad, each member can have a more direct and intimate connection with the other, creating a more intense emotional bond than larger groups.

The second feature of a dyad, according to Simmel, is that the relationship between the two members is more symmetrical than in larger social groups. This symmetry means that the two members are more equal in terms of their social status, power, and influence in the relationship. This symmetry allows for a more direct exchange of ideas and feelings, which can result in a deeper and more profound relationship.

The third key feature of a dyad is that it is unstable and can easily break down. Since there are only two members in a dyad, if one person leaves or is absent, the entire relationship is dissolved. This instability means that a dyad requires more maintenance and attention than larger social groups.

The fourth feature of a dyad is that the members of a dyad are more interdependent than in larger social groups. This interdependence means that the actions of one member have a more significant impact on the other member than in larger social groups. The members of a dyad rely on each other more heavily for emotional support, validation, and affirmation, which creates a strong emotional bond.

Finally, the fifth key feature of a dyad is that it is more intense and emotional than larger social groups. The intimacy and directness of the relationship create a more profound emotional bond, making the members of a dyad more invested in the relationship's outcome. This intensity can create a sense of exclusivity and a feeling of being in a close-knit group.

In conclusion, according to Simmel, the key features of a dyad are its small size, symmetry, instability, interdependence, and intensity. Understanding these characteristics is essential to understanding the dynamics of dyadic relationships, including romantic relationships, friendships, and other close interpersonal relationships. By examining these key features, we can better understand the unique aspects of a dyadic relationship and its impact on the individuals involved.

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The present value of the loan is approximately 4. $42,817,078.

The present value of a loan is the current worth of all future cash flows associated with the loan. To calculate the present value of the loan, we need to discount each cash flow to its present value using the market rate of 7% per annum, compounded semi-annually.

Let's break down the cash flows:

1. $11 million is received now and has no discounting since it's already in present value.
2. $22 million is received at the end of month 6. We need to discount it to its present value. Since it's six months in the future, we need to calculate the present value of $22 million in six months at a rate of 7% per annum, compounded semi-annually.
3. $11 million is received at the end of 12 months. We need to discount it to its present value. Since it's one year in the future, we need to calculate the present value of $11 million in one year at a rate of 7% per annum, compounded semi-annually.

To calculate the present value, we can use the formula:

PV = FV / (1 + r/n)^(n*t)

Where:
PV is the present value,
FV is the future value,
r is the interest rate,
n is the number of compounding periods per year, and
t is the number of years.

Let's calculate the present value of each cash flow:

1. PV of $11 million received now = $11 million

2. PV of $22 million received in six months:
PV = $22 million / (1 + 0.07/2)^(2*0.5)
PV = $22 million / (1.035)^(1)
PV ≈ $21,233,298

3. PV of $11 million received in one year:
PV = $11 million / (1 + 0.07/2)^(2*1)
PV = $11 million / (1.035)^(2)
PV ≈ $10,583,780

Now, let's add up the present values of each cash flow to find the total present value of the loan:

Total PV = $11 million + $21,233,298 + $10,583,780
Total PV ≈ $42,817,078

Rounded to the nearest dollar, the present value of the loan is approximately $42,817,078.

Based on the provided answer choices, the closest option to the calculated present value is (4) $42,524,656.

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Answer:

0.18

Step-by-step explanation:

Answer:

.18

Step-by-step explanation:

The experiment occurred 45 times, lemon was selected 8 times.

Probability the next chew will be lemon:

8/45=0.17777... = .18

Answer:

The rectangle is 3.5 yd x 4 yd

Step-by-step explanation:

Area = length x width = lw

l = length = 2w - 3

w = width

Area = 14(2w - 3)(w) = 14

2w² - 3w - 14 = 0

Use quadratic equation to find the 2 roots of w:  a = 2, b = -3, c = -14

w = 3.5, -2     disregard the negative root

width = 3.5 yd

length = 2(3.5) - 3 = 4 yd

The dimensions of the rectangle are approximately 2.23 yards by 1.46 yards.

We are assuming the width of rectangle to be "x" yards. Then, the length would be (2x - 3) yards, since it is 3 yards less than double the width. The formula for the area of a rectangle is A = l x w, so we can plug in the values we know:

14 = (2x - 3) x x

Expanding the brackets:

14 = 2x² - 3x

Put this equation=0:

2x² - 3x - 14 = 0

Using the quadratic formula:

x = (3 ± √(3² + 4 x 2 x 14)) / (2 x 2)

x = (3 ± √97) / 4

We can ignore the negative root, since the width cannot be negative. Therefore,

x ≈ 2.23

This is the width of the rectangle. To find the length, we can plug this value back into the expression we derived earlier:

length = 2x - 3

length ≈ 1.46

Therefore, the dimensions of the rectangle are approximately 2.23 yards by 1.46 yards

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Answer:

D

Step-by-step explanation:

it -4<x<8 your answer is d