Write the equation for the function represented

There are 495 different ways in which a committee of 4 people can be formed from a group of 12 people in the baking club.

To solve this problem, we can use the combination method, which is a mathematical technique used to count the number of combinations that can be formed from a set of items. The formula for the combination method is:

ⁿCₓ= n! / (x! * (n-x)!)

Where n is the total number of items in the set, r is the number of items to be selected, and the exclamation mark denotes the factorial function. The factorial of a positive integer n is defined as the product of all positive integers up to and including n.

Now, let's apply the combination method to the problem at hand. We are given that there are 12 people in the baking club, including Mark, and we need to form an executive committee of 4 people. Using the formula above, we can calculate the number of possible committees as follows:

¹²C₄= 12! / (4! * (12-4)!)

= (1211109) / (4321)

= 495

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Answer:

A prism is a three-dimensional shape with two congruent and parallel polygonal bases connected by parallelogram-shaped sides. The base shape can vary, so a prism can have rectangular, triangular, or other polygonal bases. When you search up a prism on the Internet, the first result that appears is a rectangular prism. We cannot provide much help without further elaboration, as all of the answers are types of prisms.

Answer:

Prisms can be both triangle and rectangle. if you can't circle or choose 2 answers then you should've been given a picture. hope it helps

x = 1/2 × 68

  = 34

That's the rule just its half also y is the same thing while x and y are looking at the same arc

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Answer: look it up-

Step-by-step explanation:

Answer:

Step-by-step explanation

The tens place is what we have to compare to determine the greater of the given numbers -7295 and 7259

To determine which number, 7259 or -7295, is greater, we can compare their place values starting with their leftmost digit.

7295 and 7259 have sevens in the thousands place; 7259 also has one; however, when we compare the next digit -7295 has twos while 7259 only has one in its hundreds place.

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Answer:

5/16 with bar notation is written as 0.3125, where the bar is placed over the digit "5" to indicate that it repeats infinitely. This notation is used to represent a repeating decimal, where the digit or group of digits after the bar repeats infinitely without terminating. In this case, the digit "5" repeats infinitely after the decimal point.

Answer:

The bar notation is used to indicate that a digit or a sequence of digits repeats indefinitely. To express 5/16 with a bar notation, we need to find the decimal equivalent of 5/16 and identify any repeating digits.

To convert 5/16 to a decimal, we can perform the division as follows:

0.3125

The decimal equivalent of 5/16 is 0.3125. Since there are no repeating digits, we cannot express it with a bar notation.

The curved length DE of the given triangle is calculated as: 15.75

Pythagoras Theorem is defined as the way in which you whereby you can find the missing length of a right angled triangle.

The triangle has three sides, namely the hypotenuse (which is always the longest side), Opposite side (which doesn't touch the hypotenuse) and finally, the adjacent side (which is located between the opposite and the hypotenuse).

Pythagoras is in the form of; a² + b² = c²

Applying the Pythagoras theorem to triangle ABC gives:

AB = √(12² + 9²)

AB = √225

AB = 15

We are told that DE is 5% longer than AB. Thus:

DE = 1.05 * 15

DE = 15.75

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Answer:

Step-by-step explanation:

Let x be the number of adult tickets Travis bought, and y be the number of children tickets he bought.

We know that Travis bought a total of 14 tickets, so x + y = 14.

We also know that the total cost of the tickets was $54, so 5x + 3y = 54.

We can use the first equation to solve for y in terms of x: y = 14 - x.

Substituting this into the second equation, we get:

5x + 3(14 - x) = 54

Simplifying and solving for x, we get:

5x + 42 - 3x = 54

2x + 42 = 54

2x = 12

x = 6

Therefore, Travis bought 6 adult tickets and 14 - 6 = 8 children tickets.

to find maximum wage of number equality of boy adult and child.

I mean: 48 = 6.8

12 person from here

2 person remain

6 $ remain as well

6 = 2 child ticket

so the answer is 6

The system of equations have infinite solution.

We have to given that;

The system of equations are,

⇒ y = 1/2 x +3

⇒ 2y = x +6

Here, Equation (i);

⇒ y = 1/2 x +3

⇒ 2y = x + 6

Which is same as (ii).

Now, We can draw system of equations we can see that both line are coincide.

Hence, The system of equations have infinite solution.

Thus, The system of equations have infinite solution.

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The limit of the given function as x approaches infinity is 0.

To find the limit of the given function as x approaches infinity, we can use L'Hospital's Rule since we have an indeterminate form of type ∞/∞: lim (x → ∞) ln(x)/√x

Step 1: Apply L'Hospital's Rule by taking the derivative of both the numerator and the denominator with respect to x: Derivative of ln(x) = 1/x Derivative of √x = 1/(2√x)

Step 2: Create a new fraction with the derivatives and find the limit: lim (x → ∞) (1/x) / (1/(2√x))

Step 3: Simplify the expression: lim (x → ∞) (1/x) * (2√x) = lim (x → ∞) (2√x) / x

Step 4: Rewrite the expression as: lim (x → ∞) (2/√x)

Step 5: As x approaches infinity, the expression converges to: (2/∞) = 0

So, the limit of the given function as x approaches infinity is 0.

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Answer:

.

Step-by-step explanation:

.

Using the information provided, no triangle will be formed.

This is shown by, summing the angles

The number of triangles to be formed considering the given angles is achieved knowing the basic properties of triangle which is:

With this knowledge, we sum the angles of the triangle

= 112 + 54 + 16

= 182

No triangle is formed as the sum is not equal to 180 degrees

If the angles are summed to 180 degrees, this is a criterion of formation of unlimited number of triangle

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The height of the tower after adding 1 more box to it is 144 cm.

The current height of the tower can be determined using division, addition, and multiplication.

Division, addition, and multiplication are three of the four basic mathematical operations, including subtraction.

The number of identical cube-shaped boxes stacked = 8 boxes

The height of the 8 boxes = 128 cm

The height of each of the 8 boxes = 16 cm (128 ÷ 8)

The number of the additional box added to the tower = 1

The current number of boxes = 9 (8 + 1)

The total height after adding the additional box = 144 cm (9 x 16)

Thus, after adding 1 more box, Ella's tower has a height of 144 cm.

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The radius of the circle is approximately 286.26 meters.

We have,

We can use the formula for the length of an arc of a circle, which is:

s = r x [tex]\alpha[/tex]

where s is the arc length, r is the radius of the circle, and alpha is the central angle in radians.

To use this formula, we need to convert the central angle from degrees to radians.

We know that the circle has a central angle of alpha = 3,

so:

alpha (in radians) = (3/180) x π = 0.0524 radians

where π is the mathematical constant pi (approximately equal to 3.14159).

Now we can solve for the radius, r:

s = r x α

15 = r x 0.0524

r = 15 / 0.0524

r ≈ 286.26 meters

Therefore,

The radius of the circle is approximately 286.26 meters.

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The rate at which the circumference is growing when the water covers 50 ft is found to be at  0.019 ft/s.

The formula for the area of a circle is shown as  :

A = πr^2

where A = area

π = 3.142

r = radius

We will differentiate with respect to time, :

dA/dt = 2πrn xdr/dt

we have that dA/dt = 3 ft²/s

3 = 2π(25) x dr/dt

we calculate for  dr/dt,

dr/dt = 3/(50π) =  0.019 ft/s

In conclusion, if a person is making an ice rink by pouring water out of a hose. If water is spreading in a circular shape and the area covered by water grows with the rate of 3 ft?/sec, the rate at which the circumference is growing when the water covers 50 ft is found to be at  0.019 ft/s.

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There are 30 different pairs that can be formed from the 6 men and 5 women.

The number of different mixed doubles tennis pairs can be calculated by multiplying the number of choices for the first player by the number of choices for the second player. For the first player, there are 6 men to choose from, and for the second player, there are 5 women to choose from. Therefore, the number of different mixed doubles tennis pairs is:

6 x 5 = 30

Therefore, there are 30 different pairs that can be formed from the 6 men and 5 women.

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Eagles; they have a larger mean value of about 22 points. Therefore, option C is the correct answer.

The best measure of center to compare the team records for the season would be the mean value, as it takes into account all the points earned in each game and provides an average value.

In this case, the Eagles have a larger mean value of about 22 points compared to the Falcons, who have a mean value of about 20.9 points. Therefore, the Eagles had the best overall record for the season.

Therefore, option C is the correct answer.

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Answer:

Each term has five more than the previous term

Step-by-step explanation:

The difference in each term is 5.

12 + 5 = 17

17 + 5 = 22

22 + 5 = 27

And so on. Thus, each term has five more than the one before it. 17 has 5 more than 12.

The probability of randomly selecting an applicant who is on drugs is 71% under the given condition that  test has a 2% false positive rate and 1% false negative rate and suppose 5% of all applicants are using illegal drugs.

Let us consider  the probability of a person on drugs as P(D) = 0.05.
The probability of a person not on drugs is P(¬D) = 0.95.
The probability of a positive test result given that the person is on drugs is P(T|D) = 1 - False Negative Rate = 0.99.
The probability of a positive test result given that the person is not on drugs is P(T|¬D) = False Positive Rate = 0.02.

Applying Bayes' theorem, we can evaluate the probability that a randomly selected applicant is on drugs
P(D|T) = (P(T|D) × P(D)) / (P(T|D) × P(D) + P(T|¬D) × P(¬D))
= (0.99 × 0.05) / (0.99 × 0.05 + 0.02 × 0.95)
≈ 0.71
Converting into percentage
= 0.71 × 100
= 71%

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Answer:

a=9

Step-by-step explanation:

a= 9/4 =36/4 = 9

The probability of choosing a blue marble, then a red marble is 0.222

From the question, we have the following parameters that can be used in our computation:

Red = 3 marbles

Blue = 6 marbles

If the marbles were replaced, then we have

P(Blue) = 6/9

P(Red) = 3/9

So, we have

The probability of choosing a blue marble, then a red marble is

P = 6/9 * 3/9

Evaluate

P = 0.222

Hence, the probability of choosing a blue marble, then a red marble is 0.222

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Karolina ran 1.66 miles on Wednesday.

It is given that Karolina ran 1.38 miles on Monday.

She ran 2.17 miles on Tuesday.

We have to find how many miles she ran on Wednesday.

Let she ran 'D' miles on Wednesday.

It is also given that Karolina ran total of 5.21 miles on Monday, Tuesday, and Wednesday.

According to information we can form an equation which is,

1.38 + 2.17 + x = 5.21

3.55 + x = 5.21

3.55 + x - 3.55 = 5.21 - 3.55 [Subtracting 3.55 from both sides]

x = 1.66

Hence Karolina ran 1.66 miles on Wednesday.

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To be 90% certain that the projected percentage is off by no more than one percentage point, the epidemiologist must survey at least 968 women.

(a) First, we need to find the critical value of the standard normal distribution that corresponds to a 90% confidence level. We can do this using a standard normal distribution table or a calculator. The critical value is approximately 1.645.

(b) We also need to estimate the proportion of women who give birth. Let's assume that a prior study found this proportion to be 0.6. This will be our point estimate.

(c) Finally, we can use the formula for the margin of error to determine the sample size:

margin of error = critical value * standard error

where the standard error is given by:

standard error = sqrt[(point estimate * (1 - point estimate)) / sample size]

margin of error = 0.01

Plugging in the values we have:

0.01 = 1.645 * sqrt[(0.6 * 0.4) / sample size]

Solving for the sample size:

sample size = (1.645 / 0.01)^2 * 0.6 * 0.4

sample size ≈ 968

Therefore, the epidemiologist needs to survey at least 968 women to be 90% confident that the estimated percentage is in error by no more than one percentage point.

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A portable cooler with dimensions 19 inches * 14 inches * 14 inches has a volume of 3724 cubic inches.

A prism is a 3-Dimensional shape that is bound by plane figures on all sides. The ends face of the prism are identical and are called bases. A rectangular prism is known as a cuboid. All the faces of the prism are rectangles and it has 6 faces, two on ends and 6 laterally.

Volume is the measurement of space that is occupied by an object. The volume of the cuboid is calculated by

V = l * b * h

l is the length of the cuboid

b is the breadth of the cuboid

h is the height of the cuboid

Given, l = 19 inches

b = 14 inches

h = 14 inches

V = 19 * 14 * 14

= 3724 cubic inches

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The probability that you will come out ahead is 16.9%.

The probability of winning a single bet on red is 18/38 because there are 18 red squares out of a total of 38 squares (18 red, 18 black, and 2 green).

The probability of losing a single bet on red is 20/38 because there are 20 non-red squares out of a total of 38 squares.

The expected value of a single bet on red is:

(18/38) x 1 + (20/38) x (-1) = -0.0526

This means that for every $1 bet on red, you can expect to lose about 5.3 cents on average.

Now, if you play 30 times, betting $1 on red each time, the total amount you bet will be $30. The expected value of your total winnings will be:

-0.0526 x 30 = -$1.58

This means that, on average, you can expect to lose about $1.58 if you play 30 times and bet $1 on red each time.

The probability of coming out ahead after 30 bets is the probability of winning more than $30 - $1.58 = $28.42.

To calculate this probability, we need to use the binomial distribution with n=30 and p=18/38. Let X be the number of times you win:

P(X > 30 - 1.58) = P(X > 28.42)

Using a binomial distribution calculator, we find that this probability is approximately 0.169 or 16.9%.

Therefore, the probability of coming out ahead after 30 bets of $1 on red is about 16.9%.

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Answer:

This gives you 1000 pounds. So, a piano grand that weighs 0.5 ton has a weight of 1000 pounds.

Step-by-step explanation:

Answer:

a ton is 2,000 lbs so 0.5 tons would be 1,000 lbs

Step-by-step explanation:

and rn i need a comically large pianoto fall on top of my head :D

Answer:

Step-by-step explanation:

To solve this problem, we can use the following formula:

Total amount of money = Amount saved + Amount earned per week * Number of weeks

We want to find the number of weeks, so we can rearrange the formula to solve for Number of weeks:

Number of weeks = (Total amount of money - Amount saved) / Amount earned per week

Substituting the values we have:

Number of weeks = ($250 - $45) / $20

Number of weeks = $205 / $20

Number of weeks = 10.25

Therefore, it will take Wendell 10.25 weeks to have enough money to buy a new tennis racket.

I hope that helps! Let me know if you have any other questions.

The {x} - intercept and {y} - intercept for the given line is (-7.5, 0)

and (0, 5.5) respectively.

Given is a straight line plotted on the graph as shown in the image. We can say that {x} - intercept is the coordinate at which the line cuts the {x] - axis. Similarly, {y} - intercept is the coordinate at which the line cuts the {y] - axis.

From the graph given below, we can see that -

{x} intercept : (-7.5, 0)

{y} intercept : (0, 5.5)

Therefore, the {x} - intercept and {y} - intercept for the given line is (-7.5, 0)

and (0, 5.5) respectively.

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