Find f(1) for the
piece-wise function.
f(x) = -
x-2 if x <3
x-1
if x>3
· f(1) = [ ? ]

Answer:

7/1

Step-by-step explanation:

7 over 1 equals 7 which is the answer.

Answer:

What's the question? Did not understand.

The step of the five-step model of decision-making that includes studying the positives and negatives of a list of possible solutions to a problem is rate alternatives on the basis of decision criteria (option d).

In this step, after generating multiple alternatives (step a) and identifying and weighing decision criteria (step b), the focus shifts to evaluating each alternative. The decision criteria are used as a framework to assess the alternatives and determine their strengths and weaknesses. This involves studying the positives and negatives of each alternative in relation to the established criteria.

By examining the alternatives based on the decision criteria, decision-makers can gain a comprehensive understanding of the potential outcomes and consequences associated with each option. This analysis allows for an informed comparison of the alternatives, facilitating the selection of the most suitable solution.

Once the alternatives have been rated and evaluated in light of the decision criteria, decision-makers can proceed to the subsequent steps of the model, such as choosing, implementing, and evaluating the best alternative (step c). The correct option is d.

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The complete question is:

Which step of the five-step model of decision-making includes studying the positives and negatives of a list of possible solutions to a problem?

a. generate multiple alternatives

b. identify and weigh decision criteria

c. choose, implement, and evaluate the best alternative

d. rate alternatives on the basis of decision criteria

The three-digit number is 194. Using the given information:x - 3 cannot be 0.x cannot be 3.The ones digit cannot be 3, so x must be greater than or equal to 4.

Let the ones digit be x.Tens digit = x + 5Hundred digit = (x + 5) - 8 = x - 3The number is 3-digit, so the hundreds digit cannot be zero.Therefore, the ones digit is greater than or equal to 1 and less than or equal to 9.The tens digit must be greater than or equal to 0 and less than or equal to 9.The hundreds digit must be greater than or equal to 1 and less than or equal to 9.Using the given information:x - 3 cannot be 0.x cannot be 3.The ones digit cannot be 3, so x must be greater than or equal to 4.Using x = 4, x = 5, x = 6 and x = 7, we get:Tens digit = 4 + 5 = 9, hundreds digit = 4 - 3 = 1. Therefore, the number is 194.

We can use algebra to solve the problem.Using the information in the question:x - 3 = hundreds digit x + 5 = tens digit. We need to find the value of x, so we can use the equation:x - 3 = tens digit - 8x - 3 = x + 5 - 8Simplifying:x - 3 = x - 3Therefore, we have:0 = 0This means that any value of x will satisfy the given information.In other words, there are many three-digit numbers that have a tens digit that is 5 more than the ones digit and a hundreds digit that is 8 less than the tens digit. However, we also know that the hundreds digit cannot be zero.Therefore, the ones digit is greater than or equal to 1 and less than or equal to 9.The tens digit must be greater than or equal to 0 and less than or equal to 9.The hundreds digit must be greater than or equal to 1 and less than or equal to 9.Using the given information:x - 3 cannot be 0.x cannot be 3.The ones digit cannot be 3, so x must be greater than or equal to 4.Using x = 4, x = 5, x = 6 and x = 7, we get:Tens digit = 4 + 5 = 9, hundreds digit = 4 - 3 = 1. Therefore, the number is 194.

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2)  the variance of the number of claims processed is approximately 2.1173.

To calculate the variance of the number of claims processed, we need to follow these steps:

1. Calculate the mean (expected value) of the number of claims processed per hour. This can be done by multiplying each value by its corresponding probability and summing the results. In this case:

Mean (μ) = (2 * 0.11) + (3 * 0.16) + (4 * 0.27) + (5 * 0.23) + (6 * 0.13) + (7 * 0.10)

       = 0.22 + 0.48 + 1.08 + 1.15 + 0.78 + 0.70

       = 4.41

2. Calculate the squared difference between each value and the mean. Then multiply each squared difference by its corresponding probability and sum the results. In this case:

Variance (σ²) = [(2 - 4.41)² * 0.11] + [(3 - 4.41)² * 0.16] + [(4 - 4.41)² * 0.27] + [(5 - 4.41)² * 0.23] + [(6 - 4.41)² * 0.13] + [(7 - 4.41)² * 0.10]

           = (2.41² * 0.11) + (1.41² * 0.16) + (0.41² * 0.27) + (0.59² * 0.23) + (1.59² * 0.13) + (2.59² * 0.10)

           = 0.6641 + 0.3176 + 0.0459 + 0.0801 + 0.3405 + 0.6691

           = 2.1173

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Answer:

A) The Jenga game is appropriate for the middle childhood age group, typically ranging from around 6 to 12 years old.

B) Jenga promotes cognitive, physical, and socioemotional development in middle childhood through enhancing spatial reasoning and problem-solving skills, improving fine motor skills and proprioceptive input, and fostering social interaction, cooperation, and risk assessment.

Step-by-step explanation:

Jenga, a game played with rectangular blocks, can promote cognitive, physical, and socioemotional development through various concepts.

Cognitive Development: Jenga enhances spatial reasoning as players analyze the tower's structure, evaluate block stability, and strategize their moves. They mentally manipulate objects in space, building an understanding of spatial relationships and balance. Problem-solving skills are fostered as players make decisions about which block to remove, considering the consequences of their actions. They must anticipate the tower's reaction to their moves, think critically, and adjust their strategies accordingly.

Physical Development: Jenga improves fine motor skills as players carefully remove and stack blocks using only one hand. Precise finger movements, hand-eye coordination, and grip strength are required for successful manipulation of the blocks. The game also provides proprioceptive input as players gauge the weight and balance of each block, refining their sense of touch and motor control.

Socioemotional Development: Jenga promotes social interaction and cooperation when played with multiple players. Taking turns, discussing strategies, and supporting each other's successes and challenges enhance communication, collaboration, and empathy skills. Players learn to respect and consider others' perspectives, negotiate and compromise, and work together towards a common goal. Sportsmanship is nurtured as players accept both victory and defeat gracefully, fostering resilience and emotional regulation.

Furthermore, Jenga offers opportunities for developing patience and perseverance. As the tower becomes increasingly unstable, players must exercise self-control, focus, and delayed gratification. They learn to take their time, plan their moves carefully, and tolerate the suspense of potential collapse. The game also presents a low-risk environment for risk assessment, allowing children to assess the consequences of their decisions and make calculated judgments.

By engaging in Jenga, children actively participate in a multi-dimensional activity that combines physical manipulation, cognitive analysis, and social interaction. Through the concepts of spatial reasoning, problem-solving, fine motor skills, proprioceptive input, social interaction, cooperation, sportsmanship, patience, perseverance, and risk assessment, Jenga supports holistic development in cognitive, physical, and socioemotional domains.

The Correct graph is fourth one !

Answer:

Step-by-step explanation:

QUESTION :

m = (-3--1)/(-5-6) = 2/11

LAST ONE :

m = (-3--1)/(5--6) = -2/11

WITH THE REFLECTION OF F(X) , NORMALLY THE X-INTERCEPTS OF THE REFLECTED VALUE REMAIN THE SAME BUT CHANGE SIGNS. THE Y-INTERCEPTS DON'T CHANGE INCLUDINGVTHE SIGNS.

A) The probability that the sample mean is within $500 of the population mean for a sample of size 60 is 0.6611

B) The probability that the sample mean is within $500 of the population mean for a sample of size 120 is 0.7362

The EAI (Error of the Estimate) sampling problem is a specific case of the Central Limit Theorem, which states that the distribution of sample means from a population with a finite variance will be approximately normally distributed as the sample size increases.

The formula for calculating the standard error of the mean is

SE = σ/√n

where SE is the standard error, σ is the population standard deviation, and n is the sample size.

For n = 30, SE = 4,000/√30 = 729.16

A. For a sample size of n = 60, SE = 4,000/√60 = 516.40

To find the probability that the sample mean is within $500 of the population mean, we need to calculate the z-score for a range of +/- $500

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error.

For a range of +/- $500, the z-scores are

z = ($51,300 - $51,800) / 516.40 = -0.969

z = ($52,300 - $51,800) / 516.40 = 0.969

Using a standard normal distribution table, the area between z = -0.969 and z = 0.969 is 0.6611.

B. For a sample size of n = 120, SE = 4,000/√120 = 368.93

Following the same steps as above, the z-scores for a range of +/- $500 are

z = ($51,300 - $51,800) / 368.93 = -1.364

z = ($52,300 - $51,800) / 368.93 = 1.364

Using the standard normal distribution table, the area between z = -1.364 and z = 1.364 is 0.7362.

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(a) Isla's trading cards are 125% of Lily's trading cards.

(b) Lily's trading cards are 80% of Isla's trading cards.

Given that,

There are 225 trading cards and Lily has 180 trading cards.

To calculate the percentage of Isla's trading cards compared to Lily's,

We can use this formula:

⇒ Isla's trading cards / Lily's trading cards x 100%

Plugging in the values we get:

⇒ (225 / 180) x 100% = 125%

Therefore,

Isla's trading cards are 125% of Lily's trading cards.

b) To calculate the percentage of Lily's trading cards compared to Isla's, we can use the formula:

⇒ Lily's trading cards / Isla's trading cards x 100%

Plugging in the values we get:

(180 / 225) x 100% = 80%

Therefore,

Lily's trading cards are 80% of Isla's trading cards.

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We want to solve the proportion:

For doing so, we remember that solving a proportion equivals to find the variable x. We will multiply means and extremes:

This means that the value of x is 8, which is the solution of the proportion.

Given: f(x) = 10

To find: x

Solution:   We know that in general function is mapped in the form

f(x) = y

therefore we can observe from given figure that f(30)= 10

Henceforth the solution is option D. 30  

Answer:

yes

Step-by-step explanation:

First we should find a GCF for the number of boys and girls.

The gcf for the two would be 4.

Divide.

20/4 = 5

28/4= 7

therefore the ratio for boys to girls would be 5 to 7

$54.25 are required for the second purchase of lace.

Mixed numbers are formed by combining three parts: An integer, a numerator, and a denominator. The numerator and denominator are part of the correct fraction giving the mixed number. A fraction represented by a quotient and a remainder is a mixed number. For example, 2 1/3 is a mixed fraction, 2 is the quotient, and 1 is the remainder. A mixed number has a combination of an integer and a proper fraction.

Cost of each yd of lace:

= 5.60 ÷ (4/5)

= 5.60 × 5/4

= $7

Now for the cost of second purchase:

Total yd of lace to be purchased = 7 3/4 yd            [mixed fraction]

= 31/4 yd                                                                     [improper fraction]

Cost of 1 yd of lace = $7

Total cost of second purchase = (31/4) × 7

= $54.25

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Answer:

Let (x1, y1) = (-9, 5) and (x2, y2) = (3, 2) be the two points.

The formula for finding the slope between two points is:

m = (y2 - y1) / (x2 - x1)

Substituting the values, we get:

m = (2 - 5) / (3 - (-9))

m = -3 / 12

m = -1/4

Therefore, the slope between the points (-9, 5) and (3, 2) is -1/4.

Answer:

M = -1/4

Step-by-step explanation:

(y2-y1)/(x2-x1) = Slope

we use the x and y components of the given coordinates to find out the answer.

Therefore,

(2-5)/(3-(-9)) = -1/4

The type of square that has a movable head and can be used to lay out both 45° and 90° angles is called a combination square.

A combination square is a versatile measuring tool commonly used in woodworking, metalworking, and construction. It consists of a ruler or blade with a movable head that can be locked at different angles, typically 45° and 90°. The head of the square usually has a spirit level or bubble level attached to ensure accurate measurements and alignments.

The movable head allows the user to set and measure angles other than 45° and 90° as well, making it a versatile tool for various applications. The square is often used for marking and checking right angles, marking 45° angles, measuring and transferring distances, and checking the flatness or alignment of surfaces.

The combination square derives its name from the fact that it combines multiple functions in a single tool, making it convenient and efficient for tasks that require different angle measurements. It is a common and essential tool in many trades and professions where accurate and precise measurements are required.

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To determine the values of b for which the series converges, we can use the p-series test. The p-series test states that a series of the form Σ 1/n^p converges if and only if p &gt; 1.

We can express this answer using interval notation as (1, ∞).To determine the positive values of b for which the series converges, we'll analyze the series using the convergence test:Σ (1/(b * n))For this series, we can apply the Integral Test for convergence. The Integral Test states that if f(n) = 1/(b * n), where f is a positive, continuous, and decreasing function, then the series converges if the integral of f(x) from 1 to infinity converges.

Let's evaluate the integral:∫(1/(b * x)) dx from 1 to infinityWhen integrating, we get:(ln(|b * x|) / b) | from 1 to infinityTo make the integral converge, we need the upper bound (when x approaches infinity) to be finite. In other words, the natural logarithm must grow slower than b. This is true when b &gt; 1.Therefore, the positive values of b for which the series converges are given by the interval (1, ∞).

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Answer:

it is used to subtract 10 from both sides

Answer:

Definitely D

As seen in the equation both sides is being subtracted by 10

Answer:

\(P(x) = x^2+24x+5\)

Step-by-step explanation:

Functions

In a function, an independent variable, let's call it x is related to a dependent variable y and it can be expressed as:

y = f(x)

Let's consider the functions given in the question, where the equation that represents a company's yearly sales is:

\(S(x)=2x^2+24x\)

And the equation that represents the same company's yearly expenses is:

\(E(x)=x^2-5\)

The company's profit function P(x) can be found as the difference between S(x) and E(x), thus:

\(P(x) = S(x)-E(x)=2x^2+24x-(x^2-5)\)

Operating:

\(P(x) = 2x^2+24x-x^2+5\)

Simplifying, the profit function for this company is:

\(\boxed{P(x) = x^2+24x+5}\)

Answer: 4,12

Step-by-step explanation:

Bowl-O-Rama:

y = 2 + 2.50x

Bowling Pinz:

y = 4 + 2x

When you graph this, the solution is (4, 12). This represents that when you play 4 games for either company, both the prices will be the same, $12.

Answer:

$18.00

Step-by-step explanation:

Bowl-O-Rama: $4.50 times 4

Bowling Pinz: $6.00 times 3

Answer:

$23

Step-by-step explanation:

1/2 + 8 = 54

subtract 8 from both sides: 1/2 = 46

divide 46 by 1/2: 23

check your answer: 23 * 2 + 8= 54

I hope this helped, please mark Brainliest, thank you!

Answer:

Step-by-step explanation:

smelly a becasue

Answer:

a. 10560

b. 63360 in.

c. 10000 m

d. 100000 cm

e. 3.107 miles

f. 42.165 km

Step-by-step explanation:

a. 2 miles contain how many feet?

1 mile = 5280 ft

2 miles × 5280 ft / mile = 10560 ft

b. 1 mile contains how many inches?

1 ft = 12 in

1 mile × 5280 ft/mile × 12 in./ft = 63360 in.

c. 10 kilometers contain how many meters?

1 km = 1000 m

10 km × 1000 m/km = 10000 m

d. 1 kilometer contains how many centimeters?

1 km × 1000 m/km × 100 cm/m = 100000 cm

e. How many miles are in a "5k" (five-kilometer) race?

1 in. = 2.54 cm

5 km =

= 5 km × 1000 m/km × 100 cm/m × 1 in. / (2.54 cm) × 1 ft / (12 in.) × 1 mile / (5280 ft)

= 3.107 miles

f. A marathon is 26.2 miles. How many kilometers is this?

26.2 miles =

26.2 miles × 5280 ft / mile × 0.3048 m/ft × km / (1000 m) = 42.165 km

Answer:

Step-by-step explanation:

ChecK THE Picture attached for both the answers.

Hope it helps ❤️

the solution can be expressed as: θ ≈ 0.72 + 2πk, where k is an integer. The equation cos(θ) = 3/4 can be solved by taking the inverse cosine (arccos) of both sides: θ = arccos(3/4)

The equation cos(θ) = 3/4 represents the value of θ for which the cosine function equals 3/4. To find the solution, we can use the inverse cosine function (arccos) to "undo" the cosine operation and isolate θ.

The arccos function gives us the angle whose cosine is a given value. In this case, we want to find the angle θ such that cos(θ) equals 3/4. By taking the arccos of both sides, we obtain: θ = arccos(3/4)

Using a calculator or mathematical software, we can find the arccos(3/4) to be approximately 0.7227 radians. This value represents one solution to the equation.

However, since cosine is a periodic function, it repeats itself every 2π radians. Therefore, we can add or subtract any integer multiple of 2π to the solution to obtain additional solutions. In general, the solutions to the equation cos(θ) = 3/4 can be expressed as:θ = 0.7227 + 2πk, where k is an integer.

This means that the initial solution 0.7227 radians can be adjusted by adding or subtracting multiples of 2π, resulting in an infinite set of solutions. Each integer value of k corresponds to a different solution. Rounding to two decimal places, we can express the solutions as:

θ ≈ 0.72 + 2πk, where k is an integer.

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Answer:

(-3, -5)

Explanation:

Given the function:

First, make y the subject of the equation.

To choose a point that lies on the line, we test the x-values and see if we get the corresponding y-value.

Since the y-value corresponds to the point (-3, -5), the point that lies on the function is (-3, -5).

Answer:

Step-by-step explanation:

2(6-x)=3(x-1)

12-2x=3x-3

 +2x  +2x

12=5x-3

+3      +3

15=5x

3=x

i don't know if they also want you to substitute, bu if they do continue the problem

2(6-x)=3(x-1)

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

2(3)=3(2)

6=6