Which of the following graphs is a function?
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A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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Answer:

2804

Step-by-step explanation:

2504 + 140 + 160 = 2804   (hint: add the 140 + 160 first. It sums up to 300 which is easy to add to 2504)

Answer:

B

Step-by-step explanation:

Answer:

whats the question

Step-by-step explanation:

The value of imports is $304,533,333.33 and the value of exports is $311,633,333.33. So, option B is correct.

Let's denote the value of exports as E and the value of imports as I. We can then use the following system of equations to solve for E and I:

E - I = 7,100,000 (balance of trade equation)

0.12E + 0.21I = 9,148,200 (tariff revenue equation)

Multiplying the first equation by 0.12 and adding it to the second equation, we get:

0.12E - 0.12I + 0.21I = 9,148,200 + 0.12(7,100,000)

0.12E + 0.09I = 9,988,000

Multiplying both sides by 100, we can eliminate decimals:

12E + 9I = 998,800,000

We can now use this equation with the balance of trade equation to solve for E and I:

E - I = 7,100,000

12E + 9I = 998,800,000

Multiplying the first equation by 9 and subtracting it from the second equation, we get:

12E + 9I - 9E + 9I = 998,800,000 - 63,900,000

3E = 934,900,000

E = 311,633,333.33

Substituting this value into the balance of trade equation, we get:

311,633,333.33 - I = 7,100,000

I = 304,533,333.33

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Solving the quadratic function, it is found that the factors/zeros of the function are given by x = -1.5 and x = 5.

They are given by the solutions of the function, that is, the values of x for which f(x) = 0.

In this problem, the function is given by:

f(x) = -2x² + 7x + 15.

Then:

-2x² + 7x + 15 = 0.

Which is a quadratic function with coefficients a = -2, b = 7, c = 15, hence:

\(\Delta = 7^2 - 4(-2)(15) = 169\)

\(x_1 = \frac{-7 + \sqrt{169}}{2(-2)} = -1.5\)

\(x_2 = \frac{-7 - \sqrt{169}}{2(-2)} = 5\)

The factors/zeros of the function are given by x = -1.5 and x = 5.

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99.85% of adults in the city have a systolic blood pressure of less than 110 mmHg.

Using 68-95-99.7 rule, we know that

99.7% of values lie between the interval (mean - 3 × standard deviation, mean + 3 × standard deviation)

(100 - 99.7) = 0.3% values lie outside the interval (mean - 3 × standard deviation, mean + 3 × standard deviation).

Since the normal distribution is bell-curved and symmetrical,

we can say

0.3/2 = 0.15% values are less than the mean - 3 × standard deviation

and 0.3/2 = 0.15% values are greater than mean + 3 × standard deviation.

Here,

Mean + 3 × standard deviation.

= 110 + 3 × 10 = 140

So, 0.15% of values  are greater than 140

So, (100 - 0.15) = 99.85% values are less than 140.

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Answer:

The answer is above. Numbers 2 and 3

Answer: b

The answer for this question is b

The area of the triangle is same as the area of the rectangle in the third figure with length 4 mm an width 3 mm.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Area of a triangle = \(\frac{1}{2}\) b h, where b is the base and h is the height.

Here for triangle, b = 6 mm and h = 4 mm

Area of triangle =  \(\frac{1}{2}\) × 6 × 4 = 12 mm²

Area of a rectangle = l × b, where l is length and b is width.

For first figure,

Area = 6 × 3.5 = 21 mm²

For second figure,

Area = 4 × 2.5 = 10 mm²

For third figure,

Area = 4 × 3 = 12 mm²

For fourth figure,

Area = 6 × 4 = 24 mm²

Hence the rectangle in the third figure has the same area as the triangle.

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Using distributive property, the simplified form of expression 1/3 (9 + 6u) is 3 + 2u

We know that for the non-zero real numbers a, b, c, the distributive property states that, a × (b + c) = (a × b) + (a × c)

Consider an expression  1/3 (9+6u)

Compaing this expression with a × (b + c) we get,

a = 1/3

b = 9

and c = 6u

Using  distributive property for this expression we get,

1/3 × (9 + 6u)

= (1/3 × 9) + (1/3 × 6u)

= (9/3) +(1/3 × 6)u

= (3) + (6/3)u

= 3 + 2u

This is the simplified form of expression  1/3 (9+6u)

Therefore, the expression 1/3 (9+6u) = 3 + 2u

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Solve 1/3 (9+6u) using distributive property

The probability is 0.4647.

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Answer:

comparing the means of three or more groups

Step-by-step explanation:

The simplified expression is 26 - 4x.

To simplify the expression 6 - 4(x - 5), we can apply the distributive property and simplify the terms.

6 - 4(x - 5)

First, distribute -4 to the terms inside the parentheses:

6 - 4x + 20

Now, combine like terms:

(6 + 20) - 4x

Simplifying further:

26 - 4x

Therefore, the simplified expression is 26 - 4x.

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Candidates for a job are interviewed one by one until a qualified candidate is found. Thirty percent of the candidates are qualified.

In the selection process for a job, candidates are interviewed individually until a qualified candidate is identified. The word "qualified" refers to candidates who possess the necessary skills, qualifications, or experience required for the position. However, only thirty percent of the candidates in this scenario are considered qualified.

The selection process involves conducting interviews with each candidate, assessing their suitability for the job based on predetermined criteria. The interviews are typically conducted sequentially, with candidates being evaluated one by one. The process continues until a candidate is found who meets the required qualifications. It is worth noting that the thirty percent figure indicates the proportion of qualified candidates among the total pool of applicants, emphasizing that the majority of candidates do not meet the necessary criteria for the job.

This approach allows the hiring team to carefully evaluate each candidate's qualifications and choose the most suitable individual for the position. By interviewing candidates individually, the selection process aims to identify the best fit for the job based on the specific requirements and desired qualifications.

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Answer:

$390.99 is the price sale!

Step-by-step explanation:

The differnce in the height of Carrie and Julie given their rate of growth is 3 inches.

Carrie's height = 5 feet 1 inch + (2 x 5)

= 5 feet 1 inch + 10 inches

5 feet 11 inches

Julie's height = 4 feet 7 inches + 13 inches

4 feet 20 inches

Difference in height = 5 feet 11 inches - 4 feet 20 inches

I feet = 12 inches

71 inches - 68 inches

3 inches

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Ranking the speeds from the fastest unit rate to the slowest unit rate is as follows:

The unit rate describes the ratio comparing two quantities or values.

The unit rate is computed as the quotient between the numerator and the denominator

⁷/₄ miles in ²/₅ hour = 4.375 miles per hour (⁷/₄ ÷ ²/₅ )

⁴/₅ miles in ¹/₄ hour = 3.2 miles per hour (⁴/₅ ÷ ¹/₄)

¹/₄ miles in ¹/₁₀ hour = 2.5 miles per hour (¹/₄ ÷ ¹/₁₀)

¹/₂ miles in ¹/₃ hour = 1.5 miles per hour (¹/₂ ÷ ¹/₃).

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Answer:

d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

?

Answer · 0 votes

To write fractions with a common denominator, you will most likely need to scale some numbers up! I will explain how. Let's try it with the fractions 23 and 312 12 is larger than 3, so we will have to multiply the 3 by some number to equal 12. (We are really finding the Least Common Multiple of the two denominators!) To do this, you have to multiply the 3 by 4, because 3x4=12. But now the numerator doesn't match the denominator. When you scale the denominator up, you have to scale the numerator up too! So the 2 must be multiplied by 4 also. Now you have the following: 812 and 312 These fractions now have common denominators! Now they're all set for adding or subtracting fractions. Try another: 26 and 35: The least common multiple of 6 and 5 is 30. (the product of the denominators) Transform each fraction by multiplying by "1": 26⋅55 = 1030 and 35⋅66 = 1830 One last problem: 49 and 76 What is the least common multiple of 9 and 6? Could you use 54? Absolutely, but it is not the L…

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1.What’s the least common multiple (LCM) for each group of numbers? a. 6 and 15 b. 4 and 11 c. 6, 9, and 12 d. 8, 10, and 20 2.What’s the least common denominator (LCD) for each group of fractions? a. 1⁄6 and 7⁄8 b. 3⁄4 and 7⁄10 c. 7⁄12, 3⁄8 and 11⁄36 d. 8⁄15, 11⁄30 and 3⁄5 3.Insert the “equal” sign or the “not equal” sign ( = or ≠) to make each statement true. a. 18/36 _____ 1/2 b. 13/15 _____ 7/10 c. 3/5 _____ 5/9 d. 3/8 _____ 10/16 4.On a hot summer day, John drank 5⁄11 of a quart of iced tea; Gary drank 7⁄10 of a quart; and Carter drank 3⁄5 of a quart. Which man was the most thirsty? 5.What’s the largest fraction in each group? a. 5⁄6 and 29⁄36 b. 5⁄12 and 3⁄8 c. 2⁄5 and 19⁄45 d. 5⁄7, 13⁄14, and 19⁄21 e. 7⁄11 and 9⁄121 f. 1⁄2, 3⁄18, and 4⁄9 6.Reduce each of the following fractions to its simplest form. a. 12⁄18 b. 48⁄54 c. 27⁄90 d. 63⁄77 e. 24⁄32 f. 73⁄365 7.What is the next fraction in each of the following patterns? a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .? b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101. . .? c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256. . .? 8.In each pair, tell if the fractions are equal by using cross multiplication. a. 5⁄30 and 1⁄6 b. 4⁄12 and 21⁄60 c. 17⁄34 and 41⁄82 d. 6⁄9 and 25⁄36 9.This year, a baseball player made 92 hits out of 564 times at bat. Another player made 84 hits out of 634 times at bat. Did the two players have the same batting average? 10.On a test with 80 questions, Bob got 60 correct. On another test with 100 questions, he got 75 correct. Did Bob get the same score on both tests? 11.Find the missing numerators in each of the following problems. a. 10⁄15 = ⁄60 b. ⁄108 = 4⁄9 c. 7⁄11 = ⁄121 d. ⁄144 = 2⁄6 12.This handy application of LCMs is used by astronomers. All the planets in our solar system revolve around the sun. The planets occasionally line up together in their journeys, as shown in the illustration. The chart shows the time it takes each planet to make one trip around the sun. Now, imagine that the planets Earth, Mars, Jupiter, Saturn, Uranus, and Neptune aligned last night. How many years will pass before this happens again? (Hint—Find the LCM of the planets’ revolution times.) Solar System Planet Revolution Time Earth 1 year Mars 2 years Jupiter 12 years Saturn 30 years Uranus 84 years Neptune 165 years

Answer · 15 votes

1. a. 30b. 44c. 36d. 402. I don't really remember how to do these but if you cant make the denominator smaller then I belive it's a. 24b. 20c. 4d. 53.a. =b. not =c. not =d. not =4. Gary5. a. 5/6b. 5/12c. 19/45d. 13/14e. 7/11f. 1/26.a. 2/3b. 8/9c. 3/10d. 9/11e. 3/4f. 1/57.a. 36/40b. c. 8.a. yesb. noc. nod. no9. no10. yes11. a. 40b. 48c. 77d. 4812. 4,620

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Wyzant

Question

what is the common denominator for 3/4 and 2/5

Answer · 0 votes

Hi Elikem! To find the common denominator. First check to see if one of the numbers is divisible by the other. In this case 4 is not divisible by 5 and 5 is not divisible by 4. So the next step is to find the common multiple. You do this by writing out the multiples of each. 4 8 12 16 20 24 28 5 10 15 20 25 When you find a common multiple, in this case 20, you have found the common denominator. Hope this helps!I am available for online tutoring for $35 per hour sessions.

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Brainly.ph

Question

What is the least common denominator of 2/6 and 5/12​

Answer · 3 votes

Answer:12Step-by-step explanation:Rewriting input as fractions if necessary: 2/6, 5/12 For the denominators (6, 12) the least common multiple (LCM) is 12. Therefore, the least common denominator (LCD) is 12. Calculations to rewrite the original inputs as equivalent fractions with the LCD:2/6 = 2/6 × 2/2 = 4/125/12 = 5/12 × 1/1 = 5/12

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What is the LCM of 4/6 and 9?

What is the common denominator of 4 and 9?

What is the LCD of 4 and 6?

What is the lowest common denominator of 4 and 9?

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

snsnnsnsnnsnnnsn s s

Answer: 3/5 i think ;-; if its not well then uhhhhh sorry?

Step-by-step explanation:

Answer:

135.04 - 125.62 = 9.42

9.42/125.62=0.07498805

0.07498805 X 100 = 7.49880592

sales tax = 7.5%

Answer:

the answer it will be 4cm

Answer: 1.5

Step-by-step explanation:

Khan academy

The function θ : p(z) → p(z) defined as θ(x) = x is injective and surjective, therefore bijective.

The function θ(x) = x takes an element x from the set p(z) and returns the same element x. This means that for any input x in p(z), the function simply returns x as the output.

To determine whether θ is injective, we need to check if distinct inputs produce distinct outputs. In this case, since the function θ simply returns the input element x, it is evident that if two different elements are provided as input, they will always produce different outputs. Thus, θ is injective.

To assess the surjectivity of θ, we need to determine if every element in the codomain p(z) has a corresponding preimage in the domain p(z). In this scenario, since the function θ returns the same element x that is provided as input, it covers all elements in p(z). Therefore, for any given element in the codomain, there exists a preimage in the domain. Hence, θ is surjective.

Since the function θ is both injective and surjective, it is bijective. This means that for every input element x, there is a unique output element x, and every element in the codomain p(z) has a corresponding preimage in the domain p(z).

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(a) approx. 9.18%, (b) approx. 62.47%, (c) approx. 25.80%, and (d) approx. 2.28%. These probabilities were calculated based on the given mean and standard deviation of the animal's pregnancy lengths, assuming a normal distribution.

In a population of a particular animal, the lengths of pregnancies follow a normal distribution with a mean (μ) of 276 days and a standard deviation (σ) of 8 days. We can use this information to answer the following questions:

(a) To find the proportion of pregnancies that last more than 290 days, we need to calculate the area under the normal curve to the right of 290 days. This corresponds to the probability of observing a pregnancy length greater than 290 days. By standardizing the values, we can use the Z-score formula. The Z-score is calculated as (X - μ) / σ, where X is the value we are interested in. In this case, X = 290. By calculating the Z-score and consulting a standard normal distribution table or using a calculator, we find that the proportion of pregnancies lasting more than 290 days is approximately 0.0918 or 9.18%.

(b) To determine the proportion of pregnancies lasting between 264 and 282 days, we need to calculate the area under the normal curve between these two values. We can use the Z-score formula to standardize the values (X = 264 and X = 282) and find the corresponding Z-scores. Using the standard normal distribution table or a calculator, we can find the area between these Z-scores. The proportion of pregnancies lasting between 264 and 282 days is approximately 0.6247 or 62.47%.

(c) To find the probability that a randomly selected pregnancy lasts no more than 274 days, we need to calculate the area under the normal curve to the left of 274 days. By standardizing the value using the Z-score formula (X = 274), we can determine the corresponding Z-score and find the area to the left of this Z-score using the standard normal distribution table or a calculator. The probability that a randomly selected pregnancy lasts no more than 274 days is approximately 0.2580 or 25.80%.

(d) A "very preterm" baby is defined as one whose gestation period is less than 256 days. To determine the probability of a baby being born very preterm, we need to calculate the area under the normal curve to the left of 256 days. By standardizing the value using the Z-score formula (X = 256) and finding the corresponding Z-score, we can calculate the area to the left of this Z-score. The probability of a baby being born very preterm is approximately 0.0228 or 2.28%.

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The eigenvector v corresponding to the eigenvalue λ = 5 is v = [1; 1; 1].

To show that λ = 5 is an eigenvalue of matrix A, we need to find a non-zero vector v such that Av = λv.

Given A = [6 1 -1; 1 4 1; 4 2 3] and λ = 5, we substitute these values into the equation Av = λv:

[6 1 -1; 1 4 1; 4 2 3] * [x; y; z] = 5 * [x; y; z]

This gives us the following system of equations:

6x + y - z = 5x

x + 4y + z = 5y

4x + 2y + 3z = 5z

Simplifying each equation, we have:

x - y + z = 0

x - y + z = 0

x - y + z = 0

Notice that all three equations are the same. This implies that the system has infinitely many solutions, meaning there are infinitely many eigenvectors corresponding to the eigenvalue λ = 5.

We can choose any non-zero vector that satisfies the equation, such as v = [1; 1; 1]. Substituting this vector into the equation Av = λv:

[6 1 -1; 1 4 1; 4 2 3] * [1; 1; 1] = 5 * [1; 1; 1]

[6 + 1 - 1; 1 + 4 + 1; 4 + 2 + 3] = [5; 5; 5]

[6; 6; 9] = [5; 5; 5]

Both sides of the equation are equal, confirming that v = [1; 1; 1] is an eigenvector corresponding to the eigenvalue λ = 5.

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Answer: The Answer is 3rd

Answer:

Hey there!

They are congruent by AAS, where two angles and one side is congruent.

Hope this helps :)