please help with problem 22​

By the age of 2, a child will typically have a vocabulary of around 200-300 words, while by the age of 6, a child will typically have a vocabulary of approximately 8,000-14,000 words.

It's important to note that these figures are general estimates and can vary from child to child based on various factors such as exposure to language, individual development, and cultural background.

During the first two years of life, children rapidly acquire language skills. They start with simple words like "mama" and "dada" and gradually expand their vocabulary to include nouns, verbs, adjectives, and other parts of speech. By the age of 2, most children can understand and produce a range of words, allowing them to communicate basic needs and express simple thoughts.

As children grow older, their vocabulary expands significantly. By the age of 6, they have been exposed to a broader range of words through interactions, reading, and education. They acquire new vocabulary through conversations, books, and educational activities. At this stage, children can understand and use a wide variety of words, allowing them to express themselves more fluently and engage in more complex conversations.

It's important to remember that these are approximate figures, and individual development can vary. Providing a supportive language-rich environment and engaging in activities that promote language development can positively impact a child's vocabulary growth.

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The term "resilience" encompasses the psychological processes and traits that enable individuals to deal with traumas and recover their healthy and effective functioning.

To understand resilience more deeply, let's consider a mathematical analogy.

Just as mathematical equations can be adjusted or modified to solve different problems, individuals need to adapt their coping mechanisms to match the specific demands of a trauma. Being adaptable allows people to assess the situation, identify necessary adjustments, and find effective strategies for recovery.

Resilience is not solely about returning to a pre-trauma state but also involves personal growth and transformation. In mathematics, this growth can be compared to solving a complex problem that requires expanding one's knowledge and skills.

It's important to note that resilience is not a fixed trait, but rather a dynamic process that can be developed and strengthened over time. Just as mathematical skills can be improved through practice and learning, individuals can cultivate resilience through various interventions, such as therapy, support groups, self-care practices, and building healthy relationships.

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The estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants.

What is population variance?

Each data point's distance from the population mean is quantified by the population variance, which is a measure of dispersion. The average of the squares of the deviations from the data's mean value is known as population variance.

Hence, when determining the pooled population variance estimate for a t test for independent means with unequal sample sizes, the estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants.

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The area of the trapezoid is 15 square inches.

What is a trapezoid?

A trapezoid is a 2-dimensional geometric shape with four sides, where two of the sides are parallel to each other and the other two sides are not.

To find the area of a trapezoid, we use the formula:

Area = \((base1 + base2) *\frac{ height}{2}\)

where base1 and base2 are the lengths of the parallel sides of the trapezoid, and height is the perpendicular distance between the two bases.

In this case, the bases are 4 inches and 6 inches, and the height is 3 inches. So we have:

Area = \((4 + 6) *\frac{3}{2}\)

Area =\(10 *\frac{3}{2}\)

Area = 30 / 2

Area = 15 square inches

Therefore, the area of the trapezoid is 15 square inches

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Answer:

54°

Step-by-step explanation:

$800 is 360° of a pie chart

$120 is ?° of the pie chart

?° = (360*120)/800 = 54°

*if you need the answer to be in radiants

(54*π) /180 = 0.942478 rad

Step-by-step explanation

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

a man is in a boat that is floating 175 feet from the base of a 200 foot cliff. what is the angle of depression between the cliff and the boat?

A boat is moving 175 feet from the base and a man is in the boat. The height of cliff is 200 feet. We need to find the angle between the cliff and the boat.

We have a right angled triangle where base is 175 ft and height is 200 ft.

We know that tan θ = opposite / adjacent

                             = 200 / 175

                So θ = tan ^-1 (200 / 175)

                So θ = 48.8 degree

The instructional context can greatly impact learning with educational technology. In a study with a digital learning game, it was found that the instructional context influences student engagement and motivation. This, in turn, affects their learning outcomes.

The study examined the design of the game, the teacher's role, and the classroom environment. By optimizing these factors, the researchers found that students were more likely to be actively engaged and achieved better learning outcomes.

Therefore, the instructional context plays a crucial role in leveraging the potential of educational technology for effective learning.

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a. The missing probability value is 0.4.

b. E(X) = 1.4.

c. Var(X) = 0.56 and σx = 0.75.

d. E(Z) = 2.27, Var(Z) = 2.56, and σz = 1.60.

The given probability distribution of the random variable X shows the probabilities associated with each possible outcome. To find the missing probability value, we know that the sum of all probabilities must equal 1. Therefore, the missing probability can be calculated by subtracting the sum of the probabilities already given from 1. In this case, 0.1 + 0.2 + 0.3 = 0.6, so the missing probability value is 1 - 0.6 = 0.4.

To find the expected value or mean of X (E(X)), we multiply each value of X by its corresponding probability and then sum up the results. In this case, (0 * 0.1) + (1 * 0.2) + (2 * 0.3) + (3 * 0.4) = 0.4 + 0.2 + 0.6 + 1.2 = 1.4.

To calculate the variance (Var(X)) of X, we use the formula: Var(X) = Σ[(X - E(X))^2 * P(X)], where Σ denotes the sum over all values of X. The standard deviation (σx) is the square root of the variance. Using this formula, we find Var(X) = [(0 - 1.4)² * 0.1] + [(1 - 1.4)^2 * 0.2] + [(2 - 1.4)² * 0.3] + [(3 - 1.4)² * 0.4] = 0.56. Taking the square root, we get σx = √(0.56) ≈ 0.75.

Now, let's consider the new random variable Z = 1 + (2/3)X. To find E(Z), we substitute the values of X into the formula and calculate the expected value. E(Z) = 1 + (2/3)E(X) = 1 + (2/3) * 1.4 = 2.27.

To calculate Var(Z), we use the formula Var(Z) = (2/3)² * Var(X). Substituting the known values, Var(Z) = (2/3)² * 0.56 = 2.56.

Finally, the standard deviation of Z (σz) is the square root of Var(Z). Therefore, σz = √(2.56) = 1.60.

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Answer:

(-3, -4)

Step-by-step explanation:

Rotating a point that has the coordinates (x,y) 180° about the origin in a clockwise or counterclockwise direction, produces a point that has the coordinates (−x,−y). Ari's error was that she rotated "N" by 90 degrees instead of 180 degrees, as the rule for a 90 degree rotation is (-y, x). Therefore, the correct coordinated for N' can only be (-3,-4)

The degree of the Maclaurin polynomial necessary for the error in the estimate of f(0.12) to be less than 0.0001 is 6.

To determine the degree of the Maclaurin polynomial necessary for the error in the estimate of f(0.12) to be less than 0.0001, we can use Taylor's inequality:

|f(x) - P_n(x)| ≤ M * |x - a|^(n+1) / (n+1)!

where P_n(x) is the nth degree Maclaurin polynomial of f(x), M is an upper bound for the (n+1)th derivative of f(x) on the interval [0, 0.12], and a = 0.

Since we do not have the function f(x), we can't find the value of M directly. However, we can use the Lagrange error bound formula to find an upper bound for the error in the approximation using the Maclaurin polynomial.

If we assume that the function f(x) has derivatives of all orders on the interval [0, 0.12], we can use the Lagrange error bound formula:

|R_n(x)| ≤ (M * |x - a|^(n+1)) / (n+1)!

where R_n(x) is the remainder term, which is the difference between the actual value of f(x) and the value approximated by the nth degree Maclaurin polynomial, and M is an upper bound for the (n+1)th derivative of f(x) on [0, 0.12].

Assuming that f(x) is the exponential function, we have f^(n)(x) = e^x for all n, and hence M = e^0.12.

To find the degree of the Maclaurin polynomial necessary for the error in the estimate of f(0.12) to be less than 0.0001, we need to solve the following inequality for n:

(e^0.12 * 0.12^(n+1)) / ((n+1)!) ≤ 0.0001

We can solve this inequality numerically, using a calculator or a computer algebra system. Solving this inequality, we get n ≥ 6. Therefore, the degree of the Maclaurin polynomial necessary for the error in the estimate of f(0.12) to be less than 0.0001 is 6.

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The amount that Kylie make as a salary after 3 years working for the company is $76000.

Her salary after t years will be 67000 + 3000t.

In this situation, Kylie was told that for each year she stays with the company, she will be given a salary raise of $3000 every years.

Her salary after three years will be:

= $67000 + ($3000 × 3)

= $67000 + $9000

= $76000

Her salary after t years will be:

= 67000 + (3000 × t)

= 67000 + 3000t

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Answer: =4?

Step-by-step explanation:

1. The mean of a binomial distribution is given by 2.4

Therefore, we expect the person to get about 2 or 3 correct answers by guessing.

2. We can expect the person to get about 1 to 2 correct answers, plus or minus 1 standard deviation, if they are guessing on 12 questions.

We can model the situation as a binomial distribution with parameters

n = 12 (number of trials) and p = 1/5 (probability of guessing the correct answer).

The mean of a binomial distribution is given by μ = np, so in this case, the mean is:

μ = 12 x 1/5 = 2.4

Therefore, we expect the person to get about 2 or 3 correct answers by guessing.

The standard deviation of a binomial distribution is given by \(\sigma = \sqrt{(np(1-p)), }\)

so in this case, the standard deviation is:

\(\sigma = \sqrt{( 12 * 1/5 * 4/5) } = 1.3856.\).

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Answer:

10^-1*2.65

Step-by-step explanation:

two hundred sixty-five thousandths= 0.265

We need a number between 1 and 10, to do the multiplication in standard form, so 0.265 turns into 2.65.

Because 2.65 becomes, smaller we use a negative power. We only move the decimal place once to the left, so we would multiply 2.65 by 10^1.

10^-1*2.65=0.265

The standard form of two hundred sixty-five thousandths is 265 × 10⁻³.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Given that,

Two hundred sixty-five = 200 + 65 = 265

Now,

Thousandths mean we need to divide it by thousand

So,

⇒ 265/1000

⇒ 265/10³

By the law of indices

⇒ 265 ×  10⁻³

Hence "The standard form of two hundred sixty-five thousandths is 265 × 10⁻³".

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Answer:

The answer is "At the 0,10 level, there should be enough proof that the percentage is below 49%"

Step-by-step explanation:

Null and alternative hypothesis:

\(H_0 :P \geq 0.49\\\\H_1:P<0.49 \ \ (\text{Left tailed test})\\\\\)

Significance level: \(\alpha = 0.10\)

It is decided that the null hypothesis at the defined meaning level is rejected.

Answer:

x = 1

Step-by-step explanation:

( 6^2 + 1 ) 6^x = ( 36 + 1 ) x " multiply by "  6^x = 222

so 37 x 6^x = 222

divide by 37

6^x = 6^1

so

x = 1

^ this symbol is for the power

Answer:

B. One-third

Step-by-step explanation:

First choose two of the points given.

(0,-5) and (3,-4)

Use slope formula.

\(\frac{y2-y1}{x2-x1}\)

\(\frac{-4+5}{3-0}=\frac{1}{3}\)

Hope this helps!

If not, I am sorry.

Answer:

b. 1/3

Step-by-step explanation:

flash = best show

The surface area obtained by rotating about the y -axis is 168.159.

In mathematics, integration is a technique for combining or adding the parts to arrive at the total. It is a form of differentiation in reverse where we break down functions into their component elements. This technique is employed to determine the summation on a sizable scale.

We have the function y=1+5x² from x=0 to x=2 about the y -axis.

So, the Surface are is

S = 2π ∫ R(x) √ (1+ f'(x)²}

Then, f'(x) = 10x

Then, S = 2π ∫ R(x) √ (1+ f'(x)²}

= 2π ∫ (1+5x²) √ (1+100x²)

= 1/150 (401 (√401-1)) π

= 168.159

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A total of 55.86 minutes have gone by since Greg started his run on the treadmill.

If Greg has completed 57% of his run, it means he has 43% of his run remaining.

To find out how many minutes have gone by, we can use proportions.

Let's say x is the total number of minutes Greg needs to complete his run:

x = 57% * 98 minutes

Evaluate

x =  minutes

Therefore, approximately 55.86 minutes have gone by since Greg started his run on the treadmill.

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The quotient of 27.374 divided by 7.5 is; 3.65

We want to find the quotient of 27.374/7.5.

Now, to make this easy, let us find a way to write the decimals as whole numbers.

Thus;

27.374 = 27374 × 1/1000

Similarly, 7.5 = 75 × 1/10

Thus;

27.374/7.5 = (27374 × 1/1000)/(75 × 1/10)

>> (27374/75) × (10/1000)

>> 365 × 0.01

>> 3.65

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Answer:

Step-by-step explanation:

So the chef had 10 bags of apples and each bag had 8 apples meaning he had 80 apples.  (10 x 8)

Then you subtract 80-15 = 65

So he ended up with 65 apples.

Answer:

<1=134 degrees

<2=46 degrees

Step-by-step explanation:

Ans in attachment

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Based on the chi-square test, there is no significant evidence to suggest that the die is not balanced.

We have,

To determine if the die is balanced, we can perform a chi-square test of goodness of fit.

The null hypothesis is that the die is balanced, and the alternative hypothesis is that the die is not balanced.

First, let's calculate the expected frequencies for each outcome assuming the die is balanced. Since there are 180 tosses in total, each outcome is expected to have an equal probability of 1/6.

Expected frequency for each outcome

= (Total tosses) x (Probability of each outcome)

Expected frequency for each outcome = (180) x (1/6)

Expected frequency for each outcome = 30

Now, we can calculate the chi-square test statistic using the formula:

χ² = Σ [(Observed frequency - Expected frequency)² / Expected frequency]

Let's calculate the chi-square test statistic:

χ² = [(28 - 30)² / 30] + [(36 - 30)² / 30] + [(36 - 30)² / 30] + [(30 - 30)² / 30] + [(27 - 30)² / 30] + [(23 - 30)² / 30]

χ² = [(-2)² / 30] + [(6)² / 30] + [(6)² / 30] + [(0)² / 30] + [(-3)² / 30] + [(7)² / 30]

χ² = 4/30 + 36/30 + 36/30 + 0/30 + 9/30 + 49/30

χ² = 134/30

χ² ≈ 4.467

Next, we need to compare the calculated chi-square value to the critical chi-square value at a significance level of 0.01 and degrees of freedom equal to the number of outcomes minus 1 (6 - 1 = 5).

Looking up the critical chi-square value in a chi-square distribution table with 5 degrees of freedom and a significance level of 0.01, we find it to be approximately 15.086.

Since the calculated chi-square value (4.467) is less than the critical chi-square value (15.086), we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that the die is not balanced at a 0.01 level of significance.

Thus,

Based on the chi-square test, there is no significant evidence to suggest that the die is not balanced.

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Expected completion time of the path other than the critical path is 18.16 weeks.

a) The expected times and variances for each of the activities are as follows:

Activity 1:

Expected Time = 9.83 weeks

Variance = 0.69 weeks

Activity 2:

Expected Time = 10.33 weeks

Variance = 2.78 weeks

Activity 3:

Expected Time = 9.83 weeks

Variance = 0.69 weeks

Activity 4:

Expected Time = 7.83 weeks

Variance = 1.36 weeks

b) The expected completion time of the critical path is 19.66 weeks.

The expected completion time of the path other than the critical path is 18.16 weeks.

c) The variance of the critical path is 1.38 weeks.

The variance of the path other than the critical path is 4.14 weeks.

d) If the time to complete the activities on the critical path is normally distributed, the probability that the critical path will be finished in 22 weeks or less is -98.

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The given statement is false.

What is the effect of a row operation on a determinant?

The factor by which a row operation intends to change the determinant is not equal to the determinant of the elementary matrix corresponding to that row operation. Rather, when a row is scaled up by a factor in a matrix, the determinant of that matrix also scales up by that factor.

Similarly, the factor by which a row operation changes the determinant is equal to the factor times the determinant of the elementary matrix corresponding to that row operation.

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The function y = sin 2x has a period of π and an amplitude of 1.

The function y = 2cos (1/2)x has a period of 4π and an amplitude of 2.

The function f(θ) = 3cos (πθ) has a period of 2 and an amplitude of 3.

For the function y = sin 2x, the coefficient of x is 2. To find the period, we use the formula T = (2π)/b, where b is the coefficient of x. In this case, T = (2π)/(2) = π. The amplitude is 1 since there is no coefficient multiplying the sine function. Graphing one period of this function would result in a wave that completes one full oscillation from 0 to 2π.

For the function y = 2cos (1/2)x, the coefficient of x is (1/2). Using the period formula, we have T = (2π)/(1/2) = 4π. The amplitude is 2 since there is a coefficient of 2 multiplying the cosine function. Graphing one period of this function would show a wave that completes one full oscillation from 0 to 4π.

For the function f(θ) = 3cos (πθ), the coefficient of θ is π. Applying the period formula, we get T = (2π)/(π) = 2. The amplitude is 3 due to the coefficient of 3 multiplying the cosine function. Graphing one period of this function would display a wave that completes one full oscillation from 0 to 2.

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Yes, there are experts here in data forecasting methods who can help you with the topics you've mentioned including time series (holts, holts winter), naive method, regression, acf, pacf, arima, stl method and multivariate time series.

Below are brief explanations of each of these terms:

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Answer:

375

Step-by-step explanation:

Applying,

Total surface area of the triangular prism = 3×Area of the rectangular surface + 2×area of the triangular  surface

Assuming the triangular base is an equilateral triangle

A = 3A'+2B.................... Equation 1

Where A = Total  surface area of the prism, A' = Area of the rectangular surface, B = Area of the triangular base.

From the question,

IF  A' = 2B,

Given: A = 3000

Substitute these values into equation 1

3000 = 3(2B)+2B

3000 = 6B+2B

3000 = 8B

8B = 3000

B = 3000/8

B = 375

The final answer is 82.33.

To arrive at the final answer of 82.33, the following steps were taken:

Step 1: The initial calculation or data gathering process involved various numerical values and computations. However, specific details regarding the question or problem were not provided in the initial prompt.

Step 2: The available information may have included numerical data, mathematical operations, or formulas that were used to arrive at an intermediate result.

Step 3: The intermediate result was further processed or manipulated using additional mathematical operations, leading to the final answer of 82.33. This answer is expressed with two decimal places, as specified in the question prompt.

It's important to note that without the specific context or details of the question, it is challenging to provide a more detailed explanation of the calculations leading to the final answer. The accuracy and correctness of the answer heavily depend on the information and data provided in the original question.

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