determine whether the statement is true or false. if f and g are differentiable, then d dx [f(g(x))]

Answer:

17.9 degrees

Step-by-step explanation:

tangent x= 3.2/9.9

tangent x= 0.323

x=tan^-1(0.323)

x=17.9 degrees

The p-value of this chi-squared goodness of fit test is 0.770 which is the the second option. Since the p-value (0.770) is greater than the significance level (0.05), we fail to reject the null hypothesis. This means there is insufficient evidence to conclude that the dice are not fair based on the observed frequencies.

To perform a chi-squared goodness of fit test to assess if the observed frequencies of the sums from rolling the dice 200 times significantly deviate from the expected probabilities. The followings are the steps to determine the answer.

State the null and alternative hypotheses:

- Null Hypothesis (H₀): The dice are fair, and the observed frequencies match the expected probabilities.

- Alternative Hypothesis (H₁): The dice are not fair, and the observed frequencies differ significantly from the expected probabilities.

- Set the significance level (α): The significance level determines the threshold for rejecting the null hypothesis. Let's assume α = 0.05.

Calculate the expected frequencies: Multiply the expected probabilities for each sum by 200 to obtain the expected frequencies for each sum.

Expected Frequencies:

- Sum: 2 3 4 5 6 7 8 9 10 11 12

- Exp: 5.56 11.11 16.67 22.22 27.78 33.33 27.78 22.22 16.67 11.11 5.56

Calculate the chi-squared test statistic:

- Compute the chi-squared value for each sum using the formula: (Observed Frequency - Expected Frequency)² / Expected Frequency.

- Sum up all the chi-squared values to obtain the test statistic.

Observed Frequencies:

- Sum: 2 3 4 5 6 7 8 9 10 11 12

- Obs: 3 11 15 29 33 20 31 25 21 8 4

Chi-Squared Test Statistic:

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

Determine the degrees of freedom (df):

- The degrees of freedom for a goodness of fit test is equal to the number of categories (sums) minus 1.

df = Number of Categories - 1 = 11 - 1 = 10

Calculate the p-value:

- The p-value represents the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true. We can use a chi-squared distribution table or a calculator to find the p-value associated with the test statistic and degrees of freedom.

Given the test statistic and degrees of freedom, we can calculate the p-value. In this case, the p-value is approximately 0.770.

The complete question must be:

You are stuck at home with your family during a quarantine. To pass time, you play games with your siblings Lisa and Maggie. In the course of 10 games, Maggie wins all of them and you begin to suspect that she is cheating by rigging the dice. To check this, you roll two dice 200 times (observing the sum of the numbers facing up) that were being used for the games:

Sum of Two Dice 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Number of Occurrences 3, 11, 15, 29, 33, 20, 31, 25, 21, 8, 4

Perform a chi-squared goodness of fit test to test the null hypothesis that the dice are fair versus the alternative that the dice are not fair. What is the p-value of this test? options 0.011, 0.770, 0.301, 0.230

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The inverse Laplace transform of the function F(s) = se^(-4s)/(s^2 + 8s + 41) can be found by applying partial fraction decomposition and using known Laplace transform pairs.

First, we factorize the denominator of the function: s^2 + 8s + 41 = (s + 4)^2 + 25. This gives us complex roots: -4 + 5i and -4 - 5i.

Next, we express the function F(s) as a sum of partial fractions: F(s) = A/(s + 4) + (Bs + C)/(s^2 + 8s + 41), where A, B, and C are constants to be determined.

By equating the numerators, we get: se^(-4s) = A(s^2 + 8s + 41) + (Bs + C)(s + 4).

Expanding and comparing coefficients, we find A = -1/25, B = -1/25, and C = 4/25.

Now, we can take the inverse Laplace transform of each term using known Laplace transform pairs. The inverse Laplace transform of A/(s + 4) is -e^(-4t)/25, and the inverse Laplace transform of (Bs + C)/(s^2 + 8s + 41) is (4sin(5t) - cos(5t))e^(-4t)/25.

Therefore, the inverse Laplace transform of F(s) is given by f(t) = -e^(-4t)/25 + (4sin(5t) - cos(5t))e^(-4t)/25.

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First, convert the mixed fraction into an improper fraction.

\(2\dfrac{2}{5} = \dfrac{12}{5}\)

Divide the improper fraction by 6 since the sandwhich will be cut into 6 even sections.

\(\dfrac{12/6}{5} = \dfrac{2}{5}\)

Thus, each section is 2/5 feet long. Let me know if you have any questions, thanks!

Answer:

x+(x+7)=91

Step-by-step explanation:

Hope this helps :)

Answer:   your answer for the smaller number is 38.5 and the larger number is 52.5.

Step-by-step explanation:

To make sure it's right, I just add the numbers together.

Your Problem:

91 ÷ 2 = 45.5

45.5 + 7 = 52.5

45.5 - 7 = 38.5

52.5 + 38.5 = 91

Given that, the area of a circular swimming pool is approximately 18 m². We need to find the radius of the circular swimming pool.

We know that the formula to find the area of a circle is given by the equation:

A = πr²

Here, A represents the area of the circle, π represents the mathematical constant \pi  (3.14), and r represents the radius of the circle.We can use this formula to find the radius of the given circular swimming pool.

We can rearrange the formula as:

r = sqrt(A/π)

On substituting the given value of area A = 18 m² and the value of pi as 3.14, we get:

\(r = \sqrt{18/3.14}\)

≈ \(\sqrt{5.73}\)

≈ 2.39 m

Therefore, the radius of the circular swimming pool is approximately 2.39 meters. This is the solution to the problem. A circle is a two-dimensional shape, which means it has an area but no volume. The area of a circle is defined as the amount of space inside the circular boundary. It is equal to the product of π and the square of the radius of the circle.

We can use the formula A = πr² to find the area of a circle, where A is the area of the circle, π is the mathematical constant \(\pi\) (3.14), and r is the radius of the circle.

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Answer:

(5+-1) (2+2

Step-by-step explanation:

Answer:h=16+2+vt +s

Step-by-step explanation:

For the probability of any particular event occurring is 7 /10 then odds of favoring the event which is not occurring in the form of a: b is equal to

7 : 3.

As given in the question,

Probability of any particular event occurring is equal to 7 /10

Probability of any particular event not occurring is = 1- (7/10)

                                                                                    = (10 -7) /10

                                                                                    = 3/10

Probability of the odds favoring the events which are not occurring

= (7 /10) / (3/10)

= ( 7 × 10) / (3 × 10)

= 7 /3

Odds favoring the events which are not occurring in the form a: b

= 7 : 3

Therefore, for the probability of any particular event occurring is 7 /10 then odds of favoring the event which is not occurring in the form of a: b is equal to 7 : 3.

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Answer: M = Five over three

Of the given options, "Oligarchic rule must be abolished in South Africa" most closely represents Nelson Mandela's belief as spoken in his inaugural address.

Nelson Mandela's inaugural address marked a pivotal moment in South Africa's history, as he became the country's first democratically elected president after decades of apartheid rule. In his speech, Mandela emphasized the need for equality, justice, and the dismantling of oppressive systems. While the specific phrase "oligarchic rule must be abolished in South Africa" may not be directly mentioned, the sentiment aligns with Mandela's vision for a democratic and inclusive South Africa.

Mandela strongly believed in the principles of democracy, freedom, and equal rights for all South Africans. His fight against apartheid was rooted in the belief that the system of racial segregation and discrimination was unjust and had to be dismantled. Mandela spoke out against the continued apartheid system and laws, advocating for their complete elimination. He recognized that apartheid, although it may have been deemed understandable by some in the past, was fundamentally wrong and had to be eradicated for the sake of a unified and prosperous nation. In his inaugural address, Mandela emphasized reconciliation and the importance of building a united South Africa. While the exact phrase "apartheid was once an understandable policy in South Africa, but not anymore" may not be present, Mandela's words conveyed the idea that the old system of apartheid was no longer acceptable or justifiable. He sought to move the country forward by embracing a new era of equality, where all citizens, regardless of race or background, could participate fully in the democratic process and enjoy equal rights and opportunities.

In conclusion, while the provided options do not directly mirror Nelson Mandela's exact words, the statement that "oligarchic rule must be abolished in South Africa" best reflects his belief in dismantling oppressive systems and establishing a democratic society based on equality and justice.

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Answer:

(-1, 9)

Step-by-step explanation:

given

\(y = - 3x + 6 \\ and \\ y = 9 \\ then \: we \: need \: to :\ find \: x \: so \: that \: when \: plugged \\ to \: - 3x + 6 \: the \: result \: is \: 9 \\ by \: transitive \: rule \\ y = 9 = - 3x + 6 \\ 9 = - 3x + 6 \: (substract \: both \: sides \: with \: 6) \\ 3 = - 3x \: (divides \: both \: sides \: with \: - 3) \\ - 1 = x\)

Answer:

the answer is c

Step-by-step explanation:

because i just took the test

d. It is impossible to determine how the Gini coefficient will change as it will depend on the original income distribution.

The Gini coefficient is a measure of income inequality in a society. It takes into account the entire income distribution, not just the average or total increase in income. The change in the Gini coefficient depends on how the income increase is distributed among different income groups.

If the income increase is distributed equally among all households, then the Gini coefficient would stay the same because the relative income differences between households remain unchanged. However, if the income increase is concentrated among higher-income households, it is likely that the Gini coefficient would increase, indicating a higher level of income inequality.

On the other hand, if the income increase is disproportionately distributed to lower-income households, it is possible for the Gini coefficient to decrease, indicating a reduction in income inequality.

Therefore, without knowing the initial income distribution and how the income increase is distributed across households, it is impossible to determine how the Gini coefficient will change over the 10-year period.

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To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them.

The problem with either the mean or the median as a measure of center in this case is that the data is not separated by gender, and the shoe size distributions for men and women are likely to be different. Therefore, computing the mean or median shoe size across all students may not accurately represent the typical shoe size for men or women separately.

For example, if the men in the sample have, on average, larger shoe sizes than the women, then the mean shoe size across all students may be biased towards the larger sizes, even though the majority of the students are women. On the other hand, if there are a few male students with very large shoe sizes, then the median shoe size across all students may be biased towards the larger sizes as well, even if most of the students are women with smaller shoe sizes.

To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them. Alternatively, a better measure of center might be to report the mode, which represents the most common shoe size in the data.

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\(4 \times + 5 \times + 135 = 180\)

\(9 \times + 135 = 180 \\ 9 \times = 45 \\ \times = 45\)

By using percentage, it can be calculated that

Percentage decrease in the screen time for Lora  = 40 %

What is percentage?

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example 9% means \(\frac{9}{100}\). Here 9 is expressed as a fraction of 100

Here, Percentage decrease will be calculated

Screen time for Lora last week = 840 minutes

Screen time for Lora this week = 504 minutes

Decrease in screen time for Lora = (840 - 504) minutes

                                                        = 336 minutes

Percentage decrease in the screen time for Lora = \(\frac{336}{840}\times 100\) = 40 %

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Jill earned $207 last week for picking 370 containers.

According to the information given, Jill picks corn and is paid at a piecework rate.

She receives 55 cents per container for the first 300 containers picked, and then she receives 60 cents per container for every container picked beyond 300.

Last week, Jill picked 370 containers. To calculate how much she earned, we can break it down into two parts:

the first 300 containers and the remaining 70 containers.

For the first 300 containers, Jill earns 55 cents per container. So, the amount she earned for the first 300 containers is:

300 containers x $0.55/container = $165

For the remaining 70 containers, Jill earns 60 cents per container. So, the amount she earned for the remaining 70 containers is:

70 containers x $0.60/container = $42

To find out the total amount Jill earned, we add the amounts she earned for the first 300 containers and the remaining 70 containers:

$165 + $42 = $207

Therefore, Jill earned $207 last week for picking 370 containers.

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Answer:

one

Step-by-step explanation:

3(x - 2) = 22 - x

3x - 6 = 22 - x

3x + x = 22 + 6

4x = 28

4x/4 = 28/4

x = 7

The measurement of angle DBC is equal to 33°, here we have to know the meaning of angle.

Angle is the measurement distance between two straight line or ray when they meet and it can also say that their one part is opening and other part is joint.

We have given that, ∠ABD = 4x, ∠DBC = 3x and measure of angle ABC is equal to 77°.

So ∠ABD + ∠DBC = ∠ ABC

⇒  4x + 3x = 77°

⇒ 7x = 77°

⇒ x = 11°

So, ∠ ABD = 4x = 4 * 11 = 44°

and, ∠DBC = 3x = 3 * 11 = 33°

Therefore, angle DBC is equal to 33°.

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Complete Question:

What is the measure of angle DBC if the measure of angle ABD is represented by 4x, the measure of angle DBC is represented by 3x and the measure of angle ABC is 77° ?

The integral S/2 sinθ(x) cos²(x) dx is equivalent to the integral (E) Sou du.

To determine the equivalent integral of S/2 sinθ(x) cos²(x) dx, we can use the trigonometric identity:

cos²(x) = (1 + cos(2x))/2

Substituting this into the integral, we have:

S/2 sinθ(x) cos²(x) dx = S/2 sinθ(x) (1 + cos(2x))/2 dx

Now, we can distribute the sinθ(x) term:

= S/4 [sinθ(x) + sinθ(x) cos(2x)] dx

Using the trigonometric identity sinθ(x) cos(2x) = (1/2)sin(2x)sinθ(x), we get:

= S/4 [sinθ(x) + (1/2)sin(2x)sinθ(x)] dx

Factoring out sinθ(x), we have:

= S/4 sinθ(x) [1 + (1/2)sin(2x)] dx

Now, comparing this with the given options, we can see that the equivalent integral is:

(E) S u du

Therefore, the integral S/2 sinθ(x) cos²(x) dx is equivalent to the integral (E) Sou du.

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The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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The width of a rectangular prism with a surface area of 930 square units is  21.4 units.

What is the surface area of the rectangle?

The area of the rectangle can be calculated by multiplying l×w, The units associated with the surface area will always be units squared. The area is the result of multiplying two dimensions, length, and width, which can be represented as a power of 2.

The surface area of the rectangular prism is given by:

SA = 2lw + 2lh + 2wh

Where,

l: length

w: width

h: height

Therefore, by substituting values we have:

the surface area of 930 square units if its length is 12 units and its height is 9 units.

SA = 2lw + 2lh + 2wh

930 = 2(12)w + 2(12)(9) + 2w(9)

930 = 24w + 33 + 18w

930 - 33 = 24w + 18w

897 = 42w

w = 897/42

w = 21.4

Hence, the width of a rectangular prism with a surface area of 930 square units is  21.4 units.

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Answer:

16

Step-by-step explanation:

48/3 = 16    <- Per minute

Answer:

-30

Step-by-step explanation:

Since the diver went down 30 feet it would be -30 from where they started

Answer:

D- Recording the reaction time of participants in a study who were asked to press a button as soon as they see a certain picture on a screen.

Step-by-step explanation:

The situation is an example of an observational study is "Recording the reaction time of participants in a study who were asked to press a button as soon as they see a certain picture on a screen:.

When researchers monitor the effect of a risk factor, diagnostic test, therapy, or other intervention without attempting to influence who is or is not exposed to it in observational studies.

For example: Consider someone standing on a popular street in a New York neighborhood asking passers-by how many dogs they have, then analyzing the data to see if more pet food businesses are needed in the area.

As we know that in an observational study, the sample whose test/survey is been taken is completely random.

Therefore, the situation that is an example of an observational study is " Having customers fill out a questionnaire about their favorite brand of toothpaste".

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Answer:

The chemical element loses 4% of its weight everyday

Step-by-step explanation:

Here, we are interested in knowing the percentage weight loss of the chemical each day.

The key to answering this is looking at the expression inside the bracket.

We can express M(t) = 169•(0.96)^t as

M(t) = 169•(1-0.04)^t

So what this means is that we need to find the percentage value corresponding to 0.04 since it is a constant term here

Mathematically, 0.04 is same as 4/100, so we can clearly say that the constant percentage loss is 4%

Answer:

0.96

Step-by-step explanation:

The exponential function modeling the mass of the sample is of the form M(t)=A⋅Bt. Therefore, AAA determines the initial mass of the sample (when Clemence began studying it) and BBB determines the daily change in the mass of the sample.

The mass of the sample is multiplied by \it{0.96}0.960, point, 96 every day. Since 0.96<10.96<10, point, 96, is less than, 1, the mass of the sample shrinks by a factor of 0.960.960, point, 96 every day.

Every day, the mass of the sample shrinks by a factor of 0.960.960, point, 96.

Answer:

p=1

Step-by-step explanation:

isolate the variable by dividing each side by factors that don't contain the variable.

Answer: p=1

Step-by-step explanation: you write the equation 11p - 4 = 6p + 1

You add four to both sides and then you subtract six from both sides

Then it's 5p= 5

Then you when you divide it gives you 1

11p-4=6p+4

5p=5

p=1

The equation are given as

1. The equation is given as

The answer is

2. The equation is given as

The answer is