A company is designing a new cylindrical water bottle. The volume of the bottle will be 220 cm cubed 3. The height of the water bottle is 8. 9 cm. What is the radius of the water​ bottle? Use 3. 14 for π

The equation of the tangent line to the graph of f(x) = 2 - 4x² at (-2,-14) is y = 16x + 18.

To determine an equation of the line tangent to the graph of f(x) = 2 - 4x² at (-2,-14),

Find the derivative of the given function, f(x).

The derivative of f(x) = 2 - 4x² is given by:

f'(x) = -8x

To find the slope of the tangent line at x = -2, we need to evaluate the derivative at x = -2:

f'(-2) = -8(-2) = 16

So, the slope of the tangent line at x = -2 is 16.

We can use the point-slope form of a line to find the equation of the tangent line:

y - (-14) = 16(x - (-2))

y + 14 = 16(x + 2)

y + 14 = 16x + 32

y = 16x + 18

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The polynomial which is not equivalent to (5x – 2)(-2x + 4) is -10x + 20x + 4x – 8 and is therefore denoted as option A.

This is referred to as a type of algebraic expression in which the exponents of all variables should be a whole number.

(5x – 2)(-2x + 4) when expanded will give:

-10x² + 20x + 4x – 8 which can be rewritten as the following below:

This is therefore the reason why -10x + 20x + 4x – 8 was chosen as the correct choice.

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The options are:

A) -10x + 20x + 4x – 8

B) 4x + 20x – 10x2 – 8

C) -8 + 24x – 10x2

D) -10x2 + 24x – 8

Answer:

2.5 km

Step-by-step explanation:

X= -2

Explanation: the photos are in order :)

Answer:

x = -2

Step-by-step explanation:

3/5 +3/10x = 4/5 + 2/5x

Step 1. Change every fraction into the same denominator

6/10 + 3/10 x = 8/10 + 4/10x

Step 2. Subtract 3/10x

6/10 = 8/10 + 1/10x

Step 3. Subtract 8/10

-2/10 = 1/10x

x = -2

A quadratic function in standard form that represents each area as a function of the width is; A = -x² + 20

We are told that she is enclosing a new garden and has 40 ft of fencing.

Now, let the two sides be labelled x and y.

We know that area of a rectangle is;

A = length * width

Thus;

A = xy

Now, since she has 40 ft of fencing, then it means that;

y = 0.5(40) - x

y = 20 - x

Thus, the area expressed in quadratic function formula is;

A = x(20 - x)

A = 20x - x²

A = -x² + 20

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Complete question is;

Write a quadratic function in standard form that represents each area as a function of the width.

Remember to defi ne your variables

Answer:

f’(x) = x -2/7

Step-by-step explanation:

Let f(x)= y

Thus;

y = x + 2/7

x = y-2/7

So the inverse f’(x) = x - 2/7

Step-by-step explanation:

1, x = -4 and y = 0

2, 3a =6 and 2b = -8

a =2 and b = -4 by dividing both side of equate equations respectivily.

3, quadrant-IV

4, on x-axis

5, i, 7

ii, 5

6 i) -3

ii) -2

Answer:

x = 36

Step-by-step explanation:

x/48 = 48/64

64x = 2304

x = 36

Unfortunately, we cannot determine the value of B50 as there is not enough information provided in the question. We only know that G' (x) is equal to F(x), but we do not know the exact function of F(x) or any other values of B0, B1, B2, B3, and B4. In order to solve for B50, we would need more information such as the specific values of the coefficients or additional equations. Without that information, we cannot calculate the value of B50.

The question presents a function G(x) with five coefficients, B0, B1, B2, B3, and B4, and asks for the value of B50. However, the question also introduces F(x) and states that G' (x) = F(x), but does not provide any additional information on either function. Without knowing more information about F(x) or any of the coefficients in G(x), it is impossible to determine the value of B50.

In conclusion, the question does not provide enough information to solve for the value of B50. The introduction of F(x) and the equation G' (x) = F(x) does not provide any additional information on the specific values of the coefficients in G(x) and therefore cannot be used to calculate B50.

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Answer:

x = 15°

Step-by-step explanation:

Linear pair = 180°

⇒ (6x - 5) + (6x + 5) = 180°

⇒ 12x = 180°

⇒ x = 15°

Since line m is parallel to line n, (6x - 5) and (6x + 5) are a linear pair.

Linear pair means that the sum of two angles equaling 180°.

\((6x - 5) + (6x + 5) = 180\)

Step-by step calculations:

Opening the parenthesis:

\((6x - 5) + (6x + 5) = 180 \\\\6x - 5 + 6x + 5 = 180\)

Combining like terms:

\(6x - 5 + 6x + 5 = 180 \\\\ (6x + 6x) + (-5 + 5) = 180\)

Simplify the LHS:

\((6x + 6x) + (-5 + 5) = 180\\\\(12x) = 180\)

Divide 12 both sides and simplify:

\(\frac{12x}{12} = \frac{180}{12} \\\\ x = 15\)

Thus, the value of x is 15.

Answer:

x=−2/5

y−2

Step-by-step explanation:

5x+2y=−10

Step 1: Add -2y to both sides.

5x+2y+−2y=−10+−2y

5x=−2y−10

Step 2: Divide both sides by 5.

5x

5

=

−2y−10

5

x=

−2

5

y−2

Answer: x- intercept: (-2, 0)   y- intercept:  (0,_5)

Step-by-step explanation:

The expression representing the population at time t years, given an initial population of 4 million and a growth rate of 7% per year, is 4 * (1.07)^t million.

To represent the population at a given time t years, we start with the initial population of 4 million. Since the population is growing at a rate of 7% per year, we multiply the initial population by a factor of (1 + 0.07) for each year. This factor represents the growth rate plus 1, as 1 represents the initial population.

Therefore, the expression to represent the population at time t years is 4 * (1.07)^t million, where t represents the number of years. This expression takes into account the initial population and the compounded growth over time.

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There are 72 positive integers less than 180 that relatively prime to 180.

To determine the number of positive integers less than 180 that are relatively prime to 180,

we need to calculate Euler's totient function, often denoted as φ(n). Euler's totient function counts the number of positive integers less than n that are coprime (relatively prime) to n.

The value of φ(n) can be calculated using the formula:

φ(n) = n × (1 - \(\frac{1}{p1}\)) × (1 - \(\frac{1}{p2}\) × ... ×(1 - \(\frac{1}{pk}\))

Where p1, p2, ..., pk are the distinct prime factors of n.

In this case, the prime factorization of 180 is: \(2^2\) × \(3^2\) × 5.

Using the formula, we can calculate φ(180) as follows:

φ(180) = 180 × (1 - \(\frac12\)) × (1 - \(\frac13\)) × (1 -\(\frac 15\))

       = 180 × (\(\frac12\)) × (\(\frac23\)) × (\(\frac45\))

       = 72.

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Answer:

-5/3

Step-by-step explanation:

Answer:

38

Step-by-step explanation:

Answer:

34 i got it right

Step-by-step explanation:

The values of E(X) = 3.25 and Var(X) ≈ 2.238 for the number of spades in a hand of 13 cards chosen at random from a 52-card deck.

To find E(X) and Var(X) for the number of spades in a hand of 13 cards chosen at random from a 52-card deck, we will use the concepts of probability and statistics.

E(X), or the expected value, is the average number of spades you would expect to get in a hand of 13 cards. To find E(X), we can use the formula:

E(X) = (Number of spades in the deck / Total number of cards in the deck) * Number of cards drawn

E(X) = (13 spades / 52 cards) * 13 cards drawn
E(X) = (1/4) * 13
E(X) = 3.25

So, the expected number of spades in a 13-card hand is 3.25.

Next, let's find Var(X), or the variance, which is a measure of how much the number of spades can vary from the expected value. We can use the formula for variance of a hypergeometric distribution:

Var(X) = (Number of cards drawn * Number of spades * Number of non-spades) / ((Total number of cards in the deck)^2 * (Total number of cards in the deck - 1))

Var(X) = (13 cards drawn * 13 spades * 39 non-spades) / ((52 cards)^2 * (52 cards - 1))
Var(X) = (13 * 13 * 39) / (52 * 52 * 51)
Var(X) ≈ 2.238

So, the variance for the number of spades in a 13-card hand is approximately 2.238.

In summary, E(X) = 3.25 and Var(X) ≈ 2.238 for the number of spades in a hand of 13 cards chosen at random from a 52-card deck.

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Stephen makes the mistake in the expression as he uses the 4 in the root and the 3 in the power and the expression actually is: ∛(16)/e

We start with the expression:

exp( (4/3)*ln(2) - 1)

Here we can use that:

exp(ln(x)) = x.

and e^(a + b) = e^a*e^b.

the first step here is:

e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)

So the first step of Stephen is correct, but the first step of Helen is not, you can not simplify the expression in that way.

now, we have that:

a*ln(x) = ln(x^a)

then we can write:

(4/3)*ln(2) = ln(2^(4/3))

and e^(ln(2^(4/3)) = 2^(4/3)

then we have:

e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e

now we can write this as:

∛(2^4)/e

Here is where Stephen makes the mistake, he uses the 4 in the root and the 3 in the power.

The expression actually is: ∛(16)/e

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The data suggests that the incidence rate of Autism Spectrum Disorder (ASD) may be higher in the particular state compared to the national average.

To determine if the incident rate of ASD is higher in the state compared to the national average, we can compare the observed incidence rate in the state with the known national rate. In the particular state, out of a random sample of 33,700 children, 1,440 were diagnosed with ASD. This gives us an observed incidence rate of approximately 4.27% (1,440/33,700). On the other hand, the national average incidence rate is stated as 1 out of 88 children, which is approximately 1.14% (1/88).

By comparing the observed incidence rate in the state (4.27%) with the national average (1.14%), it suggests that the incident rate of ASD is higher in the state than nationally. However, to draw a more definitive conclusion, further statistical analysis is required. Factors such as the representativeness of the sample and potential confounding variables should be considered. Additionally, it is important to note that this analysis assumes that the national average incidence rate is an accurate representation of the true rate, and any differences observed could be due to chance or other factors specific to the state.

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\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)

A researcher's results should be considered fraudulent if data were changed in order to support the hypothesis. This is a serious ethical violation and goes against the scientific method. Overall, it is important for researchers to adhere to ethical standards and maintain the integrity of their research.

Explanation:

A researcher's results should be considered fraudulent if data were changed in order to support the hypothesis. This is a serious ethical violation and goes against the scientific method. Additionally, if animals were used while conducting experiments, the researcher should have followed ethical guidelines and obtained proper approval and care for the animals. If a survey was used to collect data, the researcher should have ensured the survey was properly designed and administered to avoid any biases or errors. Finally, if participants were not debriefed after completion of the study, this could be seen as unethical and potentially harmful to their well-being. Overall, it is important for researchers to adhere to ethical standards and maintain the integrity of their research.

The scientific method requires researchers to conduct experiments in a transparent and objective manner. This means that the researcher should design experiments to test hypotheses, collect data systematically, and analyze data objectively. Any manipulation of data to support a hypothesis undermines the scientific method and is considered unethical. Researchers who intentionally manipulate data can be considered fraudulent and may face disciplinary action.

If animals were used in the experiment, the researcher should have followed ethical guidelines and obtained proper approval and care for the animals. Ethical guidelines ensure that animals are treated humanely, minimize their pain and discomfort, and maximize their welfare. Researchers who violate these guidelines can be considered fraudulent and may face disciplinary action.

If a survey was used to collect data, the researcher should have ensured that the survey was properly designed and administered to avoid any biases or errors. Surveys can be susceptible to various sources of error, including sampling errors, measurement errors, and non-response bias. Researchers who fail to address these sources of error can produce biased or invalid results, which can be considered fraudulent.

Finally, if participants were not debriefed after completion of the study, this could be seen as unethical and potentially harmful to their well-being. Debriefing allows participants to understand the purpose of the study, ask questions, and voice any concerns they may have. Participants who are not debriefed may feel deceived or harmed by the study, which can damage their trust in research and researchers.

In summary, researchers must adhere to ethical standards and maintain the integrity of their research. This includes avoiding data manipulation, following ethical guidelines for animal welfare, ensuring that surveys are properly designed and administered, and debriefing participants after completion of the study. Failure to do so can result in fraudulent research and harm to participants, animals, and the scientific community as a whole.

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The Cat can travel 59 miles in 1 hour. If the trip lasts 2 hours, then to find the distance between city A and B we can use the next proportion:

Solving for x:

The distance between City A and City B is 118 miles

Complete question :

Kayla is framing a square painting with side lengths of x+5 inches. The total area of the painting and the frame has a side length of 3x-6. inches. Write an expression for the area of the frame. Then find the cost of the material for the frame if x = 16. The material for the frame will cost 0.07 per square inch

Answer:

8x² - 46x + 11 ;

$92.61

Step-by-step explanation:

Side length of square painting = x + 5

Area of square painting = (x +5)²

Side length of Total area of square painting + frame = 3x - 6

Total area = (3x - 6)²

Area of frame :

(3x - 6)² - (x +5)²

(3x - 6)(3x-6)

9x² - 18x - 18x +. 36 = 9x² - 36x + 36

(x +5)(x+5) = x²+5x+5x+25 = x² + 10x + 25

9x² - 36x + 36 - (x² + 10x + 25)

9x² - 36x + 36 - x² - 10x - 25

8x² - 46x + 11

Area of frame = 8x² - 46x + 11

8(16^2) - 46(16) + 11

= 1323 in²

1323 * 0.07 = $92.61

Answer:

i). If p = 7, then each person would get 5 cookies, with 1 cookie left over.

ii). If p = 10, then each person would get 3 cookies, with 6 cookies left over.

iii). If p = 11, then each person would get 3 cookies, with 3 cookies left over.

Step-by-step explanation:

First option is wrong because 5 dividing 36 is 7, not 6. It would remain 1, not 4.

Second option is correct because 36 divided by 7 would give you 5 remaining 1.

Third option is correct because 8 dividing 36 is 4, but will remain 4, not 3.

Fourth option is correct because 36 divided by 10 is 3, then will remain 6.

Fifth option is correct because 36 divided by 11 is 3, remaining 3.

Answer:

B,D,E

Step-by-step explanation:

edge

The expression that represents the probability of Seth and Anna being selected for the team is 15 C2.

This is because 15 C2 (which is the same as choosing 2 members out of 15 without regard for order) represents the number of possible two-person teams that can be selected from the 15 members of the club, and the probability of Seth and Anna being selected is one of those possible teams. The total number of possible two-person teams is given by 15 C2 = (15!)/(2!(15-2)!), which simplifies to 105. Therefore, the probability of Seth and Anna being selected is 1/105.

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Being 95% confident in an inference means that, based on the statistical analysis performed, there is a 95% probability that the true population parameter (in this case, μ) falls within the calculated confidence interval (in this case, (1000, 2100)).

Confidence intervals are used in statistics to estimate the true value of a population parameter (such as the mean, μ) based on a sample of data. In this case, the confidence interval is (1000, 2100).

The confidence level, in this case, 95%, represents the probability that the calculated confidence interval contains the true population parameter. This means that if the same statistical analysis were repeated multiple times, we would expect the true population parameter to fall within the confidence interval in approximately 95% of those repetitions.

The confidence interval is calculated based on the sample data and the chosen confidence level. In this case, the interval (1000, 2100) was calculated based on the sample data and a 95% confidence level.

The interpretation of the confidence interval (1000, 2100) is that there is a 95% probability that the true population parameter, μ, falls within this interval. It does not mean that there is a 95% probability that the interval contains the true value of μ; rather, the confidence level reflects the long-term frequency of intervals that will contain the true value of μ when similar analyses are repeated.

Therefore, based on the given information, we can conclude that being 95% confident in an inference means that there is a 95% probability that the true population parameter, μ, falls within the calculated confidence interval of (1000, 2100).

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Option-c is correct that is F.DIST.RT(x, Deg_freedom1, Deg_freedom2) when the right-tailed probability for a value x on the F(df1,df2) distribution.

Given that,

We have to find which option is correct  for the right-tailed probability for a value x on the F(df1,df2) distribution.

We know that,

returns the degree of diversity (right-tailed) F probability distribution for two data sets. This function can be used to compare the levels of diversity between two data sets. For instance, you may compare the test results of high school freshmen who are men and women to see if there is a difference in the variability between the sides.

Syntax

F.DIST.RT(x,deg_freedom1,deg_freedom2)

The following arguments are used with the F.DIST.RT function syntax:

The value at which the function should be evaluated.

Degrees of freedom numerator required: Deg freedom1.

Degrees of freedom in the denominator, required by Deg freedom2.

Therefore, Option-c is correct that is F.DIST.RT(x, Deg_freedom1, Deg_freedom2) when the right-tailed probability for a value x on the F(df1,df2) distribution.

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