Ultra Capsules were advertised as having 751 mg of vitamin B3
per capsule. A consumer's group hypothesizes that the amount of
vitamin B3 is more than what is advertised. What can be concluded
with an

The differential equation y'' - 9y' + 9y = 0 can be transformed into an auxiliary equation r^2 - 9r + 9 = 0 by using the characteristic equation.

Let's solve the auxiliary equation:r^2 - 9r + 9 = 0(r - 3)^2 = 0r = 3 (repeated root).

Thus, the general solution is given by y = (c1 + c2t) e^(3t), where c1 and c2 are arbitrary constants.

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Answer:

10 shelves

Step-by-step explanation:

out of the other choices, 10 is most suitable to divide with 80

The length of VW to the nearest tenth of a foot is 41.1 feet.

In triangle UVW, the measure of angle ZW is 90°, the measure of angle ZU is 11°, and WU is 42 feet. We need to find the length of VW.Let's use the Pythagorean theorem:According to the Pythagorean theorem, in a right-angled triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

(ZW)^2 = (ZU)^2 + (WU)^2,As per the question,ZW = 90°ZU = 11°WU = 42 feet.Substituting the values, we get;(90)² = (11)² + (42)²8100 = 121 + 1764 = 1885Now, let's apply sine and cosine ratios to find the length of VW.cos (ZU) = VW / WUVW = WU x cos (ZU)VW = 42 x cos (11°)VW = 41.07 feet

Hence, the length of VW to the nearest tenth of a foot is 41.1 feet.

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i cant understand your question define briefly

The p-value for testing the hypothesis that the proportion of unemployed people in Karachi city is not equal to 30% based on a sample of 100 people with 35 unemployed individuals is approximately 0.275.

To test the hypothesis, we compare the sample proportion of unemployed individuals (35 out of 100) with the hypothesized proportion of 30%. We then calculate the p-value, which represents the probability of obtaining a sample proportion as extreme as or more extreme than the observed proportion, assuming that the null hypothesis is true.

In this case, the p-value of 0.275 indicates that there is a 27.5% probability of obtaining a sample proportion of unemployed individuals as extreme as or more extreme than the observed proportion of 35%. Since this p-value is greater than the typical significance level of 0.05, we fail to reject the null hypothesis.

This means that there is not enough evidence to conclude that the proportion of unemployed people in Karachi city is significantly different from 30%. However, it is important to note that failing to reject the null hypothesis does not necessarily mean that the null hypothesis is true; it simply means that we do not have sufficient evidence to support the alternative hypothesis.

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Answer:

linear

Step-by-step explanation:

y = mx + b is equation for linear functions

A dependent variable that maintains constant measurements throughout an experiment will be depicted by a straight, horizontal line in a graph.

In an experiment, the dependent variable is the variable being measured, and it is expected to change in response to changes in the independent variable. However, if the dependent variable remains constant throughout the experiment, it indicates that it is not affected by the independent variable.

When such a situation arises, the data points for the dependent variable will be located at the same level or value, resulting in a horizontal line in the graph.

This straight, horizontal line represents the constant measurements of the dependent variable, and it can provide valuable insights into the nature of the relationship between the independent variable and the dependent variable.

A dependent variable that maintains constant measurements throughout an experiment may indicate a flaw in the experimental design, such as an incorrect assumption about the nature of the relationship between the independent variable and the dependent variable, or an uncontrolled confounding variable.

Therefore, it is important to carefully analyze the data and the experimental design to identify and address any potential issues.


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The value of angle m∠FCG is 27.5.

x = 25

x = 35

We have,

1.

GCH and ECD are alternate angles.

This means,

GCH = 125 = ECD

And,

ECG and DCH are alternate angles.

This means,

ECG = DCH = x

Now,

GCH + ECD + ECG + DCH = 360

125 + 125 + x + x = 360

250 +2x = 360

2x = 360 - 250

2x = 110

x = 55

Now,

ECG = ECF + FCG

55 = ECF + FCG

ECF and FCG are equal.

So,

m∠FCG = 55/2 = 27.5

2.

The straight angles are formed by (5x + 20) and (2x - 5).

So,

5x + 10 + 2x - 5 = 180

7x + 5 = 180

7x = 180 - 5

7x = 175

x = 25

3.

2x + 43 and 2x - 3 are on the same side of the parallel lines.

So,

2x + 43 + 2x - 3 = 180

4x + 40 = 180

4x = 180 - 40

4x = 140

x = 35

Thus,

The value of angle m∠FCG is 27.5.

x = 25

x = 35

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Answer:

6/20 can I get brainliest pleast

Step-by-step explanation:

\( \frac{70}{100} \times 20 = 14 \\ 20 - 14 = 6 \\ \)

there is a chance that the teacher will pick a student without brown eyes 6/20 times

The probability that the reimbursement is greater than 3000 but less than 9000, given that the loss exceeds the deductible, is 0.2355.

We are given that the loss under a liability policy is modeled by an exponential distribution. This means that the amount of the loss that exceeds the deductible follows an exponential distribution.

The insurance company will cover the amount of the loss in excess of a deductible of 2000. So, we are interested in calculating probabilities related to the reimbursement amount (Y) given that the loss exceeds the deductible.

We are given that the probability that the reimbursement is less than 6000, given that the loss exceeds the deductible, is 0.50. Mathematically, this can be expressed as:

P(Y ≤ 6000 | X > 0) = 0.50

where X is the amount of the loss that exceeds the deductible.

Using the memoryless property of the exponential distribution, we can rewrite the probability as:

P(X ≤ 4000) = 0.50

This is because P(Y ≤ 6000 | X > 0) is equivalent to P(X ≤ 4000) since the deductible is 2000.

From the given probability, we can determine the parameter λ of the exponential distribution. We have:

P(X > 2000) = e^(-λ*2000) = 0.5

Solving for λ, we find:

λ = ln(0.5)/(-2000) ≈ 0.00034657

Now, we want to calculate the probability that the reimbursement is greater than 3000 but less than 9000, given that the loss exceeds the deductible:

P(3000 < Y ≤ 9000 | X > 0)

Using the memoryless property, we can rewrite this as:

P(X > 1000) - P(X > 7000)

Substituting the value of λ we found earlier, we have:

P(3000 < Y ≤ 9000 | X > 0) = e^(-λ1000) - e^(-λ7000)

Plugging in the value of λ, we can calculate the probability:

P(3000 < Y ≤ 9000 | X > 0) ≈ e^(-0.34657) - e^(-2.426) ≈ 0.3226 - 0.0871 ≈ 0.2355

Therefore, the probability that the reimbursement is greater than 3000 but less than 9000, given that the loss exceeds the deductible, is approximately 0.2355.

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The breadth of the rectangular plot is equal to the area divided by the length. Therefore, the breadth of the plot is 180 divided by 15, which is equal to 12 meters.

The area of a rectangular plot is equal to the length multiplied by the breadth. This means that if the area of the plot is 180 square meters and the length is 15 meters, then the breadth can be calculated by dividing the area by the length. Therefore, the breadth of the plot is 180 divided by 15, which is equal to 12 meters. This means that the area of the plot is equal to 15 multiplied by 12 which is equal to 180 square meters. As the area and the length are given, the breadth can be easily calculated by dividing the area by the length. This is a simple way to calculate the breadth of a rectangular plot when the area and the length are known.

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The probability that exactly 7 rivets fail the test is approximately 0.0483.

To calculate this probability, we first define p as the probability that a rivet will hold a 200 lb. force without any deformation. Thus, the probability of a rivet failing to hold a 200 lb. force is 1 - p. In this case, p is given as 0.99, so the probability of a rivet failing is 0.01.

Next, we let X represent the number of rivets that fail the test. Since the number of rivets tested is 500, we can model X as a binomial random variable with parameters n = 500 (the number of trials) and p = 0.01 (the probability of failure).

We want to find the probability that exactly 7 rivets fail the test, which can be denoted as P(X = 7).

This probability can be calculated using the binomial probability formula:

P(X = 7) = (500C7) * (0.01^7) * (0.99^(500-7))

Here, (500C7) represents the number of ways to choose 7 rivets out of 500, which is calculated as 500! / (7! * (500-7)!).

Evaluating this expression, we find that P(X = 7) is approximately 0.0483.

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Answer:

=0.0000541

Step-by-step explanation:

\(\frac{0.00541}{10^2}\)
\(\frac{0.00541}{100}\)
\(=0.0000541\)

Answer:0.0000541

Step-by-step explanation:

Firstly, you'll simplify 10².

10²÷0.00541 ---> 100 ÷ 0.00541

Then, you'll divide 100 by 0.00541.

100 ÷ 0.00541 ---> 18484.2883549

Time taken by Adam to complete his seventh lap of the circular track as per given data is equal to 1minute 28seconds.

As given in the question,

Time taken by Adam to complete hi first lap of circular track = 1 min 58 sec

First term t₁ = 1 minute 58seconds

Time taken by each successive lap is 5seconds less then the previous lap

Common difference 'd' = -5seconds

let time taken to complete the seventh lap be t₇

t₇ = t₁ + ( 7 - 1 ) d

⇒ t₇ = 1 minute 58 seconds + ( 6 ) (- 5seconds)

       =  1 minute 58 seconds - 30seconds

      = 1 minute 28 seconds

Therefore, the time taken by Adam to complete his seventh lap is equal to

1 minute 28 seconds.

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Answer:

i think its 18

Step-by-step explanation:

The probability that any individual sampled at random from this population would have a length of 40 mm or larger is: 1 - 0.9082 = 0.0918 or approximately 9.18%.

To calculate the probability that any individual sampled at random from this population would have a length of 40 mm or larger, we need to use the normal distribution function.

Let's assume that the lengths of the organisms follow a normal distribution with mean μ = 36 mm and standard deviation σ = 3 mm.

So, the z-score corresponding to 40 mm is:

z = (x - μ) / σ

z = (40 - 36) / 3

z = 4 / 3

Using a standard normal distribution table or calculator, we can find that the probability of a random variable being less than or equal to a z-score of 4/3 is 0.9082.

Therefore, the probability that any individual sampled at random from this population would have a length of 40 mm or larger is:1 - 0.9082 = 0.0918 or approximately 9.18%.

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Answer:

The sum is 2635

Step-by-step explanation:

I did this problem

Answer:

the ordered pair (0, 1/6)

Step-by-step explanation:

To reflect a function across the y-axis, we replace every occurrence of x with -x. Therefore, the function g(x) is given by:

g(x) = f(-x) = 1/6(2/5)^(-x)

To find an ordered pair on g(x), we need to choose a value of x and evaluate g(x). For example, if we choose x = 0, then:

g(0) = 1/6(2/5)^(-0) = 1/6

Therefore, the ordered pair (0, 1/6) is on the graph of g(x).

The upward unit normal to the surface 7cosθ = 10−13 at (9, θ, 0) is (-7√3/13, 0, 2√3/13).

To find the upward unit normal to the given surface, we need to determine the gradient vector of the surface at the specified point. The gradient vector represents the direction of the steepest ascent on the surface.

First, we rewrite the equation of the surface as cosθ = (10−13)/7. Taking the derivative of both sides with respect to θ, we get -sinθ = 0. Rearranging, we have sinθ = 0, which implies θ = 0 or π.

Since we are interested in the point (9, θ, 0), we consider the case when θ = 0. Plugging this value into the equation, we have cos(0) = (10−13)/7, which simplifies to cos(0) = -3/7.

The gradient vector at the point (9, 0, 0) is (-7√3/13, 0, 2√3/13). This vector represents the direction of the upward unit normal to the surface at that point.

Therefore, the upward unit normal to the surface 7cosθ = 10−13 at (9, θ, 0) is (-7√3/13, 0, 2√3/13).

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Here, angle MGN = angle NGO

Therefore, 5x-6=11x-42

or, 5x-11x = -42+6

or, -6x = -36

or, x = -36/-6

or, x = 6

The answer is 6.

Answer:

The answer is 6 hope it helps

Step-by-step explanation:

Answer:

G 1.0=10^-9, exponents are usually used with a ^ yw

Step-by-step explanation:

For a larger input size of 320,000 elements, it will take 240 ms to sort each half and 24 ms to merge the sorted halves, resulting in a total time of 264 ms.

The given information describes the time required for sorting and merging operations on two different input sizes. For 80,000 elements, it takes 18 ms to sort each half, resulting in a total of 36 ms for sorting. Merging the two sorted halves with 80,000 numbers in each takes 40 - 18 = 22 ms.

When the input size is doubled to 320,000 elements, the sorting time for each half increases to 240 ms, as it scales linearly with the input size. The merging time, however, remains constant at 4 ms since the size of the sorted halves being merged is the same.

Thus, the total time for sorting and merging 320,000 elements is the sum of the sorting time (240 ms) and the merging time (4 ms), resulting in a total of 264 ms.

Therefore, based on the given information, the total time required for sorting and merging 320,000 elements is 264 ms.

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Answer:

9 · x - 16

Explanation:

Nine times a number: 9 · x

Decreased by 16: - 16

Put them together: 9 · x - 16

Answer:

no x² + 5x + c is a perfect square

Step-by-step explanation:

The probability of randomly guessing the correct answer of 6 is 1/10, which is equal to 0.1 or 10%.

If you are asked to provide the first (leftmost) nonzero digit of the Avogadro constant and you have no prior knowledge, making a random guess leaves you with a 1 in 10 chance of guessing correctly.

Since there are ten possible digits (0-9) to choose from, each digit has an equal probability of being the correct answer.

Therefore, the probability of guessing the correct answer of 6 is 1 out of 10, which can be expressed as a fraction: 1/10. In decimal form, this is 0.1 or 10% as a percentage.

It's important to note that in a scenario where you lack any information or clues regarding the Avogadro constant, your random guess has an equal chance of being any of the digits.

Hence, the probability of guessing the specific correct digit of 6 is 1/10, regardless of the context or the nature of the question.

The Avogadro constant is a physical constant with a well-defined value, which is approximately 6.02214076 × 10^23 mol⁻¹. The first (leftmost) nonzero digit of this constant is 6.

If you make a random guess without any prior knowledge, the probability of guessing the correct answer of 6 is 1 out of 10 possible digits (0-9), since there are ten digits in the decimal system. Therefore, the probability of randomly guessing the correct answer of 6 is 1/10, which is equal to 0.1 or 10%.

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The website which is cheaper for Caroline to buy the spice mix is French website.

Given data ,

Let's calculate the total cost for Caroline from both websites and determine which one is cheaper.

British website:

Price for 100 g = (£0.90 / 25 g) * 100 g = £3.60

Since the British website offers free delivery, the total cost remains £3.60.

French website:

Price for 100 g = (€1.20 / 50 g) * 100 g = €2.40

Delivery cost = €0.80

On simplifying the equation , we get

To convert the price and delivery cost to pounds, we'll use the conversion rate: €1 = £0.85.

Price in pounds = €2.40 * £0.85 = £2.04

Delivery cost in pounds = €0.80 * £0.85 = £0.68

Total cost = Price in pounds + Delivery cost = £2.04 + £0.68 = £2.72

Comparing the total costs:

British website: £3.60

French website: £2.72

Hence , Caroline would pay £2.72 for the spice mix from the cheaper website, which is the French website.

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The equation of the circle passing through the point (-6, 3) having center at (5, - 4) is (x - 5)² + (y + 4)² = 170

The general equation of a circle with (h, k) representing the circle's center, and {r} represents the length of its radius is

(x – h)² + (y – k)² = r²

We can write the equation of the circle as -

(x – h)² + (y – k)² = r²

(x - 5)² + (y + 4)² = (11)² + (-7)²

(x - 5)² + (y + 4)² = 121 + 49

(x - 5)² + (y + 4)² = 170

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Answer:

see below

Step-by-step explanation:

4 brothers in total, each saves 17 per week, in 3 weeks

314+(17*4)*3 =518

yes they do have enough

How many weeks will it take for them to save enough $ to buy the gift

515 = x *(17*4) + 314

How much each of them must save per week to have enough?

515= 3(x*4) +314

Answer:

-3 x 10

Step-by-step explanation:

the first one is 5