Two ferries start moving towards each other from shores A and B. When they pass each other for the first time the distance to shore B is 100 meters. Once they reach their destinations and start traveling back at the same time. When they meet for the second time, the distance to shore A is 50 meters. What is the distance between the shores A and B? HELP will give brainliest! Its not 150 or 1700

The probability that a CD will last less than 3 years is approximately 86.65%.

The probability can be determined using the standard normal distribution. Given that the CD's lifespan follows a normal distribution with a mean of 4 years and a standard deviation of 0.8 years, we need to find the z-score for 3 years. The z-score formula is calculated as (x - μ) / σ, where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

For 3 years, the z-score is (3 - 4) / 0.8 = -1.25. Using a standard normal distribution table or a calculator, we can find that the probability corresponding to a z-score of -1.25 is approximately 0.1056 or 10.56%.

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The aim of hypothesis testing is to make inferences or conclusions about a population based on sample data. It allows us to objectively analyze the evidence provided by the data and make decisions based on that evidence. By comparing the observed data to what would be expected under a specific hypothesis, hypothesis testing helps us evaluate whether the data supports or contradicts the claim being tested.

Hypothesis testing provides a structured and systematic approach to assess the validity of a claim or hypothesis. Hypothesis testing achieves several objectives that cannot be otherwise achieved:

Objectivity: Hypothesis testing provides a framework that helps remove personal biases and subjectivity from the decision-making process. It requires formulating clear hypotheses, defining appropriate statistical tests, and following predetermined rules to reach conclusions. This objectivity ensures that decisions are based on evidence rather than personal opinions or preferences.

Quantification of uncertainty: Hypothesis testing allows us to quantify the level of uncertainty associated with the conclusions drawn from the sample data. It provides measures such as p-values and confidence intervals that indicate the likelihood of obtaining the observed results under the null hypothesis. These measures help in assessing the strength of evidence and determining the level of confidence in the conclusions made.

Generalization to the population: Hypothesis testing enables us to make inferences about the population based on the sample data. By testing a hypothesis on a representative sample, we can draw conclusions that extend beyond the observed data. This generalization provides insights and knowledge about the larger population, allowing us to make informed decisions and predictions.

Example of hypothesis testing:

Claim: A new fertilizer leads to an increase in crop yield by at least 10%.

Step 1: Formulate the null and alternative hypotheses:

Null hypothesis (H0): The new fertilizer has no effect on crop yield or increases it by less than 10%.

Alternative hypothesis (Ha): The new fertilizer increases crop yield by at least 10%.

Step 2: Set the significance level (alpha):

Determine the desired level of significance to make a decision. Let's assume alpha = 0.05.

Step 3: Collect and analyze the data:

Implement the new fertilizer on a sample of crops.

Measure the crop yield for each sample plot and calculate the sample mean.

Step 4: Conduct the hypothesis test:

Use an appropriate statistical test, such as a one-sample t-test, to compare the sample mean to the hypothesized value of 10% increase.

Calculate the test statistic and the corresponding p-value.

Step 5: Make a decision and interpret the results:

If the p-value is less than the significance level (alpha), reject the null hypothesis.

Conclude that there is evidence to support the claim that the new fertilizer increases crop yield by at least 10%.

If the p-value is greater than the significance level (alpha), fail to reject the null hypothesis. Conclude that there is insufficient evidence to support the claim.

Step 6: Draw conclusions and report the findings:

Summarize the results, including the test statistic, p-value, and the decision made.

Provide interpretations and recommendations based on the findings, considering the limitations and context of the study.

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Answer:

8:5

Step-by-step explanation:

False. The frequency polygon and the histogram are two different ways to represent data, and they have distinct characteristics.

A frequency polygon is a line graph that displays the distribution of a quantitative variable. It shows the frequency of each value or class interval on the horizontal axis and the corresponding frequencies on the vertical axis. The points on the graph are connected to form a line, which gives a visual representation of the data distribution.

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Answer:

I believe the answer is 100

Step-by-step explanation:

The effective interest on £2000 at a 3% interest rate compounded quarterly over a period of 4 years is approximately £245.15.

To calculate the effective interest, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment (including interest)

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of compounding periods per year

t = the number of years

In this case, the principal amount (P) is £2000, the annual interest rate (r) is 3% (or 0.03 as a decimal), the compounding is done quarterly (n = 4), and the investment period (t) is 4 years.

Plugging the values into the formula:

A = £2000(1 + 0.03/4)^(4*4)

= £2000(1 + 0.0075)^16

= £2000(1.0075)^16

≈ £2000(1.126825)

Calculating the future value:

A ≈ £2253.65

To find the effective interest, we subtract the principal amount from the future value:

Effective Interest = £2253.65 - £2000

≈ £253.65

Therefore, the effective interest on £2000 at a 3% interest rate compounded quarterly after 4 years is approximately £253.65.

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Answer: E only

Step-by-step explanation:

Had the test

The expressions are also equal to 1/3 is cos (90 -x).

These relations are valid for all the values of A that lies between 0° and 90°.

Given:

sin x = 1/3

Now, using property

sin \(\theta\) = cos \(( 90- \theta)\)

So, sin x= cos (90 -x)

Hence, The expressions are also equal to 1/3 is cos (90 -x).

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Answer:

A

Step-by-step explanation:

The three factors that determine the margin of error of a confidence interval for μ are the sample size (n), the standard deviation (σ) of the population, and the desired level of confidence (C).

1. Sample size (n): A larger sample size generally leads to a smaller margin of error because it provides more information about the population.
2. Standard deviation (σ): A smaller standard deviation results in a smaller margin of error since it indicates less variability in the population.
3. Level of confidence (C): A higher desired level of confidence, such as 95%, leads to a larger margin of error as it requires a wider interval to capture the true population mean with a higher degree of certainty.

Therefore, the margin of error of a confidence interval for μ depends on the sample size, standard deviation, and level of confidence. These factors affect the precision and reliability of the estimation.

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Answer:

36, 38, 40, 42, 44

Step-by-step explanation:

We can denote an even number as 2n (where n is a natural number).

Each consecutive even number will be 2 more than the previous number.

Let 1st number = 2n

⇒ 2nd number = 2n + 2

⇒ 3rd number = 2n + 4

⇒ 4th number = 2n + 6

⇒ 5th number = 2n + 8

Sum of all 5 numbers is 200.  

⇒ 2n + 2n + 2 + 2n + 4 + 2n + 6 + 2n + 8 = 200

⇒ 10n + 20 = 200

⇒ 10n = 180

⇒ n = 18

If n = 18, then 2n = 36

Therefore, the numbers are 36, 38, 40, 42, 44

Answer:

C, 100 degrees

Step-by-step explanation:

180-80=100

Answer:

C

Step-by-step explanation:

When the value of something decreases by a certain factor every unit of time, instead of by a set constant, then this is called exponential decay. When the rate is constant, this is called linear decay. Hope this helps!

Answer:

652

Step-by-step explanation:

Answer: 60

Step-by-step explanation:

6n2

n=5

6(5)2

6×10 = 60

Answer:

x=-7

Step-by-step explanation:

-x=7

/-1 on each side

x=-7

Answer:

x= -7

Step-by-step explanation:

-x = 7

Divide each side by -1

-x/-1 = 7/-1

x = -7

The back-to-back stem-and-leaf plot or parallel boxplots can be use to compare. GPAs for successful students are generally higher. A significant relationship exists between GPA and credit hours for successful students. An applicant with a 3.5 GPA is likely to be successful, as the predicted value is closer to successful students' values.

To compare the GPAs for the two groups, an appropriate graphical display could be a back-to-back stem-and-leaf plot or parallel boxplots. Based on the graph, we can observe that successful students generally have higher GPAs than unsuccessful students.

To determine if there is a significant relationship between GPA and mean number of credit hours per semester for successful students, we can use a t-test for the slope or linear regression t-test.

Given the provided computer output, with a t-value of -5.90 and a p-value of 0.000, we can reject the null hypothesis and conclude that there is a significant relationship between GPA and mean number of credit hours per semester for successful students.

Using the regression equation to predict the number of credit hours for an applicant with a GPA of 3.5,

For the successful group predicted hours = 23.514 – 2.7555(3.5) = 13.86975

For the unsuccessful group predicted hours = 24.200 – 3.485(3.5) = 12.0025

we get a predicted value of 13.86975 for successful students and 12.0025 for unsuccessful students.

Since the actual value of 14 is closer to the predicted value for successful students, we can infer that this applicant is likely to be successful in the Ph.D. program.

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--The given question is incomplete, the complete question is given

" The statistics department at a large university is trying to determine if it is possible to predict whether an applicant will successfully complete the Ph.D. program or will leave before completing the program. The department is considering whether GPA (grade point average) in undergraduate statistics and mathematics courses (a measure of performance) and mean number of credit hours per semester (a measure of workload) would be helpful measures. To gather data, a random sample of 20 entering students from the past 5 years is taken. The data are given in photo.

a. Use an appropriate graphical display to compare the GPAs for the two groups.(provide names only) Write a few sentences commenting on your display.

b. For the students who successfully completed the Ph.D. program, is there a significant relationship between GPA and mean number of credit hours per semester?

Give a statistical justification to support your response.

c. If a new applicant has a GPA of 3.5 and a mean number of credit hours per semester of 14.0, do you think this applicant will successfully complete the Ph.D. program? Give a statistical justification to support your response. "--

The given polynomial 5x² + 3x + 6 can be described as a second-degree polynomial since the highest exponent of x is 2. It can also be referred to as a quadratic polynomial since it contains a term with x². The coefficient of x² is 5, which indicates that the graph of the polynomial will open upwards since it is positive.

The constant term in the polynomial is 6, which is the y-intercept of the graph. The coefficient of x, which is 3, represents the slope of the line and is positive, indicating that the graph is increasing. Overall, this polynomial can be used to model real-world situations, such as projectile motion or financial modeling.  This is a __quadratic__ polynomial, as the highest degree of the variable (x) is 2. Quadratic polynomials have the general form ax² + bx + c, where a, b, and c are constants, and a is not equal to zero.
1. It's called a polynomial because it is an algebraic expression consisting of terms involving a variable (x) raised to a non-negative integer power.
2. The term 5x² has the highest degree (2), making it the leading term, and 5 is the leading coefficient.
3. Since the highest degree is 2, it is classified as a quadratic polynomial.
4. The polynomial has three terms: 5x² (a quadratic term), 3x (a linear term), and 6 (a constant term).
5. The constant term (6) is the value of the polynomial when x is zero.
So, the correct term to fill in the blank is "quadratic."

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The amount and numbers are 1. $217.25, 2. $710, 3. $790.25 and 4. 167.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number

1. Cost of a paperback = 25 cents = $0.25

Cost of a hardcover book = $1.25

There were 54 paperbacks and 163 hardcover books sold.

Money library raised = (0.25 × 54) + (1.25 × 163) = $217.25

2. Cost for round trip airfare = $398.60

Cost of room per night = $115.70

Cost of room for two nights = 2 × $115.70 = $231.40

Cab fare from airport to hotel = $40.00

Total fare from airport to hotel and the return = 2 × $40.00 = $80.00

Total cost = $398.60 + $231.40 + $80.00 = $710

3. Total working hour of Paula = 48 hours

Earning for first 35 hours = $14.50/h × 35

                                          = $507.50

Remaining hours = 48 - 35 = 13 hours

Earning for next 13 hours = ($14.50/h × 1.5) × 13

                                          = $282.75

Total earnings =  $507.50 + $282.75 = $790.25

4. Number of cards Will has = 26

Number of cards Liam has = 19

When they combine, total cards = 26 + 19 = 45

When father also shared, total number of cards = 3 × 45 = 135

Number of cards Nestor has = 4 × 8 = 32

Total number of cards = 135 + 32 = 167

Hence all the questions are cleared using multiplication as one of the basic operations.

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Answer:

need what done?

Step-by-step explanation:

Answer:

The inequality x + 3 < 12 can be used to determine the number of miles left to jog.

Step-by-step explanation:

It is given that:

Number of miles Beth has already jogged = 3 miles

She plans to join less than 12 miles.

Let,

x represent the number of miles left to jog.

x + 3 < 12

x + 3 - 3 < 12 - 3

x  < 9

Therefore,

The inequality x + 3 < 12 can be used to determine the number of miles left to jog.

Answer:

4 inches

Step-by-step explanation:

Answer:

Step-by-step explanation:

you’re given A=0.62 and B/A=0.93

you’re solving for B

substitute your A value of 0.62

B/0.62=0.93

same as B/0.62=0.93/1

now cross multiply

B= 0.62x0.93

B=0.5766

B=0.58

The width of the tank, which has a length 4 feet longer than its width, the height is 2 feet more than the width which is three feet.

The Hit and Trial Method is a very useful to solve the roots in a equation. In this , substituting different values of the variable and checking the equality of LHS and RHS is the trial and error method.

We have a tank ( cuboid shape) with

length, width and height and volume of tank is 105 cubic feet. Let length , width and height of tank be "l" feet , "w " feet and "h" feet.

lenght, l = w + 4

height, h = w + 2

Volume of tank , V = l× h × w

=> (w + 4 )×w × (w + 2) = 105

=> w ( w² + 6w + 8) = 105

=> w³ + 6 w²+ 8 w = 105

Using the hit and trial method to solve the above cubic equation in one variable, w.

We get, w = 3

So, the required width is 3 feet .

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Answer:22

Step-by-step explanation:

JxJy dA,

where R is the region between y2 + (x-2)2 = 4 and y = x in the first

quadrant

, is the double integral of 1 over the given region R.

Hence, we can write it as:

∫∫R 1 dA We need to evaluate this double integral by converting it into

polar coordinates

.

Here are the steps:

First, we need to convert the given curves y = x and y² + (x-2)² = 4 into

polar form

.

The polar form of the curve y = x is

r cos θ = r sin θ.

This simplifies to tan θ = 1, which gives us

θ = π/4 in the first quadrant.

Hence, the curve y = x in polar form is

r cos θ = r sin θ, or

r sin(θ - π/4) = 0.

The polar form of the circle y² + (x-2)² = is

(x-2)² + y² = 4, which simplifies to

r² - 4r cos θ + 4 = 0.

Using the quadratic formula, we get r = 2 cos θ ± 2 sin θ. Since we are only interested in the part of the circle in the first quadrant, we take the positive square root, which gives us:

r = 2 cos θ + 2 sin θ.

Now we can set up the double integral in polar coordinates:

∫∫R 1 dA = ∫π/40 ∫2cosθ+2sinθ02 cos θ + 2 sin θ r dr dθ We integrate with respect to r first:

∫π/40 ∫2cosθ+2sinθ02 cos θ + 2 sin θ r dr dθ

= ∫π/40 [r²/2]2cosθ+2sinθ0 dθ

= ∫π/40 (4 cos²θ + 8 cos θ sin θ + 4 sin²θ)/2 dθ

= 2 ∫π/40 (2 + 2 cos 2θ) dθ

= 2 [2θ + sin 2θ]π/4 0

= 2π.

It explains the given problem with complete steps of solution in polar coordinates.

Polar coordinates are useful in solving integrals involving curves that are not easy to express in

Cartesian coordinates

.

By converting the curves into polar form, we can express the double integral as an iterated integral in polar coordinates.

The region of

integration

R is defined by the curve y = x and the circle with center (2,0) and radius 2.

We convert these curves into polar form and set up the double integral in polar coordinates.

We integrate with respect to r first and then with respect to θ.

Finally, we obtain the value of the double integral as 2π.

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Answer:

x = 7/2  (or 3 1/2  or 3.5)

Step-by-step explanation:

2x + 5 = 12

2x = 7

x = 7/2  (or 3 1/2  or 3.5)

Answer:

3 or 3.5

Step-by-step explanation:

2(3)+5=12

6+5=12

Or

When you want to find x:

2x+5=12

-5=-5

2x=7

2/2x=7/2

3.5x

The transformation of the rectangles ABCD and ABCD is for the 90-degree clockwise rotation about the origin and a translation of 7 units down.

Here the transformed rectangle is  the result of two steps, including the steps of  rotation and  translation from the x-y axis, near the origin.

Here change is in such a way that,  the first rotation is a 90 clockwise rotation about the origin, where the vertex c is near to the origin,  again there is a translation of 7 units down, considering the rotated rectangle As A'B'C'D'. here the proper explanation of the process is shown in the image attached.

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To determine the revealed preference between bundles A, B, and C, we need to compare the choices made by Betty under different price conditions.  1. When prices are ($2, $4, $1), Betty chooses bundle C over bundle A. This implies that C is directly revealed preferred to A at these prices.

2. When prices are ($5, $3, $3), Betty chooses bundle A over bundle B. This implies that A is directly revealed preferred to B at these prices.

3. When prices are ($3, $1, $4), Betty chooses bundle B over bundle C. This implies that B is directly revealed preferred to C at these prices. Based on these comparisons, we can conclude the following: - Bundle C is directly revealed preferred to bundle A. - Bundle A is directly revealed preferred to bundle B. - Bundle B is directly revealed preferred to bundle C. There are no cases of indirect revealed preference, where one bundle is preferred to another through a series of choices. Therefore, each pair of bundles has a clear ordering of direct revealed preference. Bundle C is directly preferred to A, A is directly preferred to B, and B is directly preferred to C.

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Scientific claim: Bamboo provides the materials and energy for a panda to grow and function through its nutrient composition and digestive capabilities, as evidenced by the panda's specialized digestive system and bamboo's nutritional content.

Pandas rely heavily on bamboo as their primary source of food, and this is supported by evidence from previous tasks. One key piece of evidence is the panda's digestive system, which is adapted to efficiently process bamboo. Pandas possess specialized adaptations, such as enlarged molars and strong jaw muscles, that enable them to efficiently chew and break down the tough fibers of bamboo. This indicates that pandas have evolved to depend on bamboo as a crucial component of their diet.

Additionally, the nutritional composition of bamboo supports the claim. Bamboo is rich in cellulose, a complex carbohydrate that provides pandas with the necessary energy to sustain their growth and bodily functions. Although cellulose is difficult to digest for many animals, pandas possess a unique digestive system that includes a specialized gut microbiome. The gut microbiome of pandas contains bacteria that aid in the breakdown of cellulose, allowing them to extract nutrients and energy from bamboo more effectively.

Scientific reasoning further supports the claim that bamboo provides the materials and energy for pandas. Observations of wild pandas in their natural habitats have consistently shown their preference for bamboo as the main component of their diet. Studies have also revealed that pandas consume a large quantity of bamboo daily to meet their energy requirements. This aligns with the understanding that animals consume food to obtain the necessary materials and energy for growth, maintenance, and functioning.

In conclusion, the evidence from the panda's digestive system, the nutritional composition of bamboo, and the observed dietary habits of pandas support the claim that bamboo provides the materials and energy necessary for pandas to grow and function. The specialized adaptations of pandas and bamboo's nutritional content demonstrate a symbiotic relationship between the two, allowing pandas to thrive on a bamboo-based diet.

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Answer:

Sarah would have to by 4 sessions, and then the total cost of both gyms will be equal.

Step-by-step explanation:

Step-by-step explanation:

According to the problem, At Silver Gym is $25 per month, and $30 per personal training session. At Fit Factor is $65 per month and $20 per personal training session.

So, basically, each expression would be

At Silver Gym: 25 + 30x

At Fit Facto: 65 + 20x

To know the number of personal training sessions Sarah would have to buy to make them equal, we have to equalize these expressions and solve for x

25 + 30x = 65 + 20x

30x - 20x = 65 - 25

10x = 40

x = 4

Therefore, Sarah would have to by 4 sessions, and then the total cost of both gyms will be equal.

Notice that the variable is with the personal training sessions, you have to do that because a membership won't variate since the problem specifies the period of 1 month, however in one month, the number of personal training sessions do variate.