A conical paper cup is shown in the diagram below.4.5 cm16 cm7.5 cm

(a) 95% confidence interval for the difference between female and male times is (11.954, 255.591).

(b) The assumptions and conditions for the two-sample t-test are met, so we can use the results of the test and confidence interval.

a) To construct a 95% confidence interval for the difference between female and male times, we can use a two-sample t-test. Let's denote the mean time for female swimmers as μf and the mean time for male swimmers as μm. We want to test the null hypothesis that there is no difference between the two means (i.e., μf - μm = 0) against the alternative hypothesis that there is a difference (i.e., μf - μm ≠ 0).

The formula for the two-sample t-test is:

t = (Xf - Xm - 0) / [sqrt((s^2f / nf) + (s^2m / nm))]

where Xf and Xm are the sample means for female and male swimmers, sf and sm are the sample standard deviations for female and male swimmers, and nf and nm are the sample sizes for female and male swimmers, respectively.

Using the data from the plots, we get:

Xf = 917.5, sf = 348.0137, nf = 15

Xm = 783.7273, sm = 276.0625, nm = 28

Plugging in these values, we get:

t = (917.5 - 783.7273 - 0) / [sqrt((348.0137^2 / 15) + (276.0625^2 / 28))] = 2.4895

Using a t-distribution with (15+28-2) = 41 degrees of freedom and a 95% confidence level, we can look up the critical t-value from a t-table or use a calculator. The critical t-value is approximately 2.021.

The confidence interval for the difference between female and male times is:

(917.5 - 783.7273) ± (2.021)(sqrt((348.0137^2 / 15) + (276.0625^2 / 28)))

= 133.7727 ± 121.8187

= (11.954, 255.591)

Therefore, we can be 95% confident that the true difference between female and male times is between 11.954 and 255.591 minutes.

b) Assumptions and conditions for the two-sample t-test:

Independence, We assume that the observations for each group are independent of each other.

Normality, We assume that the populations from which the samples were drawn are approximately normally distributed. Since the sample sizes are relatively large (15 and 28), we can rely on the central limit theorem to assume normality.

Equal variances, We assume that the population variances for the female and male swimmers are equal. We can test this assumption using the F-test for equality of variances. The test statistic is,

F = s^2f / s^2m

where s^2f and s^2m are the sample variances for female and male swimmers, respectively. If the p-value for the F-test is less than 0.05, we reject the null hypothesis of equal variances. If not, we can assume equal variances. In this case, the F-test yields a p-value of 0.402, so we can assume equal variances.

Sample size, The sample sizes are both greater than 30, so we can assume that the t-distribution is approximately normal.

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Answer:

2x - 4 = 25x^2x^3x

Step-by-step explanation:

log(5x)(2x-4)=3x+2

2x- 4 = (5x)^(3x+2)

2x - 4 = (5x)^3x * (5x)^2

2x - 4 = 25x^2x^3x.

Answer:

Exponential form:

\((5x)^{3x+2}=2x-4\)

Step-by-step explanation:

\(\log_\text{base}(?)=\text{exponent}\)

is equivalent to \((\text{base})^\text{exponent}=?\)

So \(\log_{5x}(2x-4)=3x+2\)

is equivalent to

\((5x)^{3x+2}=2x-4\)

Among the given options, (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements must be true about the 9 measurements, excluding the outlier, when compared with the 10 measurements.

An outlier is defined as a measurement that significantly deviates from the other measurements in a data set.

In this case, one of the measurements among the 10 is identified as an outlier.

When comparing the remaining 9 measurements with the entire set of 10 measurements, the maximum value of the 9 measurements cannot exceed the maximum value of the 10 measurements because the outlier, by definition, exceeds the upper quartile or lower quartile by at least 1.5 times the interquartile range.

It is important to note that the median of the 9 measurements can be either greater than or less than the median of the 10 measurements, depending on the specific values of the measurements.

The presence of the outlier does not necessarily determine the relationship between the medians of the two sets.

Similarly, the standard deviation of the 9 measurements may or may not be less than the standard deviation of the 10 measurements.

The inclusion or exclusion of the outlier can have an impact on the standard deviation calculation, but it is not guaranteed to be lower or higher in either case.

Therefore, among the given options, the only statement that must be true is (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements.

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Answer:

2.5

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

25 divided by 10% is 2.5 gallons

12 students like science the most and can draw a model having 18 things out of which 12 are circled.

What is model in mathematics?

Consider the provided information.

Your class has 18 students. Exactly 2/3 of them say that, out of all their subjects, they like science the most.

First calculate 2/3 of 18.

= (2/3) * 18

= 2 * 6

= 12

Hence, 12 students like science the most.

We can draw a model having 18 things out of which 12 are circled.

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The correct option to model the height is

h = cosine (StartFraction pi Over 6 EndFraction t) + 9.

Here the height of the tip of the hour hand of a wall clock follows a cosine function as the time progresses since the hour hand of a clock completes one full revolution in 12 hours.

We will use the general form of a cosine function to model the height has a function of time t:

Where A is the amplitude, B is the frequency and C is the vertical shift  

Here we have

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet.

Hence, the applitude A = [9+10]/2 = 0.5.

The period of a cosine function is given by 2π/B,

Since the hour hand completes one full revolution in 12 hours, the period is 12 hours or 2π.

=> B = π/6.

The vertical shift is C = 9.

Thus, the equation that models the height h as a function of time t is:

h = 0.5 cos(π/6 t) + 9.

Therefore,

The correct option to model the height is

h = cosine (StartFraction pi Over 6 EndFraction t) + 9.

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Answer:

-13/4, -3, 16/5, 5

Step-by-step explanation:

-13÷4= -3.25

-3=-3

16÷5=3.2

5=5

For -13/4, you can just take away the negative symbol and do 13÷4, then add it on for 3.25. That does not work for every problem like this though.

Please give brainliest if I helped! :)

Answer:

Step-by-step explanation:

Answer:

20 centimeters

Step-by-step explanation:

Karina's aquarium can hold 80 liters,which is equal to 80,000cm³.The base measure 100cm by 40cm.What is the height of the aquarium in centimeters?Round your answer to the nearest hundredth.

The shape of an Aquarium = Rectangular Prism

Volume of the rectangular prism = L × Width × Height

Volume = 80 Liters = 80,000 cm³

Base = 100 cm × 40 cm

Height of the aquarium is calculated as:

80,000cm³ = 100 cm × 40 cm × h

h = 80,000cm³/100 cm × 40 cm ×

h = 20 cm

The height of the aquarium = 20cm

Answer:

20 centimeters

Step-by-step explanation:

Total 55 pairwise comparisons must be made to determine the winner in an election with 11 candidates using the pairwise comparison method.

If there are total 11 candidates contested in the election , then the number of pairwise comparisons required to determine the winner using the pairwise comparison method is:

(11-1) + (11-2) + (11-3) + ... + (11-10)

The above expression can be simplified to as 10 + 9 + 8 + ... + 1

It is an arithmetic series (AP) having a common difference of -1 and a first term of 10. To calculate the sum of an arithmetic series the following formula can be utilized to find the total number of possible comparisons :

n/2 [2a + (n-1)d]

Here, n is the total number of terms, a is the first term, and d is the common difference.

In the problem, n = 10, a = 10, and d = -1. putting these values into the formula,

10/2 [2(10) + (10-1)(-1)] = 10/2 [20 - 9] = 10/2 × 11 = 55

So, there are total 55 pairwise comparisons to be made in order to determine the winner in an election with 11 candidates.

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Answer:

36.5feet

Step-by-step explanation:

tan47º=h/34

h=36.4605=36.5feet

The tree is at height 36.5 feet if the point on the ground is 34 feet from the tree.

The angle of elevation to a nearby tree from a point on the ground is measured to be 47º

The angle of elevation is when you are measuring the angle from the floor or the ground.

\(tan47^0=h/34\)

\(34 tan47^0=h\)

h=36.4605

h=36.5 feet

Therefore the tree is at height 36.5 feet if the point on the ground is 34 feet from the tree.

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A number that goes into a greater number with no remainders is called a factor.

A factor is an integer that divides into a greater number without any remainders.

For example, the number 6 is a factor of 18 because when 18 is divided by 6, the answer is 3 with no remainders. Similarly, the number 3 is a factor of 12 because when 12 is divided by 3, the answer is 4 with no remainders.

Factors are important in mathematics because they can be used to solve equations and determine the greatest common divisor (GCD) of two or more numbers. Factors can also be used to determine prime numbers and their multiples.

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The given function, y = 12 cos [3x], we can determine the amplitude, period, and phase shift using the following formulas:

Question 1:

- Amplitude (A): The amplitude is given by A = 12, so the amplitude of the function is 12.

- Period (T): The period of the function can be found using the formula T = 2π/|B|, where B is the coefficient of x. In this case, B = 3. Substituting the values, we get T = 2π/3, which is approximately 2.09.

- Phase Shift (C/B): The phase shift can be determined by calculating C/B, where C is the horizontal shift and B is the coefficient of x. In this case, there is no horizontal shift (C = 0) and B = 3. Thus, the phase shift is 0.

Therefore, the amplitude is 12, the period is approximately 2.09, and the phase shift is 0.

Answer:

Amplitude = 12

Period = 2.09

Phase shift = 0

Question 2:

The graph of y = 3 cos (x - 2π/3) can be visualized as follows:

(Insert the graph visualization here)

From the graph, we can determine the properties of the function:

- Amplitude: The amplitude of the function is 3, as it represents the maximum value of the cosine function.

- Period: The period of the function is 2π, which can be observed from the complete cycle of the graph.

- Phase Shift: The phase shift of the function is 2π/3, which indicates a horizontal shift to the right.

In summary, the amplitude is 3, the period is 2π, and the phase shift is 2π/3.

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Solution

Given that cos θ= 3/5 and cot x < 0, then tanθ = ?

Using trigonometric function and angle

USING PYTHAGORAS therorem

Tanθ = opposite/adjacent

Temperature of refrigerators - Cannot determine. Horsepower of race car engines - Ratio. Marital status of school board members - Nominal. Ratings of television programs - Ordinal. Ages of children enrolled in a daycare - Interval

The level of measurement for the temperature of refrigerators cannot be determined based on the given information. The temperature could potentially be measured on a nominal scale if the refrigerators were categorized into different temperature ranges. However, without further context, it is not possible to determine the specific level of measurement.

The horsepower of race car engines can be measured on a ratio scale. Ratio scales have a meaningful zero point and allow for meaningful comparisons of values, such as determining that one engine has twice the horsepower of another.

The marital status of school board members can be measured on a nominal scale. Nominal scales are used for categorical data without any inherent order or ranking. Marital status categories, such as "married," "single," "divorced," etc., can be assigned to school board members.

The ratings of television programs, such as "poor," "fair," "good," and "excellent," can be measured on an ordinal scale. Ordinal scales represent data with ordered categories or ranks, but the differences between categories may not be equal or measurable.

The ages of children enrolled in a daycare can be measured on an interval scale. Interval scales have equal intervals between values, allowing for meaningful differences and comparisons. Age, measured in years or months, can be represented on an interval scale.

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Answer: =6x^2+17x−45

Step-by-step explanation:

=(2x+9)(3x+−5)

=(2x)(3x)+(2x)(−5)+(9)(3x)+(9)(−5)

=6x2−10x+27x−45

=6x2+17x−45

Answer:

\(6x^{2} -17x-45\)

Step-by-step explanation:

Use distribution then combine like-terms to simplify

A linear system with 3 equations and 4 variables by representing it with an augmented matrix and bringing the matrix to reduced row-echelon form can be solved.

A mathematical representation of a system based on the application of a linear operator is known as a "linear system" in systems theory. Ordinarily, compared to nonlinear systems, linear systems display much simpler features and properties. The automatic control theory, signal processing, and telecommunications all heavily rely on linear systems as a mathematical abstraction or idealisation.

Linear systems, for instance, are frequently used to model the propagation medium for wireless communication systems. An operator, H, that converts an input, x(t), into an output, y(t), a kind of black box description, can be used to describe a general deterministic system.

The superposition principle, or alternatively both the additivity and homogeneity properties, must be satisfied by a system to be considered linear, and only then.

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2.5(cos 5π/6  + i sin 5π/6) is the polar form  of the complex number

Complex numbers are numbers that are expressed in the form of a+ib, where a and b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1)

Given: the complex number (5√3)/4 - 5/4 i

In polar form:

(5√3)/4 - 5/4 i = r(cosθ + isinθ)

θ  = tan⁻¹( (-5/4) / (5√3 /4) )

θ = -30°

θ = -30+180 = 150°

θ = 5π/6

r = √( (5√3)/4)² +(- 5/4)²) = 2.5

Thus,

(5√3)/4 - 5/4 i = r(cosθ + isinθ)

r(cosθ + isinθ) = 2.5(cos 5π/6  + i sin 5π/6 )

Therefore, the polar form  of the complex number is 2.5(cos 5π/6  + i sin 5π/6)

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Answer:

55/99

Step-by-step explanation:

To express 0.55 repeating as a fraction, we can use the following steps:

Let x = 0.55 repeating

Multiplying both sides by 100 to eliminate the repeating decimal gives:

100x = 55.55 repeating

Subtracting the left-hand side (100x) from the right-hand side (55.55 repeating) gives:

99x = 55

Dividing both sides by 99 yields:

x = 55/99

Therefore, 0.55 repeating can be expressed as the fraction 55/99.

Answer:

B. 2.2 kilometers

Step-by-step explanation:

⭐What is the change in the cyclist's elevation?

Thus, we need to solve for the value of the height (x) of the hill.

Notice that the hill is in the shape of a right triangle. In order to find an unknown side length for right triangles, we need to use a trigonometric function.

⭐What is a trigonometric function?

First, let's see what kind of side lengths we are given (opposite, hypotenuse, or adjacent).

We are given a side length of 10km, which is the hypotenuse of the triangle, and we are given a side length of x, which is the opposite of θ (13°).

Therefore, we will use the trigonometric function sin(θ) to solve for x.

Substitute the side lengths and angle measures we are given:

\(sin(13) = \frac{x}{10}\)

Set the equation equal to x:

\(10sin(13) = x\)

Solve for x. I recommend using a scientific calculator (e.g. Desmos Scientific Calculator):

\(2.2 = x\)

∴ The cyclist's change in elevation is 2.2 kilometers.

Answer:

$279.92

Step-by-step explanation:

Leo spends $235.65 and then another $124.43. He spends a total of $360.08. $12 an hour for 52 hours is 52 * 12 = $624.

Subtract amount he worked for from the amount he spent last week and this is the equation: 624 - 360.08 = $279.92

a) The selling price of the skis is $79.80.

b) The final price is 140% of the original price.

c) The percent increase from the original price to the final price is 40%.

a) Calculation of selling price:

Markup rate is 40%

Original cost = $57

Selling price = (100% + Markup percentage) × Original cost

Selling price = (100% + 40%) × $57

Selling price = 1.4 × $57

Selling price = $79.80

b) Calculation of percentage of the original price that is the final price

Percentage of original price that is the final price = (Final price / Original price) × 100%

Percentage of original price that is the final price = ($79.80 / $57) × 100%

Percentage of original price that is the final price = 140%

c) Calculation of the percentage increase

Percentage increase = (Final value − Initial value) / Initial value × 100%

Percentage increase = ($79.80 − $57) / $57 × 100%

Percentage increase = $22.80 / $57 × 100%

Percentage increase = 40%

Therefore, The store charges $79.80 for the skis. The final price is 140% of the original price and the percent increase from the original price to the final price is 40%.

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Answer:

148°

Step-by-step explanation:

the angles are equal

Answer:

Step-by-step explanation:

(2). 1 yd ≈ 0.9144 m

1 yd³ ≈ 0.76455 m³

2 yd³ ≈ 1.53 m³ ≈ 2 m³

(3). 1 ft ≈ 0.3048 m

1 ft² ≈ 0.0929 m²

162 ft² ≈ 15.1 m²

(4). 1 mi ≈ 1.60934 km

1 mi² ≈ 2.59 km²

503 mi² ≈ 1302.8 km²

The mean GPA is greater than 2.75.

Here, we have,

A= 4.0, A- = 3.7, B+ = 3.

three, and many others.

Total the first-class factors, and overall the credit hours. Divide the overall satisfactory points by means of the overall credit score hours.

Grade Point Average (GPA):

Grade point average (GPA) is the measure used to summarize your instructional fulfillment at Griffith. After the e-book of final grades every trimester, your software and career.

GPA is calculated and could be utilized by the college to tell choices, which include the subsequent: educational progression.

Divide the total range of grade factors earned with the aid of the total number of letter-graded units undertaken.

Mean GPA = total / 50    

                 = 2.75.

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Answer:

\(r\geq -18\)

Step-by-step explanation:

\(\frac{-r}{3} \leq 6\\\rule{150}{0.5}\\(\frac{-r}{3})*3\leq 6*3\\\\-r \leq 18\\\\\frac{-r \leq 18}{-1}\\\\\boxed{ r\geq -18}\)

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The probability of tuning an engine in 20 minutes or less is 0.5

Given that the time it takes to completely tune an engine of an automobile follows an exponential distribution with a mean of 30 minutes.

Let X be the time taken to tune an engine, then X follows an exponential distribution with mean μ = 30 minutes.

The probability of tuning an engine in 20 minutes or less can be calculated as follows

P(X ≤ 20) = 1 - \(e^{-lambda*x}\)

where λ = 1/μ is the rate parameter.

So, substituting the values we get:

P(X ≤ 20) = 1 - \(e^{-20/30}\)

= 1 - \(e^{-0.6667}\)

Subtract the numbers

= 0.5

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price of 3Step-by-step explanation: