One cardiovascular research group in London, UK, studied the appearance transit times in a series of patients with cardiovascular problem. They obtained the median appearance transit time for these patients is 3.50 seconds. Inspired by the finding above, a research Group B in Newcastle, UK, wants to test if the median appearance transit time in the population is different from 3.50 second, and obtained the following observations:
Subject 1 2 3 4 5 6 7 8 9 10 11
Transit Time(sec) 3.05 3.30 5.65 2.25 2.50 3.50 2.05 3.25 3.10 2.70 3.00
Test the claim above using critical value a = 5% and comment on your findings. (7 marks)

Answer: 20 liters

Step-by-step explanation:

Let the number of liters of 15% alcohol solution be \(x\).

\(0.15x+30(0.4)=0.3(x+30)\\\\0.15x+12=0.3x+9\\\\12=0.15x+9\\\\0.15x=3\\\\x=20\)

Answer:

D. O

Step-by-step explanation:

O is the circumcenter of the Triangle and <C is the only 90 degree angle in the triangle

So basically O is the middle (the center) of the triangle.

Hope this helps fr.

The smallest possible inside length of the cubical steel tank that can hold 275 liters of water is approximately 0.640 meters.

The side length of the cube is found by converting the volume of water from liters to cubic meters, as the unit of measurement for the side length is meters.

Given that the volume of water is 275 liters, we convert it to cubic meters by dividing it by 1000 (1 cubic meter = 1000 liters):

275 liters / 1000 = 0.275 cubic meters

Since a cube has equal side lengths, we find the side length by taking the cube root of the volume. In this case, we find the cube root of 0.275 cubic meters:

∛(0.275) ≈ 0.640

Rounded to the nearest 0.001 meters, the smallest possible inside length of the tank is approximately 0.640 meters.

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Answer:

Point slope form

\(y=mx+b\)

Answer:

Step-by-step explanation:

Outcomes

Total outcomes:

To answer this question we must carefully understand the scope of the numbers of the table.

* It represents the number of adults that listen to audiobooks or not. But not all adults, just the surveyed adults.

* Nothing is said about books, only about audiobooks.

Some of the choices are tricky. For example, second and fourth choices talk about books, so they must be discarded.

The third choice refers to all adults, but the table refers only to the 640 adults that were asked.

The first choice is the best question that can be answered using the table.

SOLUTION:

(a) We want to find the ratio of the volumes of the cubes,

5 x 5 x 5 = 125

3 x 3 x 3 = 27

125 : 27

(b) Since the two cones are similar, the ratio of the heights will be the same as the ratio of the radii, which means that the ratio of the volume will be;

Answer:

98 and 7/25

Step-by-step explanation:

91x2/25+91=total price

182/25+91=total

7 and 7/25+91=total

total=98 and 7/25

To find the moments Mx and My and the center of mass of the system, we first need to calculate the total mass of the system and the coordinates of the center of mass.

Total mass of the system:
m_total = m_1 + m_2 + m_3 + m_4
m_total = 14 + 4 + 6 + 10
m_total = 34
Coordinates of the center of mass:
x_c = (m_1*x_1 + m_2*x_2 + m_3*x_3 + m_4*x_4) / m_total
y_c = (m_1*y_1 + m_2*y_2 + m_3*y_3 + m_4*y_4) / m_total

where x_i and y_i are the coordinates of mass m_i at point p_i.
x_c = (14*1 + 4*7 + 6*4 + 10*(-5)) / 34
x_c = -0.2941
y_c = (14*(-2) + 4*5 + 6*3 + 10*3) / 34
y_c = 1.3824

Therefore, the center of mass of the system is approximately (-0.2941, 1.3824).
To find the moments Mx and My, we need to use the following formulas:
Mx = ∑(m_i * y_i)
My = ∑(m_i * x_i)
Mx = 14*(-2) + 4*5 + 6*3 + 10*3
Mx = 56
My = 14*1 + 4*7 + 6*4 + 10*(-5)
My = -22

Therefore, the moments of the system are Mx = 56 and My = -22.
To find the moments Mx and My and the center of mass of the system, we will use the following formulas:
Mx = (Σ(m_i * x_i)) / Σm_i
My = (Σ(m_i * y_i)) / Σm_i
Given masses m_1 = 14, m_2 = 4, m_3 = 6, and m_4 = 10, and points p_1(1, -2), p_2(7, 5), p_3(4, 3), and p_4(-5, 3), we can calculate the moments:
Mx = [(14 * 1) + (4 * 7) + (6 * 4) + (10 * -5)] / (14 + 4 + 6 + 10)
Mx = (14 + 28 + 24 - 50) / 34
Mx = 16 / 34
Mx ≈ 0.47
My = [(14 * -2) + (4 * 5) + (6 * 3) + (10 * 3)] / (14 + 4 + 6 + 10)
My = (-28 + 20 + 18 + 30) / 34
My = 40 / 34
My ≈ 1.18

So, the center of mass of the system is approximately at point (0.47, 1.18).

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Answer:

D)

Step-by-step explanation:

The relationship between the standard deviation and variance is that the standard deviation is the square root of the variance.

The correct option is -C

Hence, the correct option is (c) Standard deviation is the square root of the variance. Variance is the arithmetic mean of the squared differences from the mean of a set of data. It is a statistical measure that measures the spread of a dataset. The squared difference from the mean value is used to determine the variance of the given data set.

It is represented by the symbol 'σ²'. Standard deviation is the square root of the variance. It is used to calculate how far the data points are from the mean value. It is used to measure the dispersion of a dataset. The symbol 'σ' represents the standard deviation. The formula for standard deviation is:σ = √(Σ(X-M)²/N) Where X is the data point, M is the mean value, and N is the number of data points.

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x - √3y - 4 = 0 → Choice A

Step-by-step explanation:

x - 4 = √3y

x - 4 - √3y = √3y - √3y

x - 4 - √3y = 0

x - √3y - 4 = 0

Given:

We need to find asymptotes of the given function.

Recall that a horizontal asymptote is a horizontal line, y=a, that has the property that either:

or

Taking the limit of the given function, we get

The horizontal asymptote is y=3.

Recall that a vertical asymptote is a vertical line, x=a, that has the property that either:

or

Taking limit to the given function, we get

If we take a=2, the limit will be infinity.

Hence the vertical asymptotes x=2.

From these two asymptotes, we can say that the first option or third option would be the graph.

Consider the point (3,2) from the first option graph.

Substitute x=3 and f(3)=2 in the given function, we get

The point (3,2) satisfies the given function.

Hence the graph of the function is

Answer:

Step-by-step explanation:

In order to solve this problem, you must find the factor to use the distributive property.

Distributive property:

→ A(B+C)=AB+AC

28r+24

4*7=28

4*6=24

Rewrite the problem down.

4*7r+4*6

Solve.

4*7r=28r

4*6=24

28r+24

I hope this helps! Let me know if you have any questions!

H0: p1 ≥ p2 (Null hypothesis: Proportion of ADHD-diagnosed students in School A is equal to or greater than in School B)

Null Hypothesis: The proportion of students diagnosed with ADHD in School A is equal to or greater than the proportion of students diagnosed with ADHD in School B.

Symbolically, the null hypothesis can be stated as:

H0: p1 ≥ p2

Where:

H0: Null Hypothesis

p1: Proportion of students diagnosed with ADHD in School A

p2: Proportion of students diagnosed with ADHD in School B

In other words, the null hypothesis assumes that there is no significant difference or that School A may have an equal or higher proportion of students diagnosed with ADHD compared to School B.

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The answer is - log x.

Here's the solution for the given problem:

Using the properties of logarithms to evaluate each of the following expressions.

2log 3 + log 4

= 0 5 122(log 3) + log 4

= log (3²) + log 4

= log (3² × 4)

= log 36

= log 6²

Now, we have the expression log 6²

Now, we can write the given expression as log 36

Thus, the final answer is log 36

Ine = In e

(b) 0 - X Ś ?

By the rule of logarithm for quotient, we have

log (1/x)

= log 1 - log x

= -log x

We can use the same rule for log (0 - x) and write it as

log (0 - x)

= log 0 - log x

= - log x

Now, we have the expression - log x

Thus, the final answer is - log x

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Hypothesis test used to test the batting average of the two given team national league and American league is given z-test.

As given in the question,

Given : Mean batting for American league is not equal to Mean batting for National league.

Therefore, hypothesis test used to test the batting average of the national league and American league is given z-test.

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17.99mm and ).705 in

Step-by-step explanation:

Answer:

0.705 inches and 1.79 centimeters are both reasonable answers (they're the same)

Step-by-step explanation:

18 milimeters is too small

7 inches is too big

The general solution of the differential equation \(dy/dx + y = e^{(7x)\) is \(y = Ce^{(-x)} + (1/8)e^{(7x)\), where C is an arbitrary constant.

To find the general solution of the given differential equation, we will use an integrating factor. The standard form of a first-order linear differential equation is dy/dx + Py = Q, where P and Q are functions of x. In this case, P = 1 and \(Q = e^{(7x)\).

The integrating factor is defined as μ(x) = e^(∫P dx). Integrating P = 1 with respect to x gives us ∫1 dx = x. Therefore, the integrating factor is μ(x) = \(e^x\).

Now, multiply both sides of the differential equation by the integrating factor:

\(e^x(dy/dx) + e^xy = e^{(8x)\).

Using the product rule, we can rewrite the left-hand side as \((e^xy)' = e^{(8x)\). Integrating both sides with respect to x gives us:

∫(eˣy)' dx = ∫e^(8x) dx.

Integrating \(e^{8x}\) gives us \((1/8)e^{(8x)\), and integrating \((e^xy)'\)with respect to x gives us eˣy. Therefore, we have:

\(e^xy = (1/8)e^{(8x)} + C\).

Simplifying the equation, we get:

\(y = Ce^{(-x)} + (1/8)e^{(7x)\),

where C is an arbitrary constant, representing the family of solutions for the given differential equation.

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Since each coupon decreases the price by 0.75, we can represent its value as (-0.75).

Then, the customer used 3 coupons, so the total discount is 3 times (-0.75), therefore the expression that represents this scenario is:

Correct option: B.

The specific range depends on the material properties and the energy levels involved.

The minimum and maximum frequencies for the acoustic and optic modes depend on the specific system or material under consideration. However, I can provide some general information.

Acoustic Mode:

The acoustic mode refers to the propagation of sound waves or vibrations in a material. In a solid, the acoustic mode can have different types, such as longitudinal and transverse modes.

The minimum frequency for the acoustic mode is typically determined by the size and physical properties of the material. In general, it can be close to zero for macroscopic objects or materials with low elasticity.

The maximum frequency for the acoustic mode depends on factors such as the speed of sound in the material and the characteristic dimensions of the system. It can range from a few kilohertz to several gigahertz.

Optic Mode:

The optic mode is related to the interaction of light with a material. It typically refers to the vibrations of charged particles (such as electrons) in a solid or the oscillations of electric or magnetic fields associated with photons.

The minimum frequency for the optic mode is typically determined by the energy gap between electronic states in the material. For example, in a semiconductor, the minimum frequency is usually in the infrared range.

The maximum frequency for the optic mode is not strictly defined, as it can extend into the terahertz, infrared, visible, ultraviolet, X-ray, and even gamma-ray regions. The specific range depends on the material properties and the energy levels involved.

It's important to note that these frequency ranges are general guidelines and can vary depending on the specific system or material being studied.

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Answer:

0.6832

Step-by-step explanation:

Given :

Mean, m = 52

Standard deviation, s = 7

-1.2 standard deviation of average = 57 - 1.2(7) = 57 - 8.4 = 48.6

2 standard deviations of average = 57 + 2(7) = 57 + 14 = 71

Zscore = (48.6 - 52) / 7 = - 0.486

Zscore = (71 - 52) / 7 = 2.714

P < -0.486) = 0.31348

P < 2.714 = 0.99668

P < 2.714 - P < -0.486 = (0.99668 - 0.31348) = 0.6832

Answer:

80

Step-by-step explanation:

\( \sin(80) = \cos(10) \\ 90 - x = 10 \\ x = 80\)

The numbers that cannot be probabilities are: square root of 2, -53, 5/3, and 1.31.

Probability is a measure of the likelihood of a particular event occurring in a random experiment. It is a value between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain to occur.

In statistics, probability is used to make predictions or draw inferences about a population based on a sample of data. For example, if we were to flip a coin, the probability of getting heads is 0.5, or 50%. In general probability can be defined as the ratio of the number of favorable outcomes to the total number of possible outcomes, which is the mathematical framework behind the random experiments.

From the set of numbers, 0, 0.08, and 3/5 are all possible values of probability.

Therefore, square root of 2, -53, 5/3, and 1.31 cannot be probabilities.

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Given,

The area of the rectangle = 6x + 12

We have to find the length and width of the rectangle.

Here,

Area of rectangle = 6x + 12 sq.ft

We can write it as,

Area of rectangle = 2(3x + 6) sq.ft

Where,

Length of the rectangle = 2 feet

Width of the rectangle = (3x + 6) feet

Otherwise,

Factorize the common terms;

Area of rectangle = 6(x) + 6(2) = 6(x + 2) sq.ft

Here,

Length of the rectangle = 6 feet

Width of the rectangle = (x + 2) feet

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Answer:

x=35°

Step-by-step explanation:

∠A+∠B+∠C=180°(ASP)

In ΔCAD, DC=DA

so, ∠DAC=∠DCA( angles opposite to equal sides are equal)

∠B=90°(given)

So, ∠DCA= 180°-(90+20)= 70°

Since ∠DCA= ∠DAC,

2x= 70°

x=35°

The value of angle A or the value of x is 35°

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

The angle A will be calculated as:-

∠A+∠B+∠C=180°(ASP)

In ΔCAD, DC=DA

so, ∠DAC=∠DCA( angles opposite to equal sides are equal)

∠B=90°(given)

So, ∠DCA= 180°-(90+20)= 70°

Since ∠DCA= ∠DAC,

2x= 70°

x=35°

Therefore the value of angle A or the value of x is 35°

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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

The cost to carpet a rectangular floor measuring 27 feet by 15 feet is $1269

Information about the problem:

The formula and procedure to solve this geometry exercise is:

A(rectangle) = length * width

A(rectangle) = 27 ft * 15 ft

A(rectangle) = 405 ft^2

By converting the area from ft^2 to yard^2, we have:

405 ft^2 * (1 yard^2 / 9 ft^2) = 45 yard^2

Calculating the cost to carpet a rectangular floor:

Cost = A(rectangle) * cost per square yard

Cost = 45 yard^2 * $28.20/ yard^2

Cost = $1269

Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft^2, m^2

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Answer:

-3

Step-by-step explanation:

The difference between 7-10 is -3. The minus sign is used because smaller number is subtracted from a larger number