1)The time (in minutes) that it takes a mechanic to change oil has an exponential distribution with mean 20.
a) Find P(X < 25), P(X > 15), and P(15 < X < 25)
b) Find the 40th percentile

Bias results from random variation and will always be present, while bias results from samples that do not represent the population. Bias can usually be reduced when the sample size is larger.

Bias is an error that occurs in statistical studies when the results are not representative of the true population. Bias can occur when the sample size is too small, or when the sample does not accurately reflect the population. This means that even if the study is perfectly designed, bias will still exist. Additionally, bias can result from samples that do not represent the population. For example, if a study is conducted on a population that is predominantly male, then the results may be biased towards male behavior. Finally, bias is usually reduced when the sample size is larger. This is because a larger sample size provides for more accurate results, as there is less of a chance that random variation will affect the data. Therefore, increasing the sample size is a helpful way to reduce bias in a study.

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Answer:

19.2 inches

Step-by-step explanation:

The arc length,s, can be calculated using the formula s=r*c, where r is the radius of the circle and c is the central angle in radians. So, for a circle with a radius of 8 inches and a central angle of 2.4 radians, the arc length would be s=8 inches*2.4 radians =19.2 inches

The arc length s cut off by an angle with a measure of 2.4 radians in a circle with a radius of 8 inches is 19.2 inches.

What is the arc length?

Arc length is a measure of the distance along a curved line segment of a circle or a curve. It represents the length of a portion of the circumference of a circle, or the distance between two points on a curved line. In mathematical terms, it is defined as the integral of the magnitude of the velocity vector along the curve. The formula for the arc length of a circle depends on the radius r and the central angle θ (measured in radians) that cuts off the arc. It is given by

s = r * θ

In this case, the radius r is 8 inches, and the central angle θ is 2.4 radians. Plugging in these values, we get:

s = 8 * 2.4 = 19.2 inches

Hence, the arc length s cut off by an angle with a measure of 2.4 radians in a circle with a radius of 8 inches is 19.2 inches.

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Answer:

When the increase in demand is greater than the decrease in supply, the equilibrium price rises and the equilibrium quantity increases.

What is economic equilibrium?

Economic equilibrium, as used in economics, is a state in which forces such as supply and demand are in balance and where, in the absence of external influences, the values of economic variables will remain constant.

The equilibrium quantity rises if the rise in demand outweighs the fall in supply. The equilibrium quantity falls if the rise in demand is smaller than the fall in supply. Equilibrium price rises in each scenario.

The supply and demand curves move in opposition to one another. However, the supply curve shifted to the left while the demand curve shifted to the right (signalling a rise in demand) (indicating a decrease in supply).

In the case increase in demand > decrease in supply

In this instance, the supply curve's leftward movement is proportionally less than the rightward change of the demand curve. So, the price and the equilibrium quantity both increase.

Therefore, the equilibrium price and quantity increases.

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Step-by-step explanation:

when multiplying factors of the same base, we can simply add the exponents.

when dividing, we subtract.

so,

z⁹xz⁶/z⁷ = xz^(9+6-7) = xz⁸

Answer:

Step-by-step explanation: First you need to know the powers, the power of a number says how many times to use the number in a multiplication. Therefore, you should be able to multiply that by ur number.

If 500 grams of flour are used, 166.66666 grams of sugar must be added, followed by 200 grams of sugar.

When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage.

A ratio is a tool for comparing like-kind quantities or illustrating relationships between them. To compare similar items, we employ ratios.

Two numbers or measurements are compared to form a ratio. The quantities being compared are referred to as the terms of the ratio. A ratio divides two amounts into equal parts, with the dividend or antecedent serving as the unit of comparison and the divisor or unit of comparison serving as the unit of comparison.

To make a cake, I combined 750g of flour, 250g of butter, and 300g of sugar.

a) 250/750 = 1/3 = 1 : 3

b) 750/300 = 15/6 = 5/2 = 5 : 2

c) 250/300 = 5/6 = 5 : 6

If 500 grams of flour are used, 166.66666 grams of sugar must be added, followed by 200 grams of sugar.

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Answer:  Decreasing, if it "Halves (cuts in half)". If it was increasing, it would probably say double.

Step-by-step explanation:

So, if it was being cut in half every two days, we would only be counting days 2, 4, and 6.

So days 2, it would be cut in half, and go from 500 to 250. Day 4, it would go from 250 to 125. The day 6, it would go from 125 to 62.5.

In 6 days, the investment will be worth $62.50

Answer:

(3y-2)(y+4)Ω

Step-by-step explanation:

real simple

Answer: 15.5^2 - 7.2^2 = 240.25 - 51.84= 188.41

188.41 square root is 13.7262522197 or 13.7

Step-by-step explanation: Hope this helps!! :))

Answer: 66.2°F

Step-by-step explanation: (19°C × 9/5) + 32 = 66.2°F

Answer is 66.2°F.

How to calculate 19 °C in °F?

The base formula for this c to f converter is

Fahrenheit = (19 °C x 9/5) + 32

                 = 66.2°F

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The coordinates of A= are also (-3,4). The answer to the query is determined by the coordinates of the second endpoint B. (x, y). The midpoint's coordinates can be calculated using the formula below:

The following are b's coordinates: B= (-7,-8) (-7,-8)

We are given the midpoint's coordinates as M= (-5,-2).

Furthermore, A='s coordinates are (-3,4). The solution to the question depends on the coordinates of the second endpoint B.

the coordinates of B (x, y). The following formula can be used to determine the midpoint's coordinates:

[tex]$& x_m=\frac{x_a+x_b}{2} \\[/tex]

[tex]$& y_m=\frac{y_a+y_b}{2}[/tex]

We know xa = -3 and xm = -5. Solve the first equation for x b :

[tex]$2 x_m=x_a+x_b \Rightarrow x_b=2 x_m-x_a[/tex]

Substituting:

[tex]$& x_b=2 \cdot(-5)-(-3)=-10+3 \\[/tex]

[tex]$& x_b=-7[/tex]

We can solve the second equation for xb and get:

[tex]$y_b=2 y_m-y_a[/tex]

Since ya = 4 and ym = -2, then:

[tex]$& y_b=2 \cdot(-2)-(4)=-4-4 \\[/tex]

[tex]$& y_b=-8[/tex]

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The timeline which correctly organizes the founding of important world religions are;

Judaism, Buddhism, Christianity, and Islam

The correct answer choice is option B.

Chronological order is the order of events from the first to the last.

Christianity was founded about 2,000 years ago.

Islam was founded about 1,400 years ago.

Hinduism was founded about 3,500 years ago.

Buddhism was founded about 2,500 years ago.

Judaism was founded about 4,000 years ago

Arrangements from the first to the last;

Therefore, the important world religions are in the order; Judaism, Hinduism, Buddhism, Christianity and Islam.

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Mean and median measures of central tendency would be affected if the outlier 11 was added to the data set.

As per the given data, the data set is 27, 20, 34, 37, 21, 42, and 39.

Mean of the data is the sum of all observations divided by the total number of observations.

Mean = [tex]$\frac{27+20+ 34+ 37+ 21+ 42+ 39}{7}[/tex]

Mean = [tex]$\frac{220}{7}[/tex]

Mean = 31.42

The median of the data for an odd number of observations is the middlemost term.

First, arrange the data in ascending order.

20, 21, 27, 34, 37, 39, 42

Middlemost term = 34.

The mode of the data is the most repeated data.

As no number is repeated there will be no mode.

As given 11 is added to the data set.

Mean = [tex]$\frac{27+20+ 34+ 37+ 21+ 42+ 39+11}{8}[/tex]

Mean = [tex]$\frac{231}{8}[/tex]

Mean = 28.8

The median of the data for an even number of observations is the average of the middle two terms.

First, arrange the data in ascending order.

11, 20, 21, 27, 34, 37, 39, 42

Median = [tex]$\frac{27+34}{2}[/tex]

Median = [tex]$\frac{61}{2}[/tex]

Median = 30.5

For the new data set also there will be no mode as there are no repeated numbers.

Comparing old and new values there is a change in the values of mean and median.

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The total number of permutations of the three tasks: 336 x 3! (3 factorial) = 40320

This question uses the combination and permutation theory. Combinations are used to calculate the total number of ways to assign the three tasks to the 8 people, and permutations are used to multiply the total number of ways to assign the three tasks by the total number of permutations of the three tasks.

given below :

1. Calculate the total number of ways to assign the three tasks to the 8 people: 8 x 7 x 6 = 336

2. Multiply the total number of ways to assign the three tasks by the total number of permutations of the three tasks: 336 x 3! (3 factorial) = 40320

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The graphed quadratic equation, in vertex form, is:

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

So the correct option is C.

Remember that for a quadratic equation with a leading coefficient a and a vertex (h, k), the vertex form is:

y = a*(x - h)^2 + k

Here we can see that the vertex is at the point (2, -5), replacing that we will get:

y = a*(x - 2)^2 - 5

We also can see that the parabola passes through (0, 7), then we can replace that to get:

7 = a*(0 - 2)^2 - 5

7 = 4a - 5

7 + 5 = 4a

12/4 = a

3 = a

The quadratic equation is:

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

The correct option is C.

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45 divided by 3 is 15. The solution has been obtained by using long division.

What is long division?

When splitting huge numbers, the task is divided into several sequential steps using the long division approach. The dividend is divided by the divisor, just like in conventional division problems, and the result is known as the quotient; occasionally, it also produces a remainder.

Using long division, we get    

   1 5  

3 | 45

-  3              (Multiplying 3 by 1, we get 3)

    1 5            (Bringing down the next number of the dividend)

-  1 5            (Multiplying 3 by 5, we get 15)

    0  

Hence, 45 divided by 3 is 15.

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Volume = a3, where an is the length of the cube's sides or edges, is how you can calculate the volume of a cube.

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It is used the observational study. A survey of high school students was conducted to see if students who take advanced classes are offered more scholarship money than students who do not take advanced classes

Now, According to the question:

"Information available from the question"

A survey of high school students was conducted to see if students who take advanced classes are offered more scholarship money than students who do not take advanced classes

Statisticians often refer to the "levels of measurement" of a variable, a measure, or a scale to distinguish between measured variables that have different properties. There are four basic levels: nominal, ordinal, interval, and ratio.

In an observational study, we measure or survey members of a sample without trying to affect them. In a controlled experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive the treatment.

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The scale factor of Figure A to Figure B is A- 5:9

From the question, we have the following parameters that can be used in our computation:

Figure A and Figure B

The scale factor of Figure A to Figure B is calculated as

Scale factor = Figure B : Figure A

Substitute the known values in the above equation, so, we have the following representation

Scale factor = 20 : 36

Evaluate

Scale factor = 5 : 9

Hence, teh scale factor is 5 : 9

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When comparing sets, a higher mean absolute deviation denotes a greater degree of dispersion of the data points from the mean and vice-versa.

What is mean absolute deviation?

The ratio of the sum of all absolute values of deviation from the central measure to the total number of observations is known as the mean absolute deviation.

We find the mean of the data set first, then use that value to calculate the mean absolute deviation of the data.

The mean absolute deviation reveals how dispersed or concentrated a group of data is around the mean. This is the data's variation.

When comparing sets, a higher mean absolute deviation denotes a greater degree of dispersion of the data points from the mean. Data points are more closely packed around the mean when the mean absolute deviation is lower.

Hence, this way the mean absolute deviation is used to compare data sets.

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Assuming the point (x, y) is in the indicated quadrant, the given ratio are as follows;

Quadrant II, x/y is a negative ratio.

Quadrant III, y/x is a positive ratio.

In Mathematics, a quadrant can be defined as the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.

This ultimately implies that, there are four (4) major quadrants in any graph and these include the following:

Now, we can determine the whether the given ratios are positive or negative:

Quadrant II, x/y = -x/y (negative ratio).

Quadrant III, y/x = -y/-x (positive ratio).

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The simplification of the expression gives 3 + √3

Simplification of an expression is defined as a way of writing an expression in the most efficient and compact form without affecting the value of the original expression

Surds are represented by square roots of non-perfect squares and are expressed using the radical symbol (√). For example, √2 is a surd, as it cannot be expressed as a finite decimal or a fraction.

√3(√3 - 1) =  (√3)*√3 + (√3)*1

                 = 3 + √3

Therefore, the expression can be simplified as 3 + √3

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Using a standard normal distribution table or a z-table gives us

P(¯Z≤0.8181)≈0.20662

Let us write down some of the parameters and statistics that are given in the question.

Population mean thickness

μ=4mm.

Population standard deviation

σ=1.1mm.

Random sample size

n=100.

Let the random normal variable

¯X denote the average thickness of the sample.

Then according to the Central Limit Theorem,

¯X

follows a normal distribution with mean

μ¯X=μ=4

and standard deviation

σ¯X=σ√n=1.1√100=1.110=0.11.

Then we can convert ¯X

into its standard normal form ¯Z

using the following transformation:

¯Z=¯X−μ¯Xσ¯X=¯X−40.11(1)

Now the question reads that we need the probability that the average thickness of the 100 sheets is less than 3.91 mm. In other words, we need

P(¯X<3.91).

Using (2) we get

P(¯X<3.91)=P(¯Z<3.91−40.11)=P(¯Z≤0.8181)(3)

Using a standard normal distribution table or a z-table gives us

P(¯Z≤0.8181)≈0.20662

which is our answer.

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Using a standard normal distribution table or a z-table gives us

P(¯Z≤0.8181)≈0.20662

Let us write down some of the parameters and statistics that are given in the question.

Population mean thickness

μ=4mm.

Population standard deviation

σ=1.1mm.

Random sample size

n=100.

Let the random normal variable

¯X denotes the average thickness of the sample.

Then according to the Central Limit Theorem,

¯X

follows a normal distribution with mean

μ¯X=μ=4

and standard deviation

σ¯X=σ√n=1.1√100=1.110=0.11.

Then we can convert ¯X

into its standard normal form ¯Z

using the following transformation:

¯Z=¯X−μ¯Xσ¯X=¯X−40.11(1)

Now the question reads that we need the probability that the average thickness of the 100 sheets is less than 3.91 mm. In other words, we need

P(¯X<3.91).

Using (2) we get

P(¯X<3.91)=P(¯Z<3.91−40.11)=P(¯Z≤0.8181)(3)

Using a standard normal distribution table or a z-table gives us

P(¯Z≤0.8181)≈0.20662

which is our answer.

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The mass in grams of 0. 450 moles of magnesium sulfate, MgSO4 in grams is 54.2.

The mole, which is 6.0221023 molecular entities, is the basic unit of a substance. One mole of a substance is equivalent to that substance's molecular weight.

The link between moles and molar mass means that the quantity of moles in a material is equal to the product of its mass and molecular mass.

The molar mass of magnesium sulphate is:

Magnesium = 24

Oxygen = 16 x 4 = 64

Sulphate = 32

Thus, the mass of magnesium sulphate is = 24 + 64 + 32 = 120 grams.

Now, moles is equal to:

Moles = given mass/molecular mass

Putting the values:

moles = given mass / 120

0.450 x 120 = given mass

Given mass = 54g.

Thus, the given mass of the magnesium sulphate is 54 g.

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If the vector a = x + iy, then the complex conjugate of vector a is x - iy where x is the real part and b is the imaginary part.

A number that may be expressed as (a + ib), where a denotes the real component, b denotes the imaginary part, and I denotes a fictitious number called iota, which is equivalent to the root of -1. In mathematics, a conjugate is created by flipping the sign of one of a binomial's terms.

A complex number's reflection about the horizontal axis (real axis) on Arcand's plane is represented by the conjugate of that complex number.

Another definition of a complex conjugate or conjugate of a complex number is a complex number having the same real component as the original number and the opposite sign of the imaginary part while maintaining the same magnitude, i.e., the original complex number's 'i' changes to the conjugate's '-i'.

Let a = x + iy

Complex conjugate of a is

a* = x - iy

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The correct way to order these amounts from greatest to the least is 0.6 gal, 1.9 L, and 3.8 pints.

To determine this, the best is to use the same units for all the amounts, in this case, I will convert everything to liters.

Pints to liters:

1 pt = 0.47 l

3.8 pt =  x

x= 3.8 x 0.47 = 1.78 liters

Gallons to liters:

1 gal = 3.78

0.6 gal = x

3.78 x 0.6 = 2.27 liters

Based on this, the correct way to order the amount is 0.6 gallons, 1.9 liters, and 3.8 pints.

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The y coordinate of the center of the circle is k=-1 and The radius of the circle is 7 units, the value of b in the equation is 49.

A circle is a two-dimensional, symmetrical figure in mathematics. The circle's center is a place inside the circle from which all points on the circle's edge are equally far.

The radius of the circle, abbreviated "r," is the distance from the center of the circle to a point on its edge.

The diameter of the circle, which is the greatest chord of any circle, is equal to the circle's doubled radius.

2 Radius times diameter Half of the circle is represented by the semicircle, and one-fourth by the circle's quadrant.

(PART A) To determine the y-coordinate of the center of the circle, we need to complete the square for both x and y. The equation can be transformed to the standard form for a circle: (x-h)² + (y-k)² = r², where (h,k) is the center of the circle and r is the radius.

First, complete the square for x:

x² - 4x + 4 = 4 + (x² - 4x)

x² - 4x + 4 + 4 = 4 + (x² - 4x) + 4

(x-2)² = (x² - 4x + 4) + 4

Next, complete the square for y:

y² + 2y + 1 = 1 + (y² + 2y) + 1

(y+1)² = (y² + 2y) + 1

Now, substitute the completed squares back into the original equation:

(x-2)² + (y+1)² = b

So, the y-coordinate of the center is k = -1.

(PART B) The radius of the circle is 7 units, so r = 7. Substitute this value and the coordinates of the center into the standard form of the equation:

(x-2)² + (y+1)² = 49

Finally, simplify to find the value of b:

b = 49.

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The length of the patio in the drawing, according to the scale of the drawing of 12 cm : 7 m, is 36 cm.

A scale is defined to be the ratio between the size of a given original object and a new object, which is its representation but is either smaller or bigger. It refers to the relative size of an object. Sometimes it is called a scale factor.

We are given a scale of the drawing of 12 cm : 7 m. Also, the actual length of the front patio is 21 m. To find the length of the patio in the drawing, we'll use algebra.

First, we write an equation that contains the scale of the drawing and the ratio of the actual length of the front patio to the length of the patio in the drawing, which is unknown still so we use a variabel x:

12 cm / 7 m = x / 21 m

Note that we're asked to find the length of the patio in the drawing in centimeters, so we'll then need to convert from meters to centimeters. Remember that 1 meter is defined to be equal to 100 centimeters.

12 cm / (7 · 100) = x / (21 · 100)

12 cm / 700 cm = x / 2,100 cm

Finally, let's solve for x.

12 / 700 = x / 2,100

3 / 175 = x / 2,100

6,300 = 175x

175x = 6,300

x = 36

Since x = 36 and it represents the length of the patio in the drawing, it then is equal to 36 centimeters.

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