(True or False) with the correct sampling method, you expect to obtain a sample mean exactly the same as the population mean.

The distance the car was driven for if the total cost of the rental was $151.55 is 259 miles

From the question, we are to determine how far the car was driven in one day

From the given information,

The formula that represent the cost of renting the car for one day is

C= 0.45m + 35

We are to determine how far the car was driven if the total cost of the car rental was $151.55

That is,

We are to determine m when C is $151.55

Substitute C = 151.55 in the formula

151.55 = 0.45m + 35

Calculate the value of m

151.55 = 0.45m + 35

151.55 - 35 = 0.45m

116.55 = 0.45m

Therefore,

0.45m = 116.55

m = 116.55/0.45

m = 259

Hence, the car was driven for 259 miles

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Answer:

write your question in a proper way

[tex](3x^2 y^5)^3\implies \left( 3^3 x^{2\cdot 3} y^{5\cdot 3} \right)\implies 27x^6 y^{15}[/tex]

a) The relationship of the graph is drawn by using the above table is attached below:

b) Since, the time is increasing the pay of increasing is more. By this we have known the graph.

An illustration of a relation is a function graph. In set theory and modern mathematical foundations, a function is truly equal to its graph. Though it is frequently helpful to think about functions as mappings, which also include which set is the domain and which set is the codomain, it is also important to note that mappings do not just refer to the relationship between input and output. A codomain should be considered, for instance, while determining if a function is onto (surjective) or not. The codomain is not determined by the graph of a function alone.

Given, equation of pay is:

p=8.25t

Here p represents the pay and t represents the time he works.

The table is:

20          10       0       30         4           5             6

165       82.5     0      247.5    330   412.5         495

a) The relationship of the graph is drawn by using the above table:

b) Since, the time is increasing the pay of increasing is more. By this we have known the graph.

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Events A and B dependent as the occurrence of one event affect the chances of the occurrence of the other event.

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

To understand this branch, it is extremely important to know its most basic definitions, such as the formula for calculating probabilities in equiprobable sample spaces, probability of the union of two events, probability of the complementary event, etc.

Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).

Since we have given that

A be the event that Callista drives faster than the speed limit.

P(A)=0.34

B be the event that she gets to a wedding on time.

P(B)=0.45

The probability that she gets to the wedding on time given that she drives faster than the speed limit is 0.85 i.e.

P(A|B)=0.85

but for A and B to be independent ,

P(A).P(B)= P(A and B)

0.34×0.45=0.153

but,

[tex]P(A|B) = \frac{P(AnB)}{P(B)}[/tex]

P(AnB) = 0.85 x 0.45

P(AnB) = 0.3825

So, P(A∩B) does not satisfy the condition.

Hence, A and B are not independent events.

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The similarities between matrix factorization and content-based filtering and/or collaborative filtering are given below.

What is matrix factorization and collaborative filtering?

A group of cooperative filtering algorithms used in recommender systems is called matrix factorization. The user-item interaction matrix is broken down into the product of two rectangular matrices with lower dimensions by matrix factorization algorithms.

Collaborative filtering makes recommendations by simultaneously comparing similarities between users and items, addressing some of the drawbacks of content-based filtering.

collaborative filtering: user-based for example, CF calculates users' similarities in the item space. Then taking similar users's interest to do a recommendation for the target user. CF is one case of neighborhood methods.

matrix factorization amounts to mapping features of user and item via linear combination to latent factor space respectively.

Then calculating the similarity via inner-product of latent user factor and latent item factor.

CF covers local information of target user for the sake of neighborhood methods, while MF covers global information.

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The central angle of the arc in degree is 48° when a circle has a circumference of 12 units and it has an arc of length 8/5 units.

Given that,

A circle has a circumference of 12 units and it has an arc of length 8/5 units.

We have to find what is the central angle of the arc in degree.

We know that,

Circumference =12 units

Arc length =8/5= 1.6 units

If the central angle is "θ" then the length of the arc is given by

Arc length= θ/360°×circumference

Substituting values,

1.6=θ/360°×12

θ=48°

Therefore, The central angle of the arc in degree is 48° when a circle has a circumference of 12 units and it has an arc of length 8/5 units.

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A LCM is smallest number among all common multiples of the given numbers. LCM of 24 is 2³ × 3

The least common multiple is also known as LCM (or) the lowest common multiple in math. The least common multiple of two or more numbers is the smallest number among all common multiples of the given numbers

There are 3 methods to find the least common multiple of two numbers.

According to the question,

(a) LCM of 24 : 2³ × 3

(b) LCM of 2 , 6 , 12  : 2 × 2 × 3

(c) To find the LCM of two number use the prime factorization of each number and then the product of the highest powers of the common prime factors will be the LCM of those numbers.

(d) Least common factor of 12 : 2 × 2 × 3

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Answer:

Step-by-step explanation:

Solving for X in Other Triangles In any triangle, the sum of the squares of the two shorter sides is equal to the square of the length of the longest side. This is known as the Pythagorean theorem.

The range of time it could take a Monarch to reach Mexico based on the variation in travel speeds is 25 - 100 days

From the given information, Monarch butterflies travel between 25-100 miles per day during their 2,500-mile journey to Mexico in winter.

Based on the information, the shortest number of days taken will be:

= 2500 / 100

= 25 days

The longest number of days used will be:

= 2500 / 25

= 100 days.

The time range will be 25 - 100 days

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The real zeros of the quadratic function  f(x) = 2x² - 5x + 1 is between

The given quadratic function is  f(x) = 2x² - 5x + 1

Using a calculator the zeros of the function  f(x) = 2x² - 5x + 1 is solved to be

x = 2.28 OR 0.22

The value 0.22 falls between 0 and 1 = 0 < x < 1

this means greater than 0 and less than 1

The value 2.28 falls between 2 and 3 = 2 < x < 3

this means greater than 2 and less than 3

Therefore the second option is the right choice

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Answer:

  see attached

Step-by-step explanation:

You want the attached table of group size and number of groups filled in.

As you know from your early experience with multiplication and division relations, either factor of a product can be found by dividing the product by the other factor:

  P = a·b   ⇒   a = P/b, or b = P/a

Here, the total is equal to the product of the number of groups and the number in each group. That means the missing number on each line can be found by dividing the total by the known number on the line.

When the numbers are already in a spreadsheet, you can let the spreadsheet do the arithmetic.

The Formula for chain rule is dy/dx = dy/du x du/dx

The chain rule is a formula used in differential calculus to get the derivative of a composite function. According to the chain rule, if y = f(g(x)), then the instantaneous rate of change of function f with respect to g and g with respect to x leads in an immediate rate of change of f in relation to x. As a result, y' = f'(g(x)) will be supplied as the derivative of y. g'(x). One of the crucial rules in differentiation is the chain rule.

The chain rule formula is as follows for the function y = f(x), where f(x) is a composite function such that x = g(t):

Formula for chain rule

This is how the chain rule of differentiation formula is typically expressed.

dy/dx = dy/du x du/dx

Another chain rule formula looks like this:

y’ = d/dx ( f(g(x) ) = f’ (g(x)) · g’ (x).

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The propositional logic is a statement logic which is a statement that can be either true or false.

The relevant propositions in this case are

W: The roads are wet

a: There was an accident

h: Traffic was heavy

w → h when converted into an english sentence is 'If the roads were wet then traffic was heavy.'

W ∧ a when converted into an english sentence is 'The roads are wet and there was an accident.'

~(a ∧ h) when converted into an english sentence is 'It is not true that there was an accident and traffic was heavy.'

h → (a ∨ W) when converted into an english sentence is 'If the traffic was heavy then there was an accident and the roads are wet.'

W ∧ ~h when converted into an english sentence is 'The roads are wet and the traffic was not heavy.'

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The volume of the tube is increasing at the rate of 0.6 cubic millimeters per second.

The formula V = r2h, where r is the radius and h is the height, describes the volume of a cylinder.

The tube's volume is V = (2 mm)2 (20 mm), which equals 125.66 mm3.

Dr/dt = -0.1 mm/s and dh/dt = 3 mm/s are the formulas used to calculate the rate of change of the radius and height, respectively.

Using the chain rule, the rate of change of the volume is given by

dV/dt = π·2·[(2 mm)·(-0.1 mm/s) + (20 mm)·(3 mm/s)] = 0.6 mm3/s.

Therefore, the volume of the tube is increasing at the rate of 0.6 cubic millimeters per second.

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Answer:

After tax = Bill * (1 + rate)

25.30 = x * (1 + 0.08)

25.30 = x * 1.08

25.30 = 1.08x                 (divide 1.08 both side)

x = 23.43

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Step-by-step explanation:

Ellie's pre-pregnancy BMI is 38. Thus, her weight-gain goal should be 11-20 pounds for the entire pregnancy.

Having a BMI of 30 or higher during pregnancy can increase the risk of complications for you and your baby. Working with your health care provider can help you manage your risks and promote a healthy pregnancy.

If before pregnancy, you were…                      You should gain…

Underweight BMI less than 18.5                      50-62 pounds*

Normal Weight BMI 18.5-24.9                      37-54 pounds

Overweight BMI 25.0-29.9                              31-50 pounds

Obese BMI greater than or equal to 30.0      25-42 pounds

Body Mass Index (BMI) is calculated by dividing a person's height in feet by their weight in kilos or pounds (meters). The BMI of healthy pregnant women should be between 18.5-24.9.

Preconception, the time before and between pregnancies, is another name for the pre-pregnancy phase.

Therefore,

Ellie's pre-pregnancy BMI is 38. Thus, her weight-gain goal should be 11-20 pounds for the entire pregnancy.

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The Spearman correlation coefficient is used to calculate a significance test, whereas the Pearson correlation coefficient is not.

The Spearman correlation coefficient is a non-parametric measure of correlation that uses ranks rather than raw data to assess the strength of the relationship between two variables. This makes it more robust than the Pearson correlation coefficient, which relies on the assumption that the two variables have a normal distribution. Additionally, Spearman correlation coefficients are used to measure the degree of monotonicity between two variables, while Pearson correlation coefficients are not. Finally, the Spearman correlation coefficient is used to calculate a significance test, whereas the Pearson correlation coefficient is not.

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The volume of the gas at 6.4 × 10⁴ Pascals is 7.44×10⁻⁷m³.  The pressure of the gas is  5.47× 10⁶ Pascals

At a constant temperature, the volume of a gas is inversely proportional to its pressure. We can write:

V α 1/P

V = T/P   (where T is the constant of proportionality)

T = PV

SInce T₁ = T₂

Also, P₁V₁ = P₂V₂

We have pressure of 2.8 x 10⁶ Pascals and a volume of 1.7 x 10⁻⁸ m³

a) What will the volume of the gas be when its pressure is 6.4 × 10⁴ Pascals?

P₁V₁ = P₂V₂

2.8 × 10⁶ × 1.7×10⁻⁸ = 6.4 × 10⁴ × V₂

V₂ = (2.8 × 10⁶ × 1.7×10⁻⁸)/ (6.4 × 10⁴)

V₂ = 7.44×10⁻⁷m³

b) Work out the pressure of the gas when its volume is 8.7 x 10⁻⁹ m³

P₁V₁ = P₂V₂

2.8 × 10⁶ × 1.7×10⁻⁸  = 8.7 ×10⁻⁹ × P₂

P₂ = (2.8 × 10⁶ × 1.7×10⁻⁸)/ (8.7 ×10⁻⁹)

P₂ =  5.47× 10⁶ Pascals

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Amy’s monthly budget for textbooks in course supplies is $900.00

Amy's monthly budget for rent, utilities and food is $12,798.

Her monthly budget for a personal and miscellaneous cost is $2,259.

Her total monthly budget equals $15,957.

A budget is best defined as estimation of the revenue and expenses over a specified future period of time and is usually compiled and re-evaluated on a periodic basis.

Budget for textbooks:

= $900.00

Budget for rent, utilities and food:

= $12,798.

Budget for personal and miscellaneous cost:

= $2,259.

Total monthly budget:

= $900 + $12,798 + $2,259

= $15,957.

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The height of a student with an arm span of 143 cm is most accurately predicted to be 143 cm.

The lacking graph is included.

The student heights and arm spans in a classroom are depicted in the graph below.

For most people, their arm span is about equal to their height. Mathematicians say the arm span to height ratio is one to one: your arm span goes once into your height.

The x-axis represents the height in cm

The y-axis represents the arm span in cm

We must determine the height of a pupil whose arms are 143 cm long. The value of the specified arm span is not shown on the graph.

To get the best prediction of the height, we will select the line that best fits the data (the sold line in the graph shown).

Points (150, 150) and (160, 160) are on the line. The x-coordinates and y-coordinate are equivalent.

y = x is the line's equation.

A student's arm span is 143 cm,

Which is represented by the letter y. Replace the value of y in the equation for the line that best fits the data:

y = 143 = x,

Where x is a student's height.

The student stands 143 cm tall.

Therefore,

The height of a student with an arm span of 143 cm is most accurately predicted to be 143 cm.

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The required sample sizes are given as follows:

a) n = 752.

b) n = 722.

c) The added knowledge in item b has an effect, as it decreases the sample size required. The decrease is not huge because the estimate is close to 0.5, but the farther the estimate gets from 0.5, the more the sample size decreases.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The margin of error is calculated as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The variables used to calculated these bounds are listed as follows:

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

The margin of error in this problem is given as follows:

M = 0.03.

For item a, there is no previous estimate, hence we consider [tex]\pi = 0.5[/tex] and the sample size is obtained as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.645\sqrt{0.5(0.5)}[/tex]

[tex]\sqrt{n} = \frac{1.645\sqrt{0.5(0.5)}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]

n = 752. (rounding up).

For item b, the estimate is [tex]\pi = 0.6[/tex], hence the sample size is obtained as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.645\sqrt{\frac{0.6(0.4)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.645\sqrt{0.6(0.4)}[/tex]

[tex]\sqrt{n} = \frac{1.645\sqrt{0.6(0.4)}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.6(0.4)}}{0.03}\right)^2[/tex]

n = 722. (rounding up).

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The total amount Emily spent each month for 20 days will be $142.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this situation, Emily spends $4.85 on a latte and $2.25 on a scone. The total amount spent for 20 days will be:

= (4.85 + 2.25) × 20

= 7.1 × 20.

= 142

The amount is $142.

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Mr. Powel, who is our geometry teacher, told us we have a geometry test next week.

A nonrestrictive element is an element of a sentence that is not necessary for understanding the basic meaning of the sentence, but instead provides additional information. Nonrestrictive elements are usually set off with commas, while restrictive elements are not. For example, “My brother, who is an engineer, works in Chicago” is a sentence with a nonrestrictive element. The nonrestrictive element (“who is an engineer”) provides additional information about the brother, but does not provide any information about which brother is being referred to. The restrictive element “My brother who works in Chicago” does provide information about which brother is being referred to.

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The statement that is true about Denzel's experiment is that D. The outcomes do not appear to be equally likely, so a uniform probability model is not a good model to represent probabilities in Denzel's experiment.

Uniform models are only useful for equally likely probabilities, so they are ineffective here. In statistics, a uniform distribution is a type of probability distribution in which every possible outcome has an equal chance of occurring. Because each variable has an equal chance of being the outcome, the probability is constant.

All events have an equal chance of occurring in a uniform probability mode. Rolling any one side of a six-sided fair die, for example, has the same probability: one out of six. In this situation, when Denzel randomly selects a single card, writes down the number, and then places it back in the bag, the probability are different.

Therefore, the correct option is D.

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The number of toy cars that can be kept in: 9 boxes and 8 boxes is 153 and 136 respectively .

Given :

288 toy cars can be kept in either 16 boxes or 18 boxes .

if 288 toy cars kept in 16 boxes .

number of toy cars in one box = 288 / 16

= 18 toy cars

if 288 toy cars kept in 18 boxes

number of toy cars in one box = 288 / 18

= 16 toys cars

Average = 18 + 16 / 2 = 34/2 = 17 toy cars .

Number if toy cars in 9 boxes = 9 * 17

= 153 toy cars

Number of toy cars in 8 boxes = 8 * 17

= 136 toy cars

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The market price in this economy equals to $9.

Basically, a market price is the amount of money for what an asset can be sold in a market. In other word, it is the cost of the products determined with respect to the point where the demand meets supply.

The value of marginal product of labor (VMPL) is equal to the marginal product of labor (MPL) multiplied by the market price (P).

In this case, to find market price, we will divide the the value of the marginal product of labor by the marginal product of labor:

= 90/10

= $9

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Midpoint formula is used to find the centre point of a straight line.

Given :

Let ( x1 , y1 ) and ( x2 , y2) are two points on the straight line.

Midpoint :

The center point of the straight lines with two points is called as midpoint.

Midpoint formula :

( x , y ) = ( x1 + x2 / 2 , y1 + y2 / 2 )

Example :

( x1 , x2 ) = ( 1 , 5 ) and ( y1 , y2 ) = ( 2 , 4 )

( x , y ) = ( 1 + 2 / 2 , 5 + 4 /2 )

= ( 3/2 , 9/2).

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