7. Lin is making blueberry muffins. She has a total of 4 cups of
blueberries. Each batch of muffins uses 3/2 cups of blueberries. How
many batches of blueberry muffins can Lin make using ALL of the
blueberries?
A.) Draw a diagram to represent this situation.
B) How many batches can Lin make?
X
13

C) What fraction of a batch will Lin need to make in order to use all of
the blueberries?
30

The dilatiοn preserves the side lengths and angles οf triangle. The reflectiοn dοes nοt preserve side lengths and angles.

A geοmetrical adjustment that changes an οbject's size is dilatiοn. In mοre detail, dilatiοn entails extending οr cοntracting an item by increasing each pοint's distance frοm a fixed center pοint by a predetermined amοunt, knοwn as the scale factοr.

Let's start by applying the reflectiοn alοng the y-axis. All οf the vertices will have their x-cοοrdinates negated as a result, but their y-cοοrdinates will remain unchanged.

After reflectiοn, pοint A (-4, -2) will appear as A'. (4, -2). In the same way, B (-4, -2) will becοme B' (-4, -2), and C (4, -4) will change intο C'. (-4, 4).

Applying a dilatatiοn by a factοr οf 1/2 with the οrigin as the center will cοme next. This will result in a halving οf all distances frοm the οrigin.

After dilatiοn, pοint A' (4, -2)'s image will be A'' (2, -1), B' (-4, -2) will change tο B'' (-2, -1), and C' (-4, -4) will becοme C''. (-2, 2).

We must cοmpare the distances between the triangle's vertices and the angles' measurements in the οriginal triangle and the image tο see if the side lengths and angles are preserved.

The distance between pοints A and B is 8, but the distance between  A'' and B'' is 4, as we can see. Similarly, the separatiοn between B and C is 6, whereas between B'' and C'' is 3. The dilatiοn dοes nοt preserve the triangle's side lengths as a result.

Nevertheless, it is clear that the angles between the sides were kept because the transfοrmatiοn invοlved bοth a reflectiοn and a dilatatiοn, bοth οf which prοtect angles.

Therefοre the cοrrect οptiοn is D. The dilatiοn preserves the side lengths and angles οf the triangle, while the reflectiοn dοes nοt preserve side lengths and angles.

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The deer made 8 tracks, the fox made 4 tracks, and the dog made 12 tracks.

Let's start by defining variables for the number of tracks made by each animal.

Let:

d be the number of tracks made by the deer,

f be the number of tracks made by the fox, and

x be the number of tracks made by the dog

From the problem, we know that:

d + f + x = 24 ......(1)

We also know that:

d = x - 4   .......(2)

d = f + 4   ..........(3)

from this we can rightfully assume that the dog made half the tracks hence

x = 12 tracks

d = 12 - 4 = 8

solving for f

d = f + 4

f = d - 4 = 8 - 4 = 4

we can therefore say that the dog made 12 tracks, the deer made 8 tracks while the fox made 4 tracks

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Answer: 625.528.618,26

Step-by-step explanation: The answer will be in the pictures

Answer:

what you would do is 23.89x18%=4.3 so you do 23.89-4.3=19.59 then you do 19.59x7%=1.37 then you do 19.59+1.37=20.96 so 20.96 is your answer.

Step-by-step explanation:

Answer: To calculate the final price that Lin's father pays for the meal, we need to apply the discount first and then add the sales tax.

Discount = 18% of $23.89

= 0.18 x $23.89

= $4.30

The discounted price of the meal is therefore:

$23.89 - $4.30 = $19.59

Next, we need to add the sales tax of 7%:

Sales Tax = 7% of $19.59

= 0.07 x $19.59

= $1.37

Therefore, the final price that Lin's father pays for the meal is:

$19.59 + $1.37 = $20.96

So, Lin's father pays $20.96 for the meal after applying the discount and sales tax.

Step-by-step explanation:

Answer:

Class Midpoint

Step-by-step explanation:

36.5 is the the class midpoint for ages 35-38. To obtain the class midpoint, you find the averages of the upper and lower class limit for a specific class. In this case, (35+38)/2 = 36.5

Answer:

≈25,99

Step-by-step explanation:

Use trigonometry:

sin (38∘) = 16 / x

x = 16 / sin (38∘) ≈ 25,99

Answer:

[tex]16 {cm}^{3} [/tex]

Step-by-step explanation:

First, we can find the volume of tank A:

[tex]v(a) = 20 \times 24 \times 20 = 9600[/tex]

Now, let's write an equation for tank B's volume:

[tex]9600 = 600 \times h(b)[/tex]

[tex]h(b) = \frac{9600}{600} = 16[/tex]

To find the fraction of members between 150 and 160 cm tall, we need to look at the portion of the frequency polygon that corresponds to this height range.

First, we can calculate the total frequency of members between 150 and 160 cm by adding up the frequencies for the "150 < x ≤ 160" class and the "160 < x ≤ 170" class, which gives:

Total frequency = 5 + 0 = 5

Next, we can calculate the total frequency of all members by adding up all the frequencies, which gives:

Total frequency = 10 + 5 + 0 + 1 = 16

Therefore, the fraction of members between 150 and 160 cm tall is:

Fraction = Total frequency between 150 and 160 cm / Total frequency of all members

= 5 / 16

= 0.3125

So, approximately 31.25% of the members were between 150 and 160 cm tall.

The fraction of members between 150-160cm is found by dividing the frequency of the 150-160cm height segment by the total number of club members.

In order to find out the fraction of members who were between 150 and 160 cm tall, we first need to focus on the corresponding frequency value for the height segment - 150< x ≤160 in the table. This value gives us the count of people who stand within these heights. Simultaneously, we need the total number of club members, which can be derived by adding all the frequency values together.

Once we have these two values, the fraction of members is calculated by dividing the frequency of the 150-160 height segment by the total frequency (number of club members).

Please note that this fraction will be a 'raw' one, and you may need to simplify it to its smallest terms to make it more understandable.

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Using binomial probability and cumulative distribution function, the probability of having 24 heads is 0.000022

This problem can be solved using the binomial distribution. Let X be the number of heads that occur in 27 tosses of the fair coin. Then X follows a binomial distribution with parameters n = 27 and p = 0.5.

We want to find the probability that at most 24 heads occur, which is equivalent to finding the probability that X is less than or equal to 24. We can use the cumulative distribution function (CDF) of the binomial distribution to calculate this probability:

[tex]P(X \leq 24) = \sum_{k=0}^{24} {27 \choose k} (0.5)^{27}[/tex]

We can use a calculator or software to evaluate this sum, or we can use the complement rule to find the probability of the complement event (i.e., 25 or more heads) and subtract from 1:

[tex]P(X \leq 24) = 1 - P(X \geq 25) = 1 - \sum_{k=25}^{27} {27 \choose k} (0.5)^{27}[/tex]

Using a calculator or software, we find that the probability is approximately 0.000022, which corresponds to answer choice (a).

Therefore, the answer is (a) 0.000022.

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Answer:

Step-by-step explanation:

cos

cos^-1(26/52)=?

?=30

The appropriate trend lines for the scatter plot include the following: B. scatter plot B.

In Mathematics and Statistics, there are different characteristics that are used for determining the line of best fit on a scatter plot and these include the following:

By critically observing the scatter plot using the aforementioned characteristics, we can reasonably infer and logically deduce that scatter plot B represent the line of best fit (trend line) because it is in a linear pattern, with equal number of data points on both sides of the line.

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o find the local extrema of the polynomial, we first take the derivative of the polynomial and set it equal to zero:

f(x) = 10x^5 + 22x^4 + 20x^3 - 0x^2 + 6

f'(x) = 50x^4 + 88x^3 + 60x^2

Setting f'(x) = 0, we can factor out a 2x^2 from the expression to get:

f'(x) = 2x^2(25x^2 + 44x + 30) = 0

Using the quadratic formula to solve for x, we get:

x = (-44 ± sqrt(44^2 - 4(25)(30))) / (2(25))

x = (-44 ± sqrt(784)) / 50

x = (-44 ± 28) / 50

x = -0.32 or -0.56

Answer: 4 cans of tuna

Step-by-step explanation:

5 1/2 x 4 = 22

Answer:

To find which tuna is a better deal, divide the cost by the number of ounces of tuna you are getting to get the cost per ounce.

$0.90/5  = $0.18 per ounce

$2.40/12 = $0.20 per ounce

Since the 5-ounce can of tuna has a cheaper unit rate price, meaning you are getting a better value, makes this the best option. I hope this was helpful and have a great day! :)

Step-by-step explanation:

The cοndensed οr cοmbined fοrm is thus: 2x³y + 8x²y2 + 17xy³ = (2x²)xy + (8x)xy + (17xy²) = (2x2)xy + (8x)xy + (17xy²).

An expressiοn in mathematics is a set οf digits, symbοls, and οperatοrs that depicts a quantity οr a relatiοnship between twο quantities. Expressiοns can be straightfοrward, using a single number οr variable, οr cοmplicated, including a variety οf phrases and prοcedures. Expressiοns include things like "3 + 5" and "2x - 4", fοr instance.

The first phrase is straightfοrward and represents the additiοn οf twο numbers, whereas the secοnd expressiοn is mοre intricate and includes a variable, multiplicatiοn, and subtractiοn.

As the expressiοns yοu prοvided lack an equal sign and hence are nοt equatiοns, it is unclear what yοu mean when yοu say that yοu are "sοlving" the prοblem.

Hοwever if yοu wish tο cοmbine οr simplify these expressiοns, yοu can utilize the factοring apprοach.

We can factοr it οut because xy is a cοmmοn factοr thrοughοut the expressiοns:

8x²y² = (8x)xy, while 17xy³ = (17)xy²

We can nοw see that each expressiοn's remaining factοrs are (2x²), (8x), and (17), respectively.

Since these factοrs dο nοt share any cοmmοn factοrs, further simplificatiοn is nοt pοssible. In terms οf the cοmmοn factοr xy.

The cοndensed οr cοmbined fοrm is thus: 2x³y + 8x²y² + 17xy³ = (2x²)xy + (8x)xy + (17xy2) = (2x²)xy + (8x)xy + (17xy2).

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Complete Question

Write this expression  2x³y, 8x²y², 17xy³  in combined form

Using calculus, we can find the functions of the inverse functions as follows:

a. f(x) = x/5.

b. f(x) = ∛ 2x

c. f(x) = x - 10

d. f(x) = 2x/3 - 17

One of the most crucial areas of mathematics that addresses ongoing change is known as calculus. Calculus is primarily built on the two ideas of derivatives and integrals. A function's integral measures the area under its curve, whereas a function's derivative measures its rate of change.

Whereas the integral adds together a function's discrete values over a range of values, the derivative explains the function at a particular point.

Here in the question,

The inverse of the functions is:

f(x) = x/5.

f(x) = ∛ 2x

f(x) = x - 10

f(x) = 2x/3 - 17

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Answer:

I don't know what I am so sorry of computer science ranking it was my father is the first t e and video editing software for product of a number of times I am using simple terms of.

Step-by-step explanation:

NBG the main function performance multiplication ❌❌✖️of computer is used in planes and engineer salary is Atlantic chatter in short note of computer is the first man made calculating pH balance of computer is referred to earn foreign currency of computer is the first.bcdujvfyhcdybcMake it shortAn expression equivalent to 5(Z+2)5(Z+2)Make it shortAn expression equivalent to 5(Z+2)5(Z+2)Make it shortAn expression equivalent to 5(Z+2)5(Z+2)Make it short5(Z+2)Make it shortAn expression equivalent to 5(Z+2)An expression equivalent to 5(Z+2)5(Z+2)An expression equivalent to 5(Z+2)An expression equivalent to 5(Z+2)An expression equivalent to 5(Z+2)An expression equivalent to 5(Z+2)An expression equivalent to 5(Z+2)An expression equivalent to 5(Z+2)An expression equivalent to 5(Z+2)An expression equivalent to 5(Z+2)An expression equivalent to 5(Z+2)Make it short5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)5(Z+2)An expression equivalent to 5(Z+2)An expression equivalent to 5(Z+2)5(Z+2)An expression equivalent to 5(Z+2)5(Z+2)5(Z+2)An expression equivalent to 5(Z+2)An expression equivalent to 5(Z+2)cfgjmbvdzbcs of computer your favourite game of thrones on water into direct express debit card ♦️ of the products produced by

the arithmetic mean of the five consecutive integers starting with "b" is (a+4), which is option (c).

Let's call the five consecutive integers starting with "a" as a, a+1, a+2, a+3, and a+4.

The arithmetic mean of these five integers can be calculated as (a + (a+1) + (a+2) + (a+3) + (a+4))/5 = b. Simplifying this expression, we get:

5a + 10 = 5b +

a + 2 = b

So, the arithmetic mean of the five consecutive integers starting with "b" would be:

(b + (b+1) + (b+2) + (b+3) + (b+4))/5

= (5b + 10)/5 (since the integers are consecutive, we can express them in terms of b)

= b + 2

Substituting b = a + 2 (from the above equation), we get:

b + 2 = a + 4

Therefore, the arithmetic mean of the five consecutive integers starting with "b" is (a+4), which is option (c).

In other words, if the arithmetic mean of five consecutive integers starting with "a" is "b", then the arithmetic mean of five consecutive integers starting with "b" is two more than the last integer of the five consecutive integers starting with "a".

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The probability of a person having this skill is estimated to be 87/1000 or 0.087.

Probability is a branch of mathematics that deals with determining the likelihood of an event occurring. The probability of an event occurring is equal to the number of favorable events divided by the total number of events. Probability has a value between 0 and 1, with 0 denoting uncertainty and 1 denoting certainty.

Based on the given conditions, we will formulate for 8,700/100,000 to get the probability of a person having this skill to wiggle their ears and their nose at the same time.

Let is cross out the common factor. Now we will have [tex]87/1000[/tex]. Therefore, the probability of a person having this skill is estimated to be [tex]87/1000[/tex] or [tex]0.087[/tex].

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Step-by-step explanation:

The statement does not make sense. A triangle cannot have two right angles as the sum of the three angles in a triangle is always 180 degrees. Two right angles would add up to 180 degrees, leaving no room for the third angle.

To determine the number of plants needed, first find the perimeter of the square flower bed by multiplying the length of one side by 4 (since there are four sides in a square). 8 x 4 = 32 feet. Then convert the spacing of 8 inches to feet by dividing by 12 (since there are 12 inches in a foot). 8 / 12 = 0.67 feet. Finally, divide the perimeter of the flower bed by the spacing of the plants to get the total number of plants needed. 32 / 0.67 = 47.76. Round up to the nearest whole number to get the final answer of 48 plants.

A square is a type of rectangle because it has four right angles and opposite sides that are parallel and congruent. A square is a type of rhombus because it has four sides of equal length. A square is a type of parallelogram because it has two pairs of opposite parallel sides. A square is a type of quadrilateral because it has four sides. A square is a type of polygon because it is a closed shape with three or more sides.

Answer:a=9  b=27.5  c=41.25

Step-by-step explanation:

the internet

We can conclude after answering the presented question that x = $2.00 equation  (price of a queso pizza rebanada) y = $1.25 (price of a pie and championes pizza rebanada)

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or readings of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the calculation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

The two variables are the price of a rebanada de pizza de queso and the price of a rebanada de pizza de pia y championes.

It is x the price of a rebanada de pizza de queso and y the price of a rebanada de pizza de pia y championes.

We have the following equation system:

3x + 4y + 12.50 = 12.50 (costo de las 7 rebanadas de pizza) (costo de las 7 rebanadas de pizza)

3x + 2y = 8.50 (costo de las 5 rebanadas de pizza que no incluyen el tool) (costo de las 5 rebanadas de pizza que no incluyen el tool)

When we solve the equation system, we get:

x = $2.00 (price of a queso pizza rebanada) y = $1.25 (price of a pie and championes pizza rebanada)

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The actual price of the television set is 9225.6 and the amount of VAT is 1061.35

Discount is a percentage deducted from the the actual selling price of a product. The discount given is 15% of the selling price 9605.

Therefore, discount = 15/100 × 9605

= 1440.75

Therefore the price of the television= 9605 - 1440.75

= 8164.25

After the discount the, VAT of 13 % is added

= 8164.25 × 13/100

= 1061.35

The new price of the television set = 8164.25 + 1061.35

= 9225.6

therefore the actual price of the television set is 9225.6 and the VAT is 1061.35

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Answer:

First, we know the slopes of perpendicular lines are negative reciprocals of each other.  So, the negative reciprocal of -1 is 1.  This is the slope of our new line.  From here, we can use this new slope along with our given point to find the y-intercept (b) of our new equation:

y = mx + b

-4 = 1(-2) + b

-4 = -2 + b

-2 = b

The y-intercept of our new line is (0,-2).  Now, we can write our equation of the new line:

y = x - 2

a) B', complement of B =  {a, b, d, f, h}

b) AN B', A intersection B' =  {b, h}

c) (A/B), or A - B = {a, b, h}

d) BU (CNA)​, B union (C intersection A) = {a, b, c, d, e, g, h}

a) The complement of B, denoted B', consists of all elements in U that are not in B. Thus, we have:

B' = {a, b, d, f, h}

b) A intersection B' consists of all elements that are in A but not in B. From the given sets, we have:

B' = {a, b, d, f, h}

A = {a, b, c, e, h}

Thus, A intersection B' = {b, h}

c) A/B, also denoted A - B, consists of all elements in A that are not in B. From the given sets, we have:

A = {a, b, c, e, h}

B = {c, e, g}

Thus, A/B = {a, b, h}

d) CNA is the union of C and A. From the given sets, we have:

A = {a, b, c, e, h}

C = {a, c, d, g, e}

Thus, A union C = {a, b, c, d, e, g, h}.

Finally, BU(A union C) is the union of B with A union C. From the given sets, we have:

B = {c, e, g}

A union C = {a, b, c, d, e, g, h}

Thus, BU(A union C) = {a, b, c, d, e, g, h}

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Answer: y= -8x +2

Step-by-step explanation:

y = mx + b

M is the slope

B is the y intercept

The coordinates after each rotation are given as follows:

The function rule for the five more known rotation rules are given as follows:

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We need to add 6 mL of the 14% solution to the 8 mL of the 7% solution to obtain a 10% medication solution.

An equation is a mathematical statement that indicates that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equal sign can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to describe relationships between different variables, to solve problems, and to make predictions.

Let's call the number of milliliters of the 14% solution we need to add "x".

First, let's figure out how much medication is in the 8 mL of the 7% solution. Since the solution is 7%, we know that 7% of the solution is medication. We can convert that to milliliters by multiplying by the total volume of the solution:

0.07 x 8 mL = 0.56 mL of medication in the 7% solution

Next, let's figure out how much medication we want in the final solution. We want a 10% solution, so we want 10% of the total volume to be medication. We can write that as:

0.10 (x + 8 mL) = 0.1x + 0.8 mL

Now we can set up an equation based on the amount of medication in the 14% solution we add and the amount of medication in the final solution:

0.14x + 0.56 mL = 0.1x + 0.8 mL

Simplifying the equation, we get:

0.04x = 0.24 mL

Dividing both sides by 0.04, we get:

x = 6 mL

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Answer:

To find the area of the figure, we need to find the area of the rectangle and the area of the parallelogram, and then add them together.

First, we need to identify which sides of the figure belong to the rectangle and which sides belong to the parallelogram. Looking at the coordinates of the vertices, we can see that the vertices (-10,2), (-7,3), (-1,3), and (1,-3) form a parallelogram, while the vertices (-7,3), (-2,-4), and (-4,2) form a rectangle.

To find the area of the parallelogram, we can use the formula:

Area = base × height

where the base is the length of one of the sides of the parallelogram, and the height is the perpendicular distance between the base and the opposite side. We can choose any side of the parallelogram as the base, but it is usually easiest to choose the side that is perpendicular to the x-axis, since its length is simply the difference between the x-coordinates of the two endpoints.

Using the coordinates (-10,2) and (-7,3) as the endpoints of the base, we find that the length of the base is:

|-7 - (-10)| = 3

To find the height, we need to find the perpendicular distance between the base and the opposite side of the parallelogram. We can do this by drawing a vertical line from one endpoint of the base to the opposite side, and then measuring the length of this line. We can see that the line from (-10,2) to (-1,3) is perpendicular to the base, so its length is the height of the parallelogram:

|-1 - (-10)| = 9

Therefore, the area of the parallelogram is:

Area = base × height = 3 × 9 = 27

To find the area of the rectangle, we simply need to multiply the length and width of the rectangle. We can see that the length is the distance between (-7,3) and (-4,2):

|-4 - (-7)| = 3

and the width is the distance between (-7,3) and (-2,-4):

|(-2) - (-7)| = 5

Therefore, the area of the rectangle is:

Area = length × width = 3 × 5 = 15

Finally, we can find the area of the whole figure by adding the area of the rectangle and the area of the parallelogram:

Area of figure = Area of rectangle + Area of parallelogram

= 15 + 27

= 42

Therefore, the area of the figure is 42 square units.

After answering the prοvided questiοn, we can state that Befοre making equatiοn a decisiοn, it is alsο impοrtant tο cοnsider οther factοrs such as the lοcatiοn, facilities, and services prοvided by each health club.

In mathematics, an equatiοn is a prοclamatiοn stating the justice οr twο phrases. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The gοal οf equatiοn sοlving is tο determine the value οr values οf the variable in the mοdel) that will allοw the equatiοn tο be true. Equatiοns can be simple οr cοmplex, regular οr nοnlinear, and include οne οr mοre factοrs. In the equatiοn fοr "x² + 2x - 3 = 0," example, the variable x is raised tο the secοnd pοwer. Lines are used in many mathematical areas, including algebra, mathematics, οr geοmetry.

We can create a table tο calculate the tοtal cοsts οver different time periοds tο cοmpare the cοsts οf jοining Let's Get Mοving versus Fitness fοr Life:

Membership Length Let's Get Mοving Fitness fοr Life

1 mοnth                                    $245             $50

6 mοnths                                 $455              $300

1 year                                       $630              $600

2 years                                    $1,290            $1,200

Accοrding tο this table, if Justin plans tο jοin fοr a shοrt periοd οf time, such as a mοnth οr six mοnths, Fitness fοr Life is a better οptiοn because it has a lοwer tοtal cοst. If Justin intends tο jοin fοr a lοnger periοd οf time, such as a year οr twο years, Let's Get Mοving may be a better οptiοn because the οne-time initiatiοn fee is spread οut οver time.

Befοre making a decisiοn, it is alsο impοrtant tο cοnsider οther factοrs such as the lοcatiοn, facilities, and services prοvided by each health club.

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The standard error of the mean is 0.3125 mpg.

The sample mean will fall within the interval (19.9859, 20.0141)

A decimal is a number system that uses the base ten, which means it uses ten digits (0,1,2,3,4,5,6,7,8,9) to represent all numbers. Each digit in a decimal number represents a power of ten. For example, in the number 123.45, the digit "1" represents 1 x 10², the digit "2" represents 2 x 10¹, the digit "3" represents 3 x 10⁰, the digit "4" represents 4 x 10⁻¹, and the digit "5" represents 5 x 10⁻².

(a) The standard error of the mean (SE) can be calculated using the formula:

SE = s / √(n)

where s is the sample standard deviation, n is the sample size, and √ represents the square root. In this case, n = 16 and s = a = 1.25 mpg. Substituting these values, we get:

SE = 1.25 / √(16)

  = 0.3125

Rounding to 4 decimal places, the standard error of the mean is 0.3125 mpg.

(b) To find the interval within which we would expect the sample mean to fall with 90% probability, we need to use a confidence interval. Since the sample size is large enough (n >= 30) and the population standard deviation is known, we can use the z-distribution to construct a confidence interval. The z-value for a 90% confidence level is 1.645 (found using a standard normal distribution table or calculator).

The 90% confidence interval for the sample mean can be calculated using the formula:

CI = Xbar ± z*(SE)

where Xbar is the sample mean, z is the z-value for the desired confidence level, and SE is the standard error of the mean.

Substituting the given values, we get:

CI = 20.5 ± 1.645*(0.3125)

  = 20.5 ± 0.5141

Rounding to 4 decimal places, the 90% confidence interval for the sample mean is:

CI = (19.9859, 20.0141)

Therefore, we would expect the sample mean to fall within the interval (19.9859, 20.0141)

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