A research firm supplies manufacturers with estimates of the sales of their products from samples of stores. Marketing managers often look at the sales estimates and ignore sampling error. An SRS of 50 stores this month shows mean sales of 41 units of a particular appliance with a standard deviation of 11 units. During the same month last year, an SRS of 52 stores gave mean sales of 38 units of the same appliances with a standard deviation of 13 units. An increase from 38 to 41 is a rise of 7.9 % . The marketing manager is happy because sales are up 7.9 % . (a) Give a 95 % confidence interval for the difference in mean number of units of the appliance sold at all retail stores. (Enter your answer rounded to three decimal places.)

Answer: 8 senior tickets, 12 normal tickets.

Step-by-step explanation:

You can find the answer to this by creating two equations: one for the amount of tickets sold and the other for how much money was collected.

I will represent the variables as A for normal tickets and C for senior tickets.

[tex]A + C = 20\\12A + 6C = 192[/tex]

To solve this, you can solve for one of the variables. I will solve for A in the first equation:

[tex]A = 20-C\\12A + 6C = 192[/tex]

Then, you can substitute the new value of A in the second equation:

[tex]12(20-C) + 6C = 192\\240-12C+6C=192\\240-6C=192\\-6C=-48\\C=8[/tex]

Knowing that there were 8 senior tickets sold and 20 tickets sold total, we know that there were 12 normal tickets sold.

Rectangle square rhombus

Step-by-step explanation:

To calculate the surface area, the formula is the sum of the areas of all faces in a shape.

Back Prism:

1 base: 8 by 8.

4 lateral faces: 8 by 2.

One shared base: 64 – 32 = 32 square units.

Front Prism:

1 base: 8 by 4.

2 lateral faces: 8 by 2.

2 lateral faces: 2 by 4.

Therefore, one shared base: an area covered by another prism.

Total surface area: 240 square units.

A surface area is the outer part of the uppermost layer of something. This is known in maths as the amount of space covering the outside of a three-dimensional shape.

Hence, we can see that to calculate, the formula is the sum of the areas of all faces in a shape which sums up to 240 square units.

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Answer:

See explaination

Step-by-step explanation:

Please kindly check attachment for the detailed step by step solution of the given problem.

To find the closest point to y in subspace W, see the projection of y onto W. Solve the appropriate equations to find the scalars for v1 and v2. The sum of these scaled vectors will yield the closest point.

The closest point to y in the subspace W spanned by v1 and v2 can be determined using the projection formulas. First, find a and b such that a*v1 + b*v2 equals the projection of y onto W. To do this, set up the equations a*(v1 . v1) + b*(v1 . v2) = y . v1 and a*(v1 . v2) + b*(v2 . v2) = y . v2. Solve these equations for a and b. The solution will give you the scalars for v1 and v2, respectively. The vector a*v1 + b*v2 will be the closest point in W to y.

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Answer:

a) 256 m^2

Step-by-step explanation:

Area of a Trapezoid = (a+b)/2×h

*where a and b are the "top" and "bottom" lengths and h is the height

So: (13+19)/2×16= 32/2×16= 16×16 = 256 m^2

Answer:

y = (-5/3)x + 3

Step-by-step explanation:

slope intercept form: y = mx + b

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other.

First, add 9 to both sides:

3y - 9 (+9) = -5x (+9)

3y = -5x + 9

Next, divide 3 from both sides:

(3y)/3 = (-5x + 9)/3

y = (-5/3)x + 3

y = (-5/3)x + 3 is your answer.

~

Answer:

a) 1,518,000

b) 2,284,880

c) 60,720

Step-by-step explanation:

a) a. if the first letter must be Upper C comma Upper X comma Upper T comma or Upper M and no letter may be​ repeated?

We draw 5 boxes, and based on that we will see the total possible cases. There are 26 alphabets

The first box should have C or X or T or M .No letter may be repeated.

Any                    Any             Any                 Any                    Any

5 alphabets    of the            of the              of the                 of the

C,X , T , M      remaining     remaining       remaining          remaining

                   25 alphabets   24 alphabets   23 alphabets   22 alphabets

Therefore; total possible call letters = 5 × 25 × 24 × 23 × 22 = 1,518,000

b)

The first box should have C or X or T or M Repeats as allowed

Any                    Any             Any                 Any                    Any

5 alphabets    of the            of the              of the                 of the

C,X , T , M      remaining     remaining       remaining          remaining

                   26 alphabets   26 alphabets   26 alphabets   26 alphabets

Therefore Total possible call letters = 5 × 26 × 26 × 26 × 26 = 2,284,880

c)   The first box should have   C,X , T , M  and end with S

So the last place if fixed, and we now have 25 alphabets. The first box can go in 5 ways. The next box then will have only 24 letters to choose from, as the first box has taken a letter and the last box already has S in it. Repetition not allowed

Any                    Any             Any                 Any                       S

5 alphabets    of the            of the              of the                  is fixed

C,X , T , M      remaining     remaining       remaining           here

                   24 alphabets   23 alphabets   22 alphabets  

Therefore Total possible call letters = 5 × 24 × 23 × 22  × 1 =  60,720

a. 30,240 different call letters can be made if the first letter must be C, X, T, or M and no letter may be repeated. b. 11,881,376 different call letters can be made if repeats are allowed. c. 22,464 different call letters can be made if the call letters start with C, X, T, or M, have no repeats, and end with S.

a. If the first letter must be C, X, T, or M, and no letter may be repeated, the options for the first letter are 4. For the remaining 4 positions, we can choose from 25 letters (all except the first letter chosen). Therefore, the total number of different 5-letter radio station call letters is 4 * 25 * 24 * 23 * 22 = 30,240.

b. If repeats are allowed, including the first letter being C, X, T, or M, we still have 26 options for each position (including the possibility of repeating the first letter chosen). Therefore, the total number of different 5-letter radio station call letters is 26 * 26 * 26 * 26 * 26 = 26^5 = 11,881,376.

c. To have no repeats and end with the letter S, we have 24 options for the first position (all letters except C, X, T, or M) and 1 option for the last position (the letter S). For the remaining 3 positions, we can choose from 24 letters (all except the first and last position chosen). Therefore, the total number of different 5-letter radio station call letters starting with C, X, T, or M and ending with S is 4 * 24 * 24 * 24 * 1 = 22,464.

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Answer:

The production level that will maximize the revenue is 1800 (in thousands of phones produced), that is, production of 1,800,000 phones will maximize the revenue.

Step-by-step explanation:

The price per unit of phone is given as

p = 45 - 0.0125x

where x is in thousands of phones produced

Revenue = (price per unit) × (number of units)

Revenue = (45 - 0.0125x) × x

= (45x - 0.0125x²)

To find the maximum revenue, we need to obtain the maximum value of the revenue function.

R(x) = (45x - 0.0125x²)

At maximum point, (dR/dx) = 0 and (d²R/dx²) < 0

R(x) = (45x - 0.0125x²)

(dR/dx) = 45 - 0.025x

at maximum point, (dR/dx) = 0

(dR/dx) = 45 - 0.025x = 0

0.025x = 45

x = (45/0.025) = 1800

Hence, the production level that will maximize the revenue is 1800 (in thousands of phones produced)

That maximum revenue is thus

R(x) = (45x - 0.0125x²)

R(1800) = (45×1800) - (0.0125×1800²)

= 40,500

Hope this Helps!!!

To find the production level that will maximize revenue, we need to find the critical point of the revenue equation and determine if it is a maximum or minimum. Then we can find the corresponding production level.

To find the production level that will maximize revenue, we need to find the value of x that maximizes the revenue equation R(X)=X*p. The revenue equation can be written as R(X) = X*(45 - 0.0125x). To maximize revenue, we can find the x-value where the derivative of the revenue equation is equal to zero. After finding this critical point, we can check if it is a maximum or minimum by analyzing the second derivative. Finally, we can substitute this x-value back into the original equation to find the corresponding production level.

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Answer:

The painting area is approximately 28980 years old.

Step-by-step explanation:

The model for the amount of carbon-14 after t years is given by:

[tex]A(t) = A(0)e^{-0.000121t}[/tex]

In which A(0) is the original amount.

The paint contained 3% of the original carbon-14.

This means that [tex]A(t) = 0.03A(0)[/tex]. This means that we have to find t.

[tex]A(t) = A(0)e^{-0.000121t}[/tex]

[tex]0.03A(0) = A(0)e^{-0.000121t}[/tex]

[tex]e^{-0.000121t} = 0.03[/tex]

[tex]\ln{e^{-0.000121t}} = \ln{0.03}[/tex]

[tex]-0.000121t = \ln{0.03}[/tex]

[tex]t = -\frac{\ln{0.03}}{0.000121}[/tex]

[tex]t = 28980[/tex]

The painting area is approximately 28980 years old.

Answer:

D

Step-by-step explanation:

There is more than one way to solve this; the easiest way is to plug in some numbers for x. We can see the roots are (3,0) and (7,0) and the lowest point is (5,0). So when we plug in 3 or 7, we should get zero.

B: (3-3)(3-7)=0

D: 3(3-3)(3-7)=0

So we have two possible solutions, So to check, let's find a point where we can easily find the y value.

When x is equal to 4,5, or 6, there is an integer value for y. so let's plugin 5:

(5-3)(5-7)=-4

We can see when x is five, y has to be -12, so that is not the answer, thus d is the final answer.

Answer:

The weight of pears is 3.08 kg

Step-by-step explanation:

A farmer sells 7.7 kilograms of apples and pears.

3/5 of this weight is apples.

This means that the weight of apples is:

3/5 of 7.7

=> [tex]\frac{3}{5} * 7.7 = 4.62kg[/tex]

The weight of apples is 4.62 kg.

The weight of pears will therefore be:

[tex]7.7 - 4.62 = 3.08 kg[/tex]

The weight of pears is 3.08 kg.

Answer:

(a). Σx= 108, Σx^2 = 4984, Σy^2 = 2,157.

(b). 10.8, 0.1.

(C) and (d) => check explanation.

Step-by-step explanation:

To Calculate for Σx we will have to add all the values for x that is the summation of x-values.

Σx = 11 + 0 + 36 + 22 + 34 + 24 + 25 + -11 + -11 + -22 = 108.

Σx^2 = 11 × 11 + 0 × 0 + 36 × 36 + 22 × 22 + 34 × 34 + 24 ×24 + 25 × 25 + -11 × -11 + -11 × -11 + -22 × -22 = 4984.

Σy^2 = 9× 9 + -3 × -3 + 28 ×28 + 14 × 14 + 23 × 23 + 16 × 16 + 14× 14 + -3 ×-3 + -4 × -4 + -9 × -9= 2,157.

(b). Sample mean for x = 108/10 = 10.8.

Variance for x:

11 - 10.8 = 0.3

0 - 10.8 = -10.8

36 - 10.8 =25.2.

22 - 10.8=11.2.

34 - 10.8 = 23.2

24 -10.8 = 13.2.

25 - 10.8= 14.2

-11 - 10.8 = -21.8.

-11 - 10.8 = - 21.8

-22 -10.8 = -32.8.

Total=0.1

Standard deviation for x = √ s^2 = 0.3162

This can be done for y too

(c). 75% Chebyshev interval around the mean for x values = 10.8 + 2 (0.3162); 10.8 - 2(0.3162).

=> (11.4324, 10.1676).

(d). The coefficient of variation= (0.3162)/10.8 × 100 = 2.92%.

The sample means for annual returns of the Vanguard Total Stock Index (x) and Vanguard Balanced Index (y) have been computed as 10.8 and 8.5 respectively. The inclusion of bonds in a portfolio can lower overall return slightly while also reducing the risk.

The student's task revolves around the subject of statistical analysis, here applied to investment portfolio management. Their goal is to compute the sample mean (average) for two variables - x and y - which each represent annual returns for certain types of portfolios.

Portfolio x represents a 100% stock holding in the Vanguard Total Stock Index, while y represents a 60% stock and 40% bond holding in the Vanguard Balanced Index. Such portfolios carry varying degrees of risk, with all-stock portfolios generally accepted to be more volatile, yet offering higher potential returns than mixed portfolios.

In order to calculate the sample means for x and y, you simply add together all the annual returns for each, then divide by the number of years.

For x: (11 + 0 + 36 + 22 + 34 + 24 + 25 - 11 - 11 - 22)/10 = 10.8 (rounded to the nearest tenth)

For y: (9 - 3 + 28 + 14 + 23 + 16 + 14 - 3 - 4 - 9)/10 = 8.5 (rounded to the nearest tenth)

As seen, stocks did yield a higher average return over the period in consideration, though the range of returns was also much wider. By adding bonds to the portfolio (shown by y), the overall return reduced slightly, but so did the risk (variability) of returns.

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Answer:

6

Step-by-step explanation:

Answer:

(See explanation for further details)

Step-by-step explanation:

A. [tex]x^{3} + 3\cdot x^{2} - 2\cdot x + 7[/tex] : V. Four terms.

B. [tex]3\cdot a \cdot b^{6}[/tex] : I . 9th Degree Monomial (Instead, 7th Degree Monomial)

C. [tex]3\cdot x^{4} - 9 \cdot x^{3} + 5\cdot x^{8}[/tex] : VII - Equivalent to [tex]5\cdot x^{8} + 3\cdot x^{4} - 9 \cdot x^{3}[/tex]

D. [tex]7\cdot a^{3}\cdot b^{2} + 18\cdot a \cdot b^{2}\cdot c - 9\cdot a^{3}[/tex] : III - 7th degree polynomial.

E. [tex]2\cdot x^{5} - 9\cdot x^{3} + 8\cdot x[/tex] : VI - 5th degree polynomial.

F. [tex]4\cdot x^{8} - 7\cdot x^{2} + 9[/tex] : IV - Leading coefficient of 4.

G. [tex]x^{2} - 7[/tex] : II - Constant term of -7.

Answer:

∠AGB and ∠EGD are vertical angles.

∠DGC and ∠CGB are supplementary angles.

m∠EGD = 30

m∠AGF = 50

m∠EGF = 100

Step-by-step explanation:

Answer:

veryical

Step-by-step explanation:

Final answer:

Davide's age is determined by first calculating the total age of the four individuals and then subtracting the total age of the remaining three. With the given averages, Davide is found to be 10 years old.

Explanation:

The question asks us to find the age of Davide given that the average age of Aldo, Bruno, Carlo, and Davide is 16 years, but without Davide, the average age of the remaining three is 18 years.

First, we calculate the total age of all four by multiplying the average age by the number of people: 16 years × 4 = 64 years.

Next, we calculate the total age of Aldo, Bruno, and Carlo by multiplying the new average age by three: 18 years × 3 = 54 years.

Now, we can determine Davide's age by subtracting the total age of the three from the total age of all four: 64 years - 54 years = 10 years.

Therefore, Davide is 10 years old.

Answer:

100-x represents the distance that Serena hit with her 9-iron. 2(100-x) represents the distance she can hit using her driver.

When the distance is given for the 9-iron, use the distributive property to find the simplified equation, so it will be much easier to solve after you are given the information on the 9-iron. Unsolvable without 9-iron distance.

Step-by-step explanation:

Hence, it is unsolvable without [tex]9[/tex] iron distance.

What is the yards?

A yard is a unit of length in both US Customary and British Imperial Systems of Measurement.

It is equivalent to [tex]3[/tex] feet or [tex]36[/tex] inches. Its symbol is yd. It is often used to measure the length of medium-sized objects.

Here, [tex]100-x[/tex] represents the distance that Serena hit with her [tex]9[/tex]-iron, and [tex]2(100-x)[/tex]  represents the distance she can hit using her driver.

Now using the distributive property, it will be easier to solve about the information of nine-iron.

Hence, it is unsolvable without [tex]9[/tex] iron distance.

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Answer: 21

Step-by-step explanation: If you lost the numbers in order from creates to least, and cross the least and the greatest the number in the middle or median is 21

Answer:

87

Step-by-step explanation:

The expected value is the product of the probability and the outcome.

E = 0.98 (89)

E = 87.22

Rounded to the nearest integer, the expected number of classes is 87.

Answer:

x=8,3

Step-by-step explanation:

Move  

24  to the left side of the equation by adding it to both sides.

x 2−11x+24=0

Factor x2−1 1x+ 24

using the AC method.

(x−8)(x−3)=0

If any individual factor on the left side of the equation is equal to  

0 , the entire expression will be equal to 0

x−8=0   x−3=0

Set the first factor equal to  

0  and solve.

x =8

Set the next factor equal to  0  and solve.

x  = 3

The final solution is all the values that make  

( x− 8)(x−3)=0 true.

x =8,3

Solving:

Move constants to the left

[tex]x^2-11x=24\\[/tex]

write as a difference

[tex]x^2-11x+24=0[/tex]

factor

[tex]x^2-3x-8x-+24=0[/tex]

factor again

[tex]x(x-3)-8(x-3)=0[/tex]

separate

[tex](x-3)(x-8)=0[/tex]

solve all possible equations.

[tex]x-3=0\\x-8=0[/tex]

therefore, our answers are:

[tex]x=3,x=8[/tex]

First we have to figure out how much 3 bags cost using the total cost of $8.25

That means. we would do 8.25/3 and 8.25 divide by 3 equals 2.75.

Now we know that each bag costs approximately $2.75

All we have to do now is multiply 2.75 by 4 to get the cost for the total of 4  bags.

4 times 2.75 is exactly 11 dollars, if might change if theres tax.

But, the answer would be 4 bags costs $11.

Answer: It should be used 2 for type-A and 3 for type-B to minimize the cost.

Step-by-step explanation: As it is stipulated, x relates to type-A and y to type-B.

Type-A has 60 deluxe cabins and B has 80. It is needed a minimum of 360 deluxe cabins, so:

60x + 80y ≤ 360

For the standard cabin, there are in A 160 and in B 120. The need is for 680, so:

160x + 120y ≤ 680

To calculate how many of each type you need:

60x + 80y ≤ 360

160x + 120y ≤ 680

Isolating x from the first equation:

x = [tex]\frac{360 - 80y}{60}[/tex]

Substituing x into the second equation:

160([tex]\frac{360 - 80y}{60}[/tex]) + 120y = 680

-3200y+1800y = 10200 - 14400

1400y = 4200

y = 3

With y, find x:

x = [tex]\frac{360 - 80y}{60}[/tex]

x = [tex]\frac{360 - 80.3}{60}[/tex]

x = 2

To determine the cost:

cost = 42,000x + 51,000y

cost = 42000.2 + 51000.3

cost = 161400

To keep it in a minimun cost, it is needed 2 vessels of Type-A and 3 vessels of Type-B, to a cost of $161400

Answer:

All of them

Step-by-step explanation:

Answer:

A,B,C,D,E,F

Step-by-step explanation:

to sum it up all of them !

Angle 3 = 60°

Angle 4 = 60°

Step-by-step explanation:

To find angle 3 we have to use the straight angle that is formed with angle C. Angle C is the same value as angle 2 (120°) so all we have to do now is make an equation by subtracting angle C (120°) from 180°. 180°-120°=60°. So 60° is the value of angle 3.

Angle 4 is also 60° because it is the same angle as angle 3. So the value of angle 4 is 60°.

Another way to solve this problem (shown in the picture) is using the value of angle 1 (60°) and when you have the value 60° and there are triangles formed within the angle (highlighted in the picture) you know that all the angles within the triangle are going to be 60° because all angles within a triangle add up to 180°. So if we were to use this rule the equation would look like 60°+60°+60°=180°. Angle 3 in the green triangle would be equal to 60° because of the fact that one angle was already confirmed as being 60° so because of that all the angles in the triangle have to add up to 180° so the all the angles must be 60°. Angle 4 in the red triangle would also be equal to 60° for the same reason mentioned above.

So therefore the answer to this question is Angle 3 = 60° and Angle 4 = 60°

Hope this helps! If you have any more questions or you need further clarification please comment down below or message me! Good luck!

Answer:

In order for the statement to be true, the value of x has to be 19.

Step-by-step explanation:

3(x - 3) - 16 = 2(x - 8) + 10

3x - 9 - 16 = 2x - 16 + 10

3x - 25 = 2x - 6

x - 25 = - 6

x = 19

Answer:

b) 19

Step-by-step explanation:

Let's solve the problem,

→ 3(x - 3) - 16 = 2(x - 8) + 10

→ 3x - 9 - 16 = 2x - 16 + 10

→ 3x - 25 = 2x - 6

→ 3x - 2x = -6 + 25

→ [ x = 19 ]

Hence, option (b) is correct.

Answer:

The weight of a box is 10 kg.

Step-by-step explanation:

Weight of each book is 2 kg

So, the weight of 3 books is 6 kg.

Weight of a container is 4 kg

3 books and one container is in a box. We need to find the weight of the box.

It is equal to the sum of weights of 3 books and one container. So,

Total weight = 6 kg + 4 kg

W = 10 kg

So, the weight of a box is 10 kg.

Answer: 45

Explanation: Remember that dividing by a fraction is the same thing as multiplying by the reciprocal of that fraction or that fraction flipped.

Also, think of the 15 in this problem as 15/1.

So we can rewrite 15/1 ÷ 1/3 as 15/1 · 3/1.

Multiplying across the numerators and the denominators,

we find that our answer is 45/1 or just 45.

15 divided by 1/3 is equal to 45.

To divide 15 by 1/3, we can interpret it as finding how many groups of 1/3 can be made from 15.

To begin, we can convert the division of 15 by 1/3 into a multiplication problem by taking the reciprocal of 1/3, which is 3/1 or simply 3.

So, we have:

15 ÷ (1/3) = 15 x 3

Multiplying 15 by 3, we get:

15 x 3 = 45

Therefore, 15 divided by 1/3 is equal to 45.

In other words, 15 can be divided into 45 equal parts of size 1/3. Each of these parts represents the quotient when dividing 15 by 1/3.

When we multiply 1/3 by 45, we get 15. This confirms that 15 divided by 1/3 is indeed equal to 45.

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The question is missing informations. The complete question is:

Find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data. An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas. Listed bellow are the phenotype codes where 1 = smooth-yellow, 2 = smooth-green, 3 = wrinkled-yellow and 4 = wrinkled-green. Do these results make sense?

4 3 3 1 3 4 1 1 1 4 2 3 1 1

(a) The mean phenotype code is _____

(b) The median phenotype code is _____

(c) Select the correct choice bellow and fill in any answer boxes within your choice

(A) The mode phenotype code is ___

(B) There is no mode

(d) The midrange of the phenotype code is ___

Do the measures of center make sense?

A. Only the mode makes sense since the data is nominal.

B. All the measures of center make sense since the data is numerical

C. Only the mean, median and midrange make sense since the data is nominal

D. Only the mean, median and midrange make sense since the data is numerical.

Answer: (a) mean = 2.285

(b) median = 2.5

(c) A) The mode phenotype code is 1

(d) midrange = 2.5 and A. Only the mode makes sense since the data is nominal.

Step-by-step explanation: Mean and Median are the average value of a data set, however, median is the value in the middle of the set while mean is the average value a data set must be if all the values were the same.

(a) To calculate mean:

mean = [tex]\frac{4+3+3+1+3+4+1+1+1+4+2+3+1+1}{14}[/tex]

mean = 2.285

(b) To find median: The set has an even number of elements (14), so, in this case, to determine the middle term:

median = [tex]\frac{7th + 8th}{2}[/tex]

median = [tex]\frac{2+3}{2}[/tex]

median = 2.5

(c) Mode is the value which has the highest frequency. For this data set, mode = 1, since the number 1 appears 6 times.

Mode = 1

(d) Midrange is the average of the smallest and largest on the set.

midrange = [tex]\frac{1+4}{2}[/tex]

midrange = 2.5

Nominal variable is a type of variable used to name, categorize or label attributes that are being measured. Mode is the most common used measure of central tendency and with it, it is possible to determine if the set is unimodal (one mode) or multimodal (two or more modes). In conclusion, mode makes sense because data is nominal.

The mean, median, and midrange of the given phenotype codes are all 2.5.

1. Mean

The mean is the average of the data set. We sum all the phenotype codes and divide by the number of observations.

2. Median

The median is the middle value of an ordered data set. For an even number of observations, it's the average of the two middle values.

3. Mode

The mode is the value that occurs most frequently. Here, each code appears only once, so there is no mode.

4. Midrange

The midrange is the average of the highest and lowest values in the data set.

Since each code represents a distinct phenotype, the measures provide a way to summarize the data set but don't hold biological significance independently. They mainly help to understand the distribution of phenotype observations numerically.

Answer:16

Step-by-step explanation:

prime factors of 16=2x2x2x2

Prime factors of 48=2x2x2x2x3

Their greatest common factor is:2x2x2x2=16

The greatest common factor of 16 and 48 is determined by listing the factors of each number and identifying the largest factor they share. In this case, the GCF of 16 and 48 is 16.

The greatest common factor (GCF) is the highest number that divides exactly into two or more numbers. To find the GCF of 16 and 48, you can list the factors of each number and find the highest factor they share.

The factors of 16 are 1, 2, 4, 8, 16. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The largest number that appears in both lists is 16. Therefore, the GCF of 16 and 48  is 16.

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Answer:

1 1/2 cups

Step-by-step explanation:

2/4 = 1/2

(1/2) cups * 3 =  1.5 cups

Answer:

1 1/2 or 3/2 cups of flour

Step-by-step explanation:

2/4 + 2/4 + 2/4= 6/4

to simplify:

divide 6/4 by 2/2 to get 3/2

3/2 =1 1/2