i need help with #12 please help me

The data set for which the mean is most appropriate to describe the set instead of the median is; 0, 57, 847, 859, 866, 866, 872.

It follows from the task content that the answer choice for which the dataset is better described by the mean instead of the median is to be identified.

When outliers exist in a dataset, the mean is a better measure of center for the data set.

On this note, it follows that the answer choice for which the mean is a better description of the dataset is; 0, 57, 847, 859, 866, 866, 872.

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Step-by-step explanation:

The volume of a cylinder can be calculated using the formula:

V = πr^2h

where r is the radius of the cylinder, and h is the height of the cylinder.

The diameter of the pool is 14 feet, so the radius is half of that, or 7 feet. The height is 5 feet. Therefore, the volume of the pool is:

V = π(7)^2(5) ≈ 769.39 cubic feet

We can convert this volume to gallons using the conversion factor given:

1 cubic foot ≈ 7.5 gallons

Therefore:

769.39 cubic feet * 7.5 gallons/cubic foot ≈ 5,770 gallons

So the pool can contain approximately 5,770 gallons of water (rounded to the nearest whole number).

Answer:

270 degrees

Step-by-step explanation:

There are 60 minutes on a clock face, and the minute hand of a clock makes one complete revolution around the clock face in 60 minutes. This means that the minute hand turns through the angle of 360 degrees in 60 minutes.

The time from 3:30 P.M. to 4:15 P.M. is 45 minutes.

So, during this time, the minute hand of the clock turns through a fraction of a circle equal to:

Fraction of a circle = (angle turned by the minute hand) / (angle for a complete circle)

= (45 minutes) / (60 minutes)

= 3/4

Therefore, the minute hand of the clock turned through 3/4 of a circle during this time.

To find the number of degrees turned by the minute hand, we can multiply the fraction of a circle turned by the total number of degrees in a complete circle:

Degrees turned by the minute hand = (Fraction of a circle turned) x (360 degrees)

= (3/4) x (360 degrees)

= 270 degrees

Therefore, the minute hand of the clock turned through 270 degrees during this time.

The "House Vodka Martini" may sell less when its price is raised since some consumers could prefer the premium brand.

Contribution Margin = Selling Price - Total Cost

Let's start with the "House Vodka Martini":

Czarina Vodka: 2 oz * (Czarina cost per oz)

Dry Vermouth: 0.5 oz * (Dry Vermouth cost per oz)

Olive garnish: 1 * (Olive cost per unit)

Cocktail napkin: 1 * (Napkin cost per unit)

Total Cost (House Vodka Martini) = sum of the costs above

Contribution Margin (House Vodka Martini) = $4.50 - Total Cost (House Vodka Martini)

Let's solve for "Grey Goose Vodka Martini":

Grey Goose Vodka: 2 oz * (Grey Goose cost per oz)

Dry Vermouth: 0.5 oz * (Dry Vermouth cost per oz)

Olive garnish: 1 * (Olive cost per unit)

Cocktail napkin: 1 * (Napkin cost per unit)

Total Cost (Grey Goose Vodka Martini) = sum of the costs above

Contribution Margin (Grey Goose Vodka Martini) = $5.50 - Total Cost (Grey Goose Vodka Martini)

Other considerations, like client preferences and the drinks' perceived value, must also be taken into account. The "House Vodka Martini" may sell less when its price is raised since some consumers could prefer the premium brand.

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Answer:

It would take the company 11.25 days to repave the road.

Step-by-step explanation:

27 miles to repave total

2.4 repavement per day

27 / 2.4 = 11.25

Therefore, it would take the company 11.25 days to repave the road.

give question oh t is so easy

Step-by-step explanation:

To find the equation of the parabola with focus (-3,2) and directrix x-y+1=0, we can use the definition of a parabola: the set of all points that are equidistant to the focus and directrix.

Let P(x, y) be an arbitrary point on the parabola, and let d(P, directrix) be the distance from P to the directrix. The distance from P to the focus is given by the distance formula:

d(P, focus) = √[(x - (-3))^2 + (y - 2)^2] = √[(x + 3)^2 + (y - 2)^2]

Since P is equidistant from the focus and directrix, we have:

d(P, directrix) = |x - y + 1| / √(1^2 + (-1)^2) = |x - y + 1| / √2

Therefore, the equation of the parabola is given by:

d(P, focus) = d(P, directrix)

√[(x + 3)^2 + (y - 2)^2] = |x - y + 1| / √2

Squaring both sides and simplifying, we get:

(x + 3)^2 + (y - 2)^2 = (x - y + 1)^2 / 2

Expanding the right-hand side and simplifying, we get:

2(x + 3)^2 + 2(y - 2)^2 = (x - y + 1)^2

Expanding the right-hand side again and simplifying, we get:

2x^2 + 8xy + 2y^2 - 8x - 12y + 20 = 0

Therefore, the equation of the parabola is:

2x^2 + 8xy + 2y^2 - 8x - 12y + 20 = 0

which is in general form.

There are 48 students in the pottery class

30kg of clay is divided into 5/8kg chunks, and there is just enough for all of the kids. To find the number of students in the class, we need to divide the total amount of clay by the amount of clay per student.

The amount of clay per student is 5/8kg.

So, number of students = (total amount of clay) / (amount of clay per student)

Dividing the total amount of clay by the amount of clay per student, we get:

30 / (5/8) = 30 x 8/5

= 48

Therefore, there are 48 students in the pottery class

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[tex]\cfrac{7\times 10^{5}}{2\times 10^{3}}\implies \cfrac{7}{2}\times\cfrac{10^5}{10^3}\implies \cfrac{7}{2}\times 10^5\cdot 10^{-3}\implies \cfrac{7}{2}\times 10^{5-3} \\\\\\ \cfrac{7}{2}\times 10^2\implies 3.5\times 100\implies 350[/tex]

The volume of cone B is of 2.37π cubic centimeters.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The scale factor in this problem is given as follows:

k = 3/2.

Hence:

The scale factor measures the ratio of the side lengths, in units, while the volume is given in cubic units, hence the ratio of the volumes is given as follows:

Vb/Va = (2/3)³

Vb/Va = 4/27

Hence the volume of solid B is given as follows:

Vb = 4/27 x 16π

Vb = 2.37π.

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Answer:

Answer:

169.65

Step-by-step explanation:

Solving ones like these, I use the formula: Volume b/Volume a=k^3. I will be using “•” to represent multiplication, “^” is used for exponent. 16•pie is the volume for shape A, and k is 3/2. The reason why k is exponent by 3 is because this is for volume. Then, plug in the values, Volume B/16•pi=3/2^3 is what we have. With the piwer of inverse operations, we can isolate for Volume B. By multiplying 16•pi by each side, Volume B=16•pi•3/2^3. Lets do 3/2^3 first since it is following the order of PEMDAS. To recall what PEMDAS is, it is a method my school uses for solving equations. Parentheses first, Exponent next, then Multiply, Divide, Add, and subtract. Basically the order of solving any equation. 3/2^3= 27/8. Now, back to multiplying! I use desmos scientific calculator. 27/8•16•pi= =169.6460033. The qeustion says to round to the nearest hundreth, so it would be 169.65. Have a great day everybody

Step-by-step explanation:

Answer: The solutions to the equation sin x - 1 = cos x in the interval [0, 2) are x = -π/2 and x = 3π/4, in radians in terms of π.

Step-by-step explanation:sin x - 1 = cos x

Subtracting cos x from both sides:

sin x - cos x - 1 = 0

Using the identity sin(x - π/4) = sin x cos π/4 - cos x sin π/4, we get:

sin(x - π/4) = -1/√2

Taking the inverse sine of both sides, we get:

x - π/4 = -π/4 - π/2 = -3π/4

or

x - π/4 = π/2 + π/4 = π/2

Adding π/4 to both sides:

x = -3π/4 + π/4 = -π/2

or

x = π/2 + π/4 = 3π/4

Note that the interval [0, 2) contains 0, π/2, and π, but none of these values satisfy the equation. Therefore, the solutions in the given interval are:

x = -π/2 and x = 3π/4.

Hence, the solutions to the equation sin x - 1 = cos x in the interval [0, 2) are x = -π/2 and x = 3π/4, in radians in terms of π.

The inequality with the set of solutions (-14, infinity ) can be expressed as follows: x > -14

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Any value of x bigger than -14 will fulfill the inequality, according to this inequality, and the solution set contains all real numbers greater than -14 but excluding -14.

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If triangle XYZ is isosceles, then the two sides (XY and YZ) are congruent in addition to the two base angles.

Angle Y (the one at the top of the triangle) = 42 degrees

Angles X and Z are congruent because of the properties of an isosceles triangle. Let's call both angle measures "x" in our equation.

x + x + 42 = 180

2x + 42 = 180

2x = 138

x = 69

Answer: The measure of Angle Z is 69 degrees.

Hope this helps!

The composite solid has a volume of 224 inches³.

Volume is a mathematical notion that indicates how much space in three dimensions a solid, liquid, or gas occupy.

It is commonly measured in cubic length units like cubic metres, cubic feet, or cubic centimetres.

The volume of the cube must be subtracted from the volume of the rectangular prism in order to determine the volume of the composite solid.

Volume of the rectangular prism = length x width x height = 8 x 6 x 6 = 288 cubic inches

Volume of the cube = side [tex]length^3[/tex] = [tex]4^3[/tex] = 64 cubic inches

The composite solid's volume is thus:

Volume of rectangular prism - Volume of cube = 288 - 64 = 224 cubic inches.

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The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 10 - 1 = 9

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.2622

The margin of error is:

M = T*s = 2.2622*0.3 = 0.68

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 98.44 - 0.68 = 97.76 ºF

The upper end of the interval is the sample mean added to M. So it is 98.44 + 0.68 = 99.12 ºF

The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF.

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a. If a = 5, the value of n will be 17.

(b) A binomial expression for n in general

terms of “a” will be n = 4a - 3.

(a) In the case that a is equal to 5, then the expression transforms into:  

(x^(2a+1))³/(x^(a+3))² = (x^(2(5)+1))³/(x^(5+3))² = (x^11)³/(x^8)² = x^(33-16) = x^17  

Therefore, for a = 5, n = 17.

(b) We can simplify this by making use of the rules of exponents:  

(x^(2a+1))³/(x^(a+3))² = x^(6a+3)/(x^(2a+6)) = x^(6a+3-2a-6) = x^(4a-3)  

Therefore, the binomial expression for n in terms of a equals: n = 4a - 3

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The equation of the supply function is q = 20000p - 10000

Let's use the point-slope form of a linear equation:

slope = (change in quantity) / (change in price) = (10000 - 5000) / (1.50 - 1.00) = 10000 / 0.50 = 20000

Using the point-slope form with the point (1.50, 10000):

q - 10000 = 20000(p - 1.50)

Simplifying:

q = 20000p - 20000 + 10000

q = 20000p - 10000

So the equation of the supply function is q = 20000p - 10000

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The final apportionment of the 103 seats using Jefferson's method is: County A = 84 seats, County B = 119 seats, County C = 136 seats, and County D = 64 seats.

Here are the steps you can follow to apportion the 103 seats to the four counties;

Determine the population of each county; Let's assume the populations of the four counties are as follows;

County A; 250,000

County B; 350,000

County C; 400,000

County D; 200,000

Calculate the geometric mean of the populations; To calculate the geometric mean, we need to multiply the populations of all the counties together and then take the fourth root of the result.

Geometric mean = (250,000 x 350,000 x 400,000 x 200,000)^(1/4)

Geometric mean = 305,541.27

Calculate the ratio of each county's population to the geometric mean; To calculate the ratio for each county, we divide its population by the geometric mean.

County A; 250,000 / 305,541.27 = 0.8171

County B; 350,000 / 305,541.27 = 1.1458

County C; 400,000 / 305,541.27 = 1.3085

County D; 200,000 / 305,541.27 = 0.6542

Calculate the initial apportionment of seats; To calculate the initial apportionment of seats, we assign each county the number of seats equal to its ratio multiplied by the total number of seats.

County A; 0.8171 x 103 = 84.18, rounded down to 84 seats

County B; 1.1458 x 103 = 118.04, rounded up to 118 seats

County C; 1.3085 x 103 = 134.75, rounded up to 135 seats

County D; 0.6542 x 103 = 67.03, rounded down to 67 seats

Check if the initial apportionment is equal to the total number of seats; The initial apportionment gives a total of 404 seats, which is greater than the total number of seats available (103).

Adjust the apportionment to reach the total number of seats; To adjust the apportionment, we assign additional seats to each county based on their fractional remainders.

County C has the largest fractional remainder (0.75), so it gets the first additional seat.

The new apportionment is; A = 84, B = 118, C = 136, D = 65

The total number of seats is 403, so one seat is left unassigned.

We assign the last seat to the county with the largest fractional remainder, which is County B.

Therefore, the final apportionment of the 103 seats will be; County A = 84 seats, County B = 119 seats, County C = 136 seats, and County D = 64 seats.

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Let x be the number of gallons consumed by the first car.

Then, the number of gallons consumed by the second car is 65-x (since the total gas consumption is 65 gallons).

Using the formula distance = fuel efficiency x gas consumption, we can set up two equations:

First car: distance = 30x

Second car: distance = 20(65-x)

Since the total distance is 1700 miles, we can set up another equation:

Total distance: 30x + 20(65-x) = 1700

Simplifying this equation, we get:

30x + 1300 - 20x = 1700

10x = 400

x = 40

Therefore, the first car consumed 40 gallons and the second car consumed 65-40 = 25 gallons.

Let's assume that the first car traveled x miles and the second car traveled y miles during that week. We can set up two equations based on the given information:

x + y = 1700 (the combined total of miles traveled by both cars)

x/30 + y/20 = 65 (the total gas consumption)

To solve for x and y, we can use the first equation to express one variable in terms of the other. For example, we can solve for y as follows:

y = 1700 - x

Substituting this into the second equation, we get:

x/30 + (1700 - x)/20 = 65

Multiplying both sides by the common denominator 60, we can simplify the equation:

2x + 3(1700 - x) = 3900

2x + 5100 - 3x = 3900

-x = -1200

x = 1200

So the first car traveled 1200 miles during the week. We can use this value to find the second car's mileage:

y = 1700 - x = 1700 - 1200 = 500

Therefore, the second car traveled 500 miles during the week. To find the gallons of gas consumed by each car, we can use the fuel efficiency rates:

Gallons used by first car = 1200 miles / 30 mpg = 40 gallons

Gallons used by second car = 500 miles / 20 mpg = 25 gallons

So the first car consumed 40 gallons of gas and the second car consumed 25 gallons of gas during that week.

Sasha's next step is to swing arcs on both sides of the segment to intersect the first two arcs created. Option A is correct.

By doing this, she will be creating a two points of intersection on the segment. She can then draw a straight line which is connecting these two points, which will bisect the segment into two equal parts. This method of bisecting a segment is called as the compass-and-straightedge construction, and it is a fundamental technique in Euclidean geometry.

Alternatively, if you want to bisect a segment without using the compass-and-straightedge construction, you can measure the length of the segment and mark its midpoint. Then you can draw a line connecting the two endpoints through the midpoint to bisect the segment.

Hence, A. is the correct option.

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--The given question is incomplete, the complete question is

"Sasha is bisecting a segment. First, she places the compass on one endpoint, opens it to a width larger than the compass the same width and places it on the other endpoint. What is her next step? A) Swing arcs on both sides to intersect the first two arcs created. B) Swing an arc that intersects the segment. C) Swing arcs that intersect a point that is not on the segment. D) Swing an arc that intersects the opposite endpoint."--

Answer:

Step-by-step explanation:

center=(-1,1)

radius=√16=4

distance between (-1,1) and (3,1)=√[(3+1)²+(1-1)²]=√[16+0]=√16=4=radius

Hence point lies on the circle.

There are 48 students.

To find the number of students, we need to divide the total amount of clay by the weight of each portion.

We are given that there are 30kg of clay. We are also told that the clay is divided into portions of 5/8kg each.

To divide one quantity by another, we can use the following formula:

quantity ÷ weight per portion = number of portions

In this case, we can write:

30kg ÷ (5/8)kg per portion = number of portions

30kg × (8/5) portions per kg = number of portions

Simplifying, we get:

48 portions = number of portions

Therefore, there are 48 portions of clay in total. To find the number of students, we need to divide the number of portions by the number of portions per student.

Since each portion weighs 5/8kg, we can write:

1 portion = 5/8kg

number of portions per student = 1 portion/student

So, the number of students would be:

48 portions ÷ 1 portion per student = 48 students

Therefore, there are 48 students.

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The domain of the equation include the following: D. all real numbers.

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, ∞] or all real numbers.

Range = [-4, ∞}

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The probability of not getting a number 1 through 18 is b) 10 over 19.

There are a total of 38 slots on the roulette wheel, and 18 of them are numbered 1 through 18. Therefore, there are 20 slots that are not numbered 1 through 18. The probability of not getting a number 1 through 18 on a single spin of the roulette wheel is the same as the probability of getting one of the 20 non-numbered slots.

Thus, the probability of not getting a number 1 through 18 is 20/38 or 10/19.

Therefore, the answer is option b) 10 over 19.

Correct Question :

A roulette wheel has 38 slots total, 36 of which are numbered 1 through 36, and 2 green slots labeled "O" and "00." For any spin of the wheel, what is the probability of NOT getting a number 1 through 18?

a.) 9 over 19

b.) 10 over 19

c.) 1 over 19

d.) 18 over 19

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad E(\stackrel{x_2}{5}~,~\stackrel{y_2}{-10}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 5 +x}{2}~~~ ,~~~ \cfrac{ -10 +y}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE D} }{(11~~,~~4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ 5 +x }{2}=11\implies 5+x=22\implies \boxed{x=17} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ -10 +y }{2}=4\implies -10+y=8\implies \boxed{y=18}[/tex]

The probability that exactly 2 of the pencils in the package are painted green is given as follows:

p = 9/30.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

In this problem, we have a set of 30 outcomes, in which the number of outcomes in which the letter G appears exactly twice is given as follows:

9.

Hence the probability that exactly 2 of the pencils in the package are painted green is given as follows:

p = 9/30.

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The verbal expression for 0.7x-11 is "seven tenths of x minus eleven."

A scenario expressed using mathematical terms is condensed into a conversational statement. It identifies the connections between and movements made by amounts. Example: The product of a number x and one multiplied by five.

Words are present in verbal utterances. For instance, the phrase "three more than a double a number" is a verb. The algebraic equivalent of the phrase "three more than a double a number" is the expression 2x + 3.

Verbal models are another name for verbal expressiveness. When we communicate ourselves verbally, we describe the mathematical data using language. An expression becomes a verbal expression when it is written in terms or spoken in words. However, compared to verbal expression, an algebraic expression is entirely different.

The verbal expression for 0.7x-11 is "seven tenths of x minus eleven."

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Below is the proof for the given statement "BC ≅ DA, BC ║ AD ⟹ ΔABC = ΔCDA":

Statements                     Reasons

BC ≅ DA                            Given

BC || AD                             Given

∠ BCA = ∠DAC             Alternate interior angles are known to be  congruent (BC || AD)

AC ≅ CA                           Reflexive Property

∆ ABC = ∆ CDA SAS  (Side-Angle-Side) congruence theorem, by the use of statements 1, 3, and also  4.

In the above text, we are said to be given that line BC is equal to line member DA, and BC . We need to prove that the two triangles ΔABC and ΔCDA are the same.

Therefore, To prove this, we start by using the given information to find harmonious angles in both triangles. Since BC is same to other, we know that alternate interior angles are equal, so ∠ BCA is sane to ∠ DCA.

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See text below

1. Given : BC ≅ DA, BC ║ AD

Prove : ΔABC = ΔCDA

Statements                           Reasons

1. BC  ≅ DA                            ------

2. BC || AD                             ------

2. ∠ BCA = ∠DAC                  ------

4. AC ≅ CA                            ------

5.   -----                                   -------