Connections Pool Service needs to fill up a neighborhood pool in
Lakewood. They use a cylindrical tank on the truck to transport water
from the warehouse to the pool.
The tank is completely filled with water and then drains completely into the pool. The volume of the cylindrical tank is V = 36πr, where r, is the radius of the tank in feet.
The volume of the neighborhood pool is V₂ = 1/2(4/3pi r3 2) where r₂ is the radius of the pool.

a. Since V₁=V₂, write an equation that shows r1 as a function of r2.

[Hint: set them equal and solve for r₁.]

The scale factor for 7 millimeters to 5 meters is 0.0014.

The scale factor is the ratio between the scale of an original object, drawing, map, model, or blueprint compared to its representation as a larger or smaller object.

We can compute the scale factor (scaled-down) using the following formula:

Scale factor = Dimension of the new shape ÷ Dimension of the original shape

1 meter = 1,000 millimeters

5 meters = 5,000 millimeters (1,000 x 5)

The scale-down factor of 7 millimeters to 5,000 millimeters = 0.0014 (7/5,000)

The scale-up factor of 7 millimeters to 5,000 millimeters = 714.286 (5,000/7)

Thus, the scale factor is 0.0014.

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What is the scale factor?

The two plans cost the same for 550 miles of driving  and $113.5 is the total cost.

This problem is about linear equations. We assume Maya drive X miles, and the total cost is $Y, then we can get like, the first plan has an initial fee of $53 and costs an additional $0.11 per mile driven

             For plan 1:  Y = 53 + 0.11 X

The second plan has an initial fee of $42 and costs an additional $0.13 per mile driven,

              For Plan 2: Y= 42 + 0.13 X

When both plans cost the same, then

              Plan 1 = Plan 2

              53 + 0.11 X = 42 + 0.13 X

              0.13 X - 0.11 X = 53 - 42

               0.02 X = 11

[tex]$X=\frac{11}{0.02}=550$[/tex] miles

Put the value of X in equation of Plan 1, we get,

     Y = 53 + 0.11(550) = 53 + 60.5= $113.5

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The 18th term of the sequence is -83, the correct option is C.

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n-1)d, ...

Its nth term is

T_n = a + (n-1)d

(for all positive integer values of n)

And thus, the common difference is

T_{n+1} - T_n

for all positive integer values of n

Given:

The sequence=19,13,7,1...

n=18

D= 13-19

D= 6, a= 19

Now,

=a + (n+1)d

=19+(18-1)x-6

=-83

Therefore, the 18th term of the sequence will be -83

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The probability of selecting one solid chocolate and 2 cherries is given as follows:

0.1544 = 15.44%.

A probability is obtained by the division of the number of desired outcomes by the number of total outcomes.

The outcomes resulting in one chocolate and two cherries being taken are given as follows:

Hence the probability is obtained as follows:

p = 7/17 x 6/16 x 5/15 + 6/17 x 7/16 x 5/15 + 6/17 x 5/16 x 7/15

p = 0.1544 = 15.44%.

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The discount of the purchase price results in the buyer making the identical monthly payment under either purchase option, $4064.76.

Financing is the process of providing funds for business activities, making purchases, or investing. Financial institutions, such as banks, are in the business of providing capital to businesses, consumers, and investors to help them achieve their goals. The use of financing is vital in any economic system, as it allows companies to purchase products out of their immediate reach.

the PV=FV÷(1+r)^N,

here, PV is present value, FV is future value and r is the rate of discount or interst.

According to the given conditions,

if car financing at 0% ,

then car price=$36,000.

time period =48 months.

so, monthly payment =36000÷48

                                   =$750.

if financing at regular rate then, monthly interest rate is 0.5%

time=48 month.

monthly payment, if we consider same payment=$750

the discount of the purchase price will be $4064.76.

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The relationship between the plane and the cone is expressed by the statement that it is parallel to the base of the cone.

Given,

A circle is a closed, curved shape with two dimensions in geometry, alternatively we might say that a circle is a spherical form without borders or edges.

When a cone is cut by a plane that is parallel to the cone's base, a circle is the resultant cross-section.

The form that results from a plane cutting a cone at an angle such that it misses the base or the vertex is called an ellipse. (As in the figure.)

Hence When a plane cuts through a cone and the plane is parallel to the base of the cone, the result is a circle.

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The graph which represents the velocity of the free-falling rock that changes during the first four seconds is option L: Same as “J” except the line is going from top left corner to bottom right corner.

What is velocity?

The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction.

The velocity of a free-falling rock can depicted by equation of motion.

The first equation of motion, v = u + it is referred to as the velocity-time relation. On the other hand, the second equation of motion is s = ut + 1 / 2at² can be called the position-time relation. Likewise, we call the third equation of motion, v² = u²+ 2as, position – velocity relation.

The laws are: (1) Every object moves in a straight line unless acted upon by a force. (2) The acceleration of an object is directly proportional to the net force exerted and inversely proportional to the object's mass. (3) For every action, there is an equal and opposite reaction.

Since, the rock is falling freely it will form a straight line (first equation of motion) on the graph and not curved.

The rock will start to fall at an increasing speed with respect to time.

Therefore, option L is the correct answer.

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The friction force on the 40 kg crate is the product of the coefficient of static friction, μs, and the normal force on the crate. Therefore, the friction force is 40 kg ×0.5 = 20 N.

The resultant normal force on the crate is the sum of the force P and the friction force, which is

300 N + 20 N = 320 N.

The position x, measured from point A, is determined by the direction of the force P. If the force P is acting to the right, then the normal force will have a position x that is to the right of point A. If the force P is acting to the left, then the normal force will have a position x that is to the left of point A.

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The seedlings grew by 7/6 inches in the first 2 weeks.

What is LCM ?

The abbreviation LCM stands for "Least Common Multiple." The smallest multiple that two or more numbers share is known as the least common multiple.

Let' assume the growth of seedling was 'nil' at the beginning.

According to the situation,

In the first week it grew by 1/3 inches and,

In the next week it grew by  5/6 inches.

So, we can say that the total growth will be the sum of growth in the first and second week.

Hence, total growth would be 7/6 inches (i.e. 1/3 + 5/6).

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Answer: The building is in the form of a cylinder surmounted by a cone. To find the outer surface area of the building, we need to find the total surface area of the cylinder and the cone and add them together.

The total surface area of the cylinder = 2πr^2 + 2πrh = 2π(7^2) + 2π(7)(24) = 2π(49) + 2π(168) = 98π + 336π = 434π square meters

The total surface area of the cone = πr^2 + πr√(r^2 + h^2) = π(7^2) + π(7)(√(7^2 + 24^2)) = 49π + 49π(√(625)) = 49π + 49π(25) = 49π + 1225π = 1274π square meters

The outer surface area of the building is the sum of the total surface area of the cylinder and the cone, which is 434π + 1274π = 1708π square meters.

Step-by-step explanation:

We graph points A(0,3) and B(1,2) to find the solution.

What is the intercept?

An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses.

Here, we have

Given: f(x) = 3(2/3)ˣ

We first find the y-intercept

The y-intercept is the value of f(x) when the value of x is equal to zero

For x = 0

f(0) = 3(2/3)⁰ = 3

Point A(0,3)

Now, we find the value of f(x) when x = 1

f(1) = 3(2/3)¹ = 2

Point B(1,2)

Hence, we graph points A(0,3) and B(1,2) to find the solution.

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The total volume of both storages will be 76 cubic ft.

A volume is defined as the amount of space occupied by a three-dimensional solid shape. It is difficult to visualize in any shape, but it can be compared between shapes.

A compass box, for example, has a larger volume than an eraser placed inside it. We divide any two-dimensional shape into equal square units to calculate its area.

The volume of the larger box will be calculated as:-

Volume = side³

Volume = (4)³

Volume = 64 cubic ft

The volume of the smaller box = 12 cubic ft

Total volume = 64 + 12 = 76 cubic ft

Hence, the total volume of the boxes is 76 cubic ft.

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Hope it helps.

If you have any query, feel free to ask.

The volume of the cylinder is 769.3 cubic feet.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given a cylinder,

radius = 7 feet

height = 5 feet

volume of cylinder = πr²h

V = πr²h

V = 3.14*(7²)*5

V = 769.3 cubic feet

Hence the volume of a cylinder is 769.3 cubic feet.

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The estimate errors in the adjacent side and the hypothenuse are ≅ ±0.29 cm and ≅ ±0.145 cm respectively. The percentage errors in the adjacent side and hypothenuse are 2.009% & 0.502%.

Hypothenuse y₁ = 25/sin x = 25cosec x

Adjacent y₂ = 25/tan x = 25cot x

Opposite angle is 60° = π/3

Possible error, dx ≅ ±0.5° = 0.5 × π/180 = ±π/360

Differentiating y₁ = 25cosec x

dy₁ = -25(cosec x · cot x)dx

dy₁ = -25(cosec (π/3) · cot (π/3))×±π/360

= -25(2/√3)(1/√3)(±π/360)

= ≅ ±0.145 cm

Similarly

dy₂ = -25 cosec²x .dx

dy₂ = -25 cosec²(π/3) .×±π/360

= -25(2/√3)²×±π/360

≅ ±0.29 cm

So the errors in the hypothenuse = ±0.145 cm

Error in the adjacent side = ±0.29 cm

Percentage error in the adjacent side = 0.29/(25/√3) = 2.009 %

Percentage error in the hypothenuse = 0.145/(25/sin60) = 0.502%

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A) n = 50, Since the sample size is small, it is more likely that a higher value is selected as the median, and the sample would be skewed to the right tail.

What is the median value?

The median value of a set of data is the middle value when the data is arranged in order. It is the value that separates the higher half of the data from the lower half. In other words, it's the value that has half the observations below it and half the observations above it.

In a residential neighborhood, the median value of a house is $200,000, which means that half the houses in the neighborhood are worth more than $200,000 and half are worth less.

For a sample median most likely to be above $250.000, the sample size would have to be small and skewed to the right tail, where the higher values are. In this case, the answer would be

Hence, A) n = 50, Since the sample size is small, it is more likely that a higher value is selected as the median, and the sample would be skewed to the right tail.

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The longest piece of same size that can be cut from 90 inches and 72 inches pieces of wood using HCF is of length 18 inches.

So, the correct option is (c) 18.

Given that,

   Jeremy has two pieces of  90 inches and the other is 72 inches wood. He wants to cut both pieces of wood into smaller pieces of same length and length as long as possible.

Therefore, the Highest Common Factor (H.C.F.) of both the lengths will gives the highest possible length i.e between both the wooden pieces.

To find Highest Common factor,

Prime factorizations of 90 and 72 :

90 = (2 x 3 x 3) x 5

72 = 2 x 2 x (2 x 3 x 3)

2 x 3 x 3 is common factor between 90 and 72

∴ The  Highest Common Factor of 90 and 72 = 2 x 3 x 3 = 18

The longest possible length that can be cut out from both the  pieces are of length = 18 inches

Number of pieces that can be cut from 90 inches long piece = 90/18 = 5

Number of pieces that can be cut from 72 inches long piece = 72/18 =  4

Therefore, the total number of pieces of lumber  = 5+4 = 9 pieces

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The probability of there is one faulty light is 0.60%, There are two faulty lights is 0.12% and There is at least one faulty light is 0.60%.

The likelihood that an event will occur is measured by probability. It is difficult to make a complete prediction for many events. By using it, we are only able to forecast the likelihood of an event, or how likely it is, to occur. Between 0 and 1, where 1 denotes a certain event and 0 denotes an impossibility, is the range of probability. For students in class 10, probability is a crucial subject because it clarifies all of the fundamental ideas. In a sample space, there is a probability of 1 for each event.

a. Let there be 100 lights, 1/5th are faulty = 20

There is one faulty in first three, P = 3/100 × 20/100

                                                          = 0.006

                                                          = 0.60%

b. There are two faulty lights, P = 3/100 × 20/100 × 20/100

                                                          = 0.0012

                                                          = 0.12%

c. There is at least one faulty light = 3/100 ×1/5

                                                           = 0.006                                                                            

                                                           = 0.60%      

Thus, The probability of there is one faulty light is 0.60%, There are two faulty lights is 0.12% and There is at least one faulty light is 0.60%.

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Individuals basically use statistics to make decisions in financial planning and budgeting, while organizations are guided by statistics in financial policy decisions.

What exactly do you mean by statistics?

Given data :

Step 1 :

The statistics department at Brigham Young University (BYU) is doing research to contrast various teaching strategies.

For lengthy courses, two technological echelons are contrasted: standard and multimedia. Eight lecture parts with students are present. There are four teachers in all.

Step 2 :

Consider that we randomly select two professors to use standard technology and the other two to use multimedia technology. Various professors will have various teaching philosophies, which will eventually influence final grades. We won't be able to tell a teaching method from a piece of technology in this way. Regarding technological disparities, there is no assurance.

Step 3 :

The ideal plan would be to divide each teacher's lectures into two sections, one utilising normal technology and the other multimedia.

There are four blocks as a result, one for each teacher.

Variability would be reduced because they are all being taught by the same person.

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The mean number of hours worked per week by the respondents will be 37.68.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.

Number of hours worked per week                   Frequency

                       26 to 30                                              10

                        31 to 35                                              24

                       36 to 40                                              20

                        41 to 45                                               13

                       46 to 50                                               7

                        51 to 55                                               4

The mean is given as,

Mean = [28 x 10 + 33 x 24 + 38 x 20 + 43 x 13 + 48 x 7 + 53 x 4]

                                (10 + 24 + 20 + 13 + 7 + 4)

Mean = 2939 / 78

Mean = 37.68

The mean number of hours worked per week by the respondents will be 37.68.

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The slope equals the rise divided by the run: . You can determine the slope of a line from its graph by looking at the rise and run.

A line has the property that its slope remains constant throughout. Therefore, you may determine the slope by selecting any two points along the line's graph.

The definition of slope in mathematics is pretty close to how we normally define it. Slope is a mathematical term used to indicate a line's steepness and direction. A line's slope can be inferred from its graph alone, especially in relation to other lines plotted on the same coordinate plane.

slope=rise/run.

The ratio of the change in the y-value to the change in the x-value can also be used to determine slope. For instance: Given two points on the line, P = (0, -1) and Q = (4,1), we may compute

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The vector is given by  (1,4) and (1,4) for the given 2 conditons

A vector is a mathematical object that has both magnitude and direction. In physics, vectors are used to represent quantities such as velocity, force, and acceleration. In mathematics, vectors can be represented by an ordered list of numbers (also known as components or coordinates) that specify the magnitudes of the vector in different directions. Vectors can be added, subtracted and multiplied by scalars. They also have properties such as dot and cross product. Vectors can be represented graphically as directed line segments. They are used in various fields like physics, engineering, computer science etc.

Part 1:

The vector is given by (final -initial)

=> (5-4 , 6-2)

=> (1 , 4)

Part : 2

The 2nd vector is given by (final - initial)

=> (3-2 , 8-4)

=> (1 , 4)

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How the transformations below affect length, angles or both?

The most obvious concern is those who chose to respond to the survey may have different eating habits from those who did not respond.

One of the major worries when conducting a survey is that people who choose to reply can differ from those who choose not to. The term for this is nonresponse bias. The representativeness of the sample may be impacted by the traits, opinions, or actions of respondents that differ from those of non-respondents.

In this given case, the chef issued a survey to 1000 families, but only 150 of them responded, or 15% of the households. It's probable that those who are very interested in food or cooking will respond to the poll more frequently than others who aren't. Due to the possibility that the eating patterns of individuals who replied may not be typical of the total population, this could cause the sample to be skewed. Thus, the chef would need to consider the nonresponse bias when interpreting the results of the survey.

Complete Question:

Before opening a new restaurant, a chef wants to gather information about the eating habits of the local residents. He randomly selects 1000 households from all households in the area and mails a questionnaire to them. Of the 1000 surveys mailed, 150 are returned. Which of the following is the most obvious concern with how this information is gathered?

(A)Mailing questionnaires instead of conducting in-person interviews produce a convenience sample.

(B)Those who chose to respond to the survey may have different eating habits from those who did not respond.

(C)Only residents from the local area were polled.

(D)The chef must conduct a census in order to avoid all sources of bias.

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The surface area of the rectangular prism is: 312 ft².

The surface area of rectangular prism can be calculated using the formula that is given as:

Surface area (SA) = 2(w * l + h * l + h * w), where l is the length, w is the width, and h is the height of the rectangular prism.

Given the following dimensions of the rectangular prism as:

length (l) = 12 ft

width (w) =  3 ft

height (h) = 8 ft

Therefore:

Surface area of the rectangular prism = 2*(3 * 12 + 8 * 12 + 8 * 3) = 312 ft²

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Someone might have arrived at the incorrect number by incorrectly counting frequencies or not accounting for every data point.

Table 1.35 should be as follows:

Number of Years in US | Frequency

2  | 3

5  | 4

7  | 2

10 | 2

12 | 2

15 | 2

20 | 2

b. This statement is incorrect because 47 percent does not equal the total number of people surveyed.

c. This statement can be fixed by saying "Four out of the nineteen people surveyed have lived in the U.S. for 5 years."

d. The fraction of people surveyed who have lived in the U.S. for five or seven years is 6/19, or 31.58%.

e. The fraction of people surveyed who have lived in the U.S. for at most 12 years is 10/19, or 52.63%.

f. The fraction of people surveyed who have lived in the U.S. for fewer than 12 years is 9/19, or 47.37%.

g. The fraction of people surveyed who have lived in the U.S. from five to 20 years, inclusive, is 12/19, or 63.16%. This can be calculated by subtracting the number of people who have lived in the U.S. fewer than five years (3) from the number of people who have lived in the U.S. 20 or more years (2), and dividing the result (12) by the total number of people surveyed (19).

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Answer:

[tex]\sqrt{\frac{P}{R} }[/tex]

Step-by-step explanation:

[tex]P=I^2*R\\[/tex]

Divide both sides by R

[tex]\frac{P}{R} =I^2[/tex]

Remove the exponent by finding the square root of each side

[tex]\frac{\sqrt{P} }{\sqrt{R} } = I[/tex]

[tex]I=\sqrt{\frac{P}{R} }[/tex]

The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

When referring to a function, "end behaviour" refers to the character of the value as the function parameter becomes closer to +∞ and -∞.

In the given table for f(x), we see that for every value of x, function f(x) is decreasing.

f(-2) = 48

f(0) = 12

f(2) = 3

f(3) = 1.5

In other words as the value of x increases, f(x) is approaching towards 0.

Now we take another function g(x) =

Now we plug in the values of x to get the values of g(x)

g(-1) =2^-1-5  

    = 1-10/2

    = -9/2

    = -4.5

g(0) =  2^0-5

     = 1 - 5 = -4

g(2) = 2^2-5

     = 4 - 5 = -1

g(3) = 2^3-5

     = 8 - 5= 3

Now we find that g(x) is increasing with the values of x.

Now we take third function h(x).

By analyzing the given graph we find

h(-4) = 2

h(0) = 3

h(1) = 5

So when we are increasing the value of x function h(x) is increasing.

Finally we conclude by the options given that f(x) is the only function which tends to 0 with the increase in the values of x.

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