Which set of data has a mean of 15 a range of 22 a median of 14 and a mode of 14?.

The total amount owed after 3 years with the given rate of interest compounded quarterly will be $2851.52.

Compound interest is applicable when there will be a change in principal amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

Given that,

Principle amount P = $2000

Rate of interest R = 12%

Compounded quarterly n = 4

Time period T = 3 years

Total amount = P{1 + R/n]^(nT)

Total amount = 2000[1 + 0.12/4]^(4×3)

Total amount = $2851.52

Hence "The total amount owed after 3 years with the given rate of interest compounded quarterly will be $2851.52".

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3. Surface area of cone is 678.24 in²

  Volume of cone is 1017.4 in³

4. Surface area of Cuboid is  1534  sq meters

  Volume of Cuboid is 4080 cubic meters

5. Surface area of cylinder is 376.8 sq centimeters

  Volume of cylinder is 549.5 cubic centimeters

What are solids ?

A three-dimensional object that is closed (which may, according to some terminology conventions, be self-intersecting). A solid is any constrained area of space that is bounded by surfaces, according to Kern and Bland (1948, p. 18). The sphere, cube, cone, and cylinder, as well as the polyhedra more broadly, are some of the most basic solids.

Cone radius r = 9 in

h height = 12 in

Slant height, l² =9²+12² = 81+144 => l=15 in

Volume = (1/3)πr²h   = (1/3)*3.14*9²*12 = 1017.4 in³

Surface area = πr² + πrl  

                      = 3.14*9²+3.14*9*15

                      =254.34 + 423.9 = 678.24 in²

Cuboid volume =17*16*15  = 4080 cubic meters

Surface area = 2 ( 17*16 + 16*15 + 15*17)  = 1534  sq meters

cylinder Volume = πr²h  = π(5)²  * 7 =   549.5 cubic centimeters

cylinder Surface area= 2πr(r + h )   = 2*3.14*5(5+7) = 376.8 sq centimeters

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Answer:

y -1 = -1/3 (x -6)

Step-by-step explanation:

The inequality that represents the number of quarters in the jar is [tex]y \geq 24[/tex].

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Tyler filled a little container with quarters and dimes and gave it to his school's foundation club. The club party getting the container inquired, "Do you end up realizing how much is in the container?" Tyler said, "I know it's something like $8.50, yet I don't have a clue about the specific sum."

Let x be the number of dimes and y be the number of quarters. Then the inequality is given as,

0.10x + 0.25y ≤ 8.50

The inequality that represents the relationship will be 0.10x + 0.25y ≤ 8.50.

The inequality that represents the number of quarters in the jar, can be get by solving the above inequality for y, 0.10x + 0.25y ≤ 8.50.  can be written as [tex]y \geq \frac{8.5 - 2.5}{0.25}[/tex]  or  [tex]y \geq \frac{8.5}{0.25}[/tex]  or [tex]y \geq 24[/tex] .

Hence, the inequality that represents the number of quarters in the jar is   [tex]y \geq 24[/tex] .

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Answer: 4 deliveries per hour

Step-by-step explanation:

16 divided by 4 = 4 deliveries

The model assumption are satisfied in histogram, residuals vs order of collection and residuals vs fitted values.

HIstogram

We can see from the histogram that the residuals are normally distributed, so the assumption that the errors are normally distributed is met.

residuals vs. the fitted values

We find a circular pattern where the errors are concentrated based on the residuals vs. the fitted values. indicating a breach of the assumption of equal variance (homoscedasticity). There is another nonlinear pattern that should be investigated.

Residuals vs. Order of collection

: Because the residuals are randomly distributed, the assumption of equal variance of the residuals is not violated.

Residuals vs. gestational length

A The gear concentration of the residuals in the shape of an oval indicate additional signals from the data that have not been modelled. As a result, the assumption of equal variance of the residuals is violated, and it may also indicate a nonlinear relationship between the dependent and independent variables. This problem can be solved by taking the log of the independent variable and normalising the data.

Parity vs. residuals

Because this is a binary variable, the plot provides no clear indication.

Residuals vs. mother's height

There is a clear oval pattern visible, indicating that the variable is violated.

Residuals vs. mother's weight

There is a clear oval pattern visible, indicating that the variable is violated.

Smoking vs. Residuals

Because this is a binary variable, the plot provides no clear indication.

Overall, this is the next step. We must examine the variables for multicollinearity. Because the residuals histogram is normally distributed, but the residuals vs fitted values has a violation.

We must determine whether the independent variables are correlated with one another. If they are correlated, we must discard the one that is least correlated with the target variable.

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let's start by grouping the terms with the variable first, so that'd be

(x² - x) -3 = 0

(x² - x + []²) = 3

now, the middle term in a perfect square trinomial is simply the product of "2" and the root of the terms on the left and right sides, so whatever that product is, we know it must yield "x" because that's our middle term above skipping its sign, so hmmm let's check around

[tex]\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] ~\dotfill\\\\ (x^2 - x +\square^2)=3 \\\\\\ 2\sqrt{\square^2}\sqrt{x^2}~~ = ~~x\implies 2\square x=x\implies \square=\cfrac{x}{2x}\implies \square=\cfrac{1}{2}[/tex]

so that's our missing value, now ( 1/2 )² is 1/4, however, let's recall that, all we're doing is borrowing from our very good friend Mr. Zero, 0, so if we add 1/4 we also have to subtract 1/4

[tex]\left(x^2-x+\cfrac{1}{4}-\cfrac{1}{4} \right)=3\implies \left(x^2-x+\cfrac{1}{4} \right)-\cfrac{1}{4}=3 \\\\\\ \left(x^2-x+\left( \cfrac{1}{2} \right)^2 \right)=3+\cfrac{1}{4}\implies \left(x-\cfrac{1}{2} \right)^2=\cfrac{13}{4}\implies x-\cfrac{1}{2}=\pm\sqrt{\cfrac{13}{4}} \\\\\\ x-\cfrac{1}{2}=\pm\cfrac{\sqrt{13}}{2}\implies x=\pm\cfrac{\sqrt{13}}{2}+\cfrac{1}{2}\implies \boxed{x=\pm\cfrac{\sqrt{13}+1}{2}}[/tex]

The ladder is 26ft far up to the wall if the bottom of a 10-foot ladder is 2 ft closer to the wall.

A unit of length is any arbitrarily defined and agreed reference standard for measuring length.

The measurement or extent of something from end to end is defined as its length. In other words, it is the larger of two or the highest of three geometrical shapes or objects' dimensions. A rectangle, for example, has length and width dimensions.

Distance on the ground = 10 feet

Length of the  ladder (hypotenuse) = x      

Height on the wall =  x-2

According to the  Pythagorean theorem of a right angle,

a²+b²=c²

100  + (x-2)²  =x²

100 + x² -4x + 4 =  x²      

100 -4x + 4 = 0              

104 - 4x = 0                  

-4x = -104              

x = 26ft

The ladder is 26ft far up to the wall.

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In order for the two-sample z statistic to be valid we need that the following assumptions hold samples must be random

data has to be continuous

each sample and population must be independent from each other

each population must be normally distributed

the population standard deviations must be known or the sample sizes must be ≥ 30

samples must be random

data has to be continuous

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The total number of cups of punch that peter makes is  13 1/6.

The sum of the values 4 1/3, 2 1/3, and 6 1/2 is required. To make adding easier, let's first turn them into improper fractions:

= 13/ 3 + 7/3 + 13/2

We can now simplify it because two of a fractions use the same denominator, resulting in the following:

= 30/3 + 13/2

Next, we must determine which of the two fractions has the lowest common denominator.

We may modify our denominator to 6 because that is the smallest number so both 2 and 3 can fit in:

= 23/3 x (2/2) + 13/2 x (3/3)

= 40/6 + 39/6

= 79/6

We should change this back into such a mixed number for our response:

= 79/6

= 13 1/6

Thus, the total number of cups of punch that Peter makes is  13 1/6.

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The correct question is-

Peter mixes 4 1/3 cups of orange juice, 2 1/3 cups of ginger ale, and 6 1/2 cups of strawberry lemonade to make some punch. What is the total number of cups of punch that Peter makes?

In the Marital Instability Over the Life Course project, when men were asked to indicate the cause of their divorce, the most common response from the men was incompatibility. And the most common response from the women was infidelity.

Marital instability is described as including the range of activities from thinking about and discussing divorce to actually filing for either separation or divorce. There are a lot of causes of marital instability, but the most common causes are money problems and lack of intimacy.

Marital Instability Over the Life Course project is a nationwide longitudinal study started in 1980 with funding from the Social Security Administration's Office of Research and Statistics and the National Institute on Aging. This study measures predicting marital instability and divorce and assessing marital quality were developed.

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The solution for this system of linear equation is (-16, -5 1/3)

What in mathematics is a linear equation?

From the first equation, x = 3y

Substituting the expression on the right for the value of x on the second equation,

                                  -2(3y) + 3y = 16

Solving for the value of y gives y = -5 1/3

With this value of y, solving for x gives x = -16

Thus, the solution for this system of linear equation is (-16, -5 1/3)

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The complete question is -

What is the solution to this system of linear equations? x − 3y = −2 x + 3y = 16

20%(20 percent) of the people  are 25 or older according to the line plot that shows the ages of people taking a driving test at a certain station one day.

Percentage signifies a fraction of a total amount and means "per 100." For instance, 45% denotes 45 out of 100. Finding the percentage of a whole in terms of 100 is what percentage calculations are all about. It can be computed manually or with the use of internet calculators.

A % is a relative figure that represents one tenth of a quantity. One percent is a hundredth part; consequently, 100 percent denotes the complete amount and 200 percent specifies twice the supplied number. percentage

The word "percent" comes from the Latin per centum, which means "hundred" or "by the hundredth.

The total number of people we have are 25

From the line plot given, we see that fived people are 25, or older

Then,

5 / 25

=  1 / 5  

= 20 %

Hence, 20% of the people  are 25 or older according to the line plot that shows the ages of people taking a driving test at a certain station one day.

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The equation that best suits the sinusoidal function model in this situation is the option:
(C) y = -12cos(1/12x)+ 12.

What is the sinusoidal funtion?

A sine-based function is one that smoothly oscillates between high and low values on a periodic basis. This type of function is known as a sinusoidal function. The cosine function, which is merely a horizontal shift of the sine function, can also be used as the foundation for sinusoidal functions.

A sine wave, also known as a sinusoidal wave or simply a sinusoid, is a mathematical curve that can be described in terms of the sine trigonometric function, whose graph it is. It is a particular kind of smooth periodic function and continuous wave.

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A closed circuit is required to carry current. If there is a break anywhere in the path, the circuit will open and no current will flow, and the metal atoms in the wire will quickly become peaceful and electrically neutral.

Current flows in a closed circuit, but electrons are left behind in an open circuit.

Imagine a gallon of water flowing through an open pipe. Water flows for a short time, but stops when all the water comes out of the pipe. If you pump water into a closed system of pipes, it will continue to flow as long as you force it to move.

Closed circuit design:

breaks are often created by design. For example, a simple light switch opens or closes the circuit that connects the light to the power source. When building a circuit, it is recommended that the battery or other power source be disconnected when the circuit is not in use. Technically, this creates an open circuit. The

extinguished flashlight is an open circuit. In the flashlight shown here, the flat black button on the bottom left controls the internal switch. A switch is nothing more than two flexible metal strips in close proximity to each other. Push the black button all the way to the right to open the switch and turn off the flashlight. The switch in the open position disconnects the bulb from the battery, creating an open circuit.So, for the light bulb in a circuit turn on when the switch is closed.

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The possible sources of inaccuracy that could have an impact on your results are -

While conducting a scientific experiment, numerous errors—either systematic or random—could happen.

Thus, more measuring is done when the bias is smaller and more measuring is done when the uncertainty is smaller.

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A power function is in the form of f(x) = kx^n, where k = all real numbers and n = all real numbers. You can change the way the graph of a power function looks by changing the values of k and n.

The power function is a function that links the true value of a parameter to the probability of rejecting a null hypothesis about the value of that parameter.

A power function is a function with a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real number. (A number that multiplies a variable raised to an exponent is known as a coefficient.) As an example, consider functions for area or volume.

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The distance traveled in 3 seconds is 3/100 miles.

The term "Distance Traveled" describes how far an object has traveled during a specified amount of time to get to its destination. Or The path that a body takes to go a specific distance at a certain speed from one location to another is known as the distance traveled.

The distance can travel in 1 minute.

In order to find the distance traveled in 1 minute, first we need to find the distance traveled in 1 second.

In 3 seconds it can travel 3/100 miles. So, in 1 second it can travel

= 3/100 × 3

= 1/100 miles.

Now, we know that in 1 minute there are 60 seconds. So, in 1 minute it can travel

= 1/100 × 60

= 1/10 × 6

= 6/10

= 0.6 mile

Hence, it can travel 0.6 miles in a minute.

Complete question:

The average sneeze can travel 3/100 mile in 3 seconds. at this rate how far can it travel in 1 minute​

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Step-by-step explanation:

x = the number

15x + x/2 = 62

30x + x = 124

31x = 124

x = 4

To figure how many paths there are from (0,0) to (50,50) on a Cartesian coordinate system is using the legal moves, move up and move right. The formula that can be used is ((x+y)¦x). Here the steps;

Each path from point (0,0) to (50,50) will contain 50 rightward steps (i.e. progressive along the x-axis) and 50 upward steps (progressive along y-axis), resulting in a total of 100 steps, therefore we have ((x+y)¦x)= ((50+50)¦50) = (100¦50) ways of creating such a path.

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The correct notation for the 8th term of the expansion (3x – 5)12 would be (3x)^(-5)8.

The term "expansion" describes the process of expanding or expanding. It can be used to describe actual expansion, such as when an organism gets bigger or a gas expands to fill a container. It can also relate to abstract notions such as the development of thoughts or knowledge. Extension in economics refers to growth in the size of the economy or in a specific sector of the economy, such as a rise in goods and services output. The process of conquering or occupying additional areas, such as when a nation extends its borders by conquest or settlement, is another definition of expansion. The act of growing larger or more extensive is generally referred to as expansion.

How to solve?

(3x – 5)12 = (3x)12 – 12(3x)11(5) + 66(3x)10(5^2) – 220(3x)9(5^3) + ... + (-5)12

The 8th term of the expansion (3x – 5)12 is (-5)8(3x)4, which can be written as (3x)^(-5)8.

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Answer:

Step-by-step explanation:

They are giving you the parts to plug into the quations that SOH CAH TOA helps  you recall

SOH =  Sin(∅) = Opp / Hyp

CAH = Cos(∅) Adj / Hyp

TOA = Tan(∅) = Opp  / Adj

if the above isn't enough help,  then look at which one of the formulas above has two parts of information given in the question and then, you need to find the last one.

I see that TOA has two parts of info, and then we only need to find Adj.  understand?

we will find X  this way.  Adj = X

use the formula and then plug in the knowns

Tan(35°) =  574 / Adj

Tan(35°) =  574 / X

X = 574 / Tan(35°)

understand how I got to that?

once you have X , use pythagoras to find Y

[tex]y^{2}[/tex] = [tex]x^{2}[/tex] + [tex]574^{2}[/tex]

got it?

the linear regression equation that represents this set of data rounding all coefficients to the nearest tenth is ŷ = 0.23571X + 75.24762

Sum of X = 120

Sum of Y = 1157

Mean X = 8

Mean Y = 77.1333

Sum of squares  = 280

Sum of products (SP) = 66

Regression Equation = ŷ = bX + a

b  = 66/280 = 0.23571

a = 77.13 - (0.24*8) = 75.24762

ŷ = 0.23571X + 75.24762

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The time taken to get to work from home with a speed of 30mph will be 40 minutes, 40mph in 30 minutes, and 50mph in 24 minutes.

Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.

Average velocity can be given as;

Average velocity = total distance / total time taken

Units of velocity are given by ⇒ meter/second

As per the given,

Time = distance/speed

Distance = 20 miles

With a speed of 30 mph

Time = 20/30 = 2/3 hour or 40 minutes

With a speed of 40 mph

Time = 20/40 = 1/2 hour or 30 minutes

With a speed of 50 mph

Time = 20/50 = 2/5 hour or 24 minutes

Hence "The time taken to get to work from home with a speed of 30mph will be 40 minutes, 40mph in 30 minutes, and 50mph in 24 minutes".

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When two of a triangle's angles and one of its included sides are congruent with the equivalent portion of another triangle, the two triangles are said to be in AAS or ASA congruency.

AAS Congruency:

Therefore, when two of a triangle's angles and one of its included sides are congruent with the equivalent portion of another triangle, the two triangles are said to be in ASA or AAS congruency.

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The slope of the given function of taxi fare mean  the rate of change of the cost of the taxi ride is $3.00 per minute..

In the situation y = mx + c the worth of m is known as the slant, (or angle), of the line. It very well may be positive, negative or zero. Lines with a positive inclination slant upwards, from left to right. Lines with a negative inclination slant downwards from left to right. Lines with a zero inclination are level.

C(x) = 3x + 2

On comparing with the general equation of line. we get

slope = 3  

slope = cost/time

Which says the rate of change of the cost of the taxi ride is $3.00 per minute.

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Disinfection of dental impressions should last b)15 minutes. So, correct option is b.

Disinfection of dental impressions is an essential routine that actually aims to protect the dental personnel, who handle impressions or casts, against exposure to diseases brought about by the contact with microorganisms such as the viruses; hepatitis B, hepatitis C, herpes, and HIV, and Mycobacterium tuberculosis (Hemalatha & Ganapathy, 2016).

Impression materials that have been exposed to the infected saliva and blood provides a significant source of such infectious agents. Dental checkups are increasing now a days very frequently.

Hence, option b is correct.

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(Complete question) is:

disinfection of dental impressions should last minutes. a)5 b)15 c)30 d)60

For the given xy-plane where point C coordinates are (6,9) then equation of the line containing point O and C is given by y = ( 3/2)x.

As given in the question,

Given xy -plane,

Coordinates of the point C are (6, 9)

Coordinates of the point O are (0, 0)

Let ( x₁ , y₁) = ( 0, 0)

(x₂ , y₂) = (6, 9)

Equation of the line containing point O and C are :

( y - y₁)/(x - x₁ ) = ( y₂ - y₁)/(x₂ - x₁)

⇒ ( y -0)/(x - 0) = ( 9 - 0)/( 6 - 0)

⇒ y / x = 9 /6

⇒ y = (3/2)x

Therefore, for the given xy-plane where point C coordinates are (6,9) then equation of the line containing point O and C is given by y = ( 3/2)x.

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In the 1980s and 1990s, many urban area kids in New York turned to "Selling Drugs" as a means of supplemental income as a means of escape.

The crack epidemic that ravaged New York City with in 1980s was beginning to fade by the early 1990s, and crime rates were also declining.

Thus, during the 1980s and 1990s, many urban area kids in New York turned to "Selling Drugs" as a means of supplemental income as a means of escape.

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