Question 3(Multiple Choice Worth 2 points)
(Effects of Changes in Data MC)

The shoe sizes of a group of middle school girls are shown.


5.5 6 7 8.5 6.5
6.5 8 7.5 8 5

If a shoe size of 7 is added to the data, how does the IQR change?
The IQR becomes a 2.5.
The IQR becomes a 1.5.
The IQR remains a 3.
The IQR remains a 2.

a) The mean number of cars owned for this sample is, 77.75

b) The standard deviation of cars owned for this sample is, 12.44

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

The following table shows the number of people that have either 0, 1, 2 or 3 cars registered in their name, from a sample of 311 people.

x       n

0      79

1       79

2      59

3      94

a) Now, the mean number of cars owned for this sample is,

⇒ Mean = (79 + 79 + 59 + 94) / 4

             = 77.75

Thus, the mean number of cars owned for this sample is, 77.75.

We know that;

Standard deviation = √ (xₐ - μ)² / N

Where, xₐ is each value from the population, μ is mean and N is number of points on data set.

Now, For a = 0, 1, 2, 3

Standard deviation = √ (xₐ - μ)² / N

Standard deviation = √(79 - 77.8)² + (79 - 77.8)²+ (59 - 77.8)²+ (94 - 77.8)²/4

Standard deviation = √1.44 + 1.44 + 353.44 + 262.44 / 4

Standard deviation = √154.69

Standard deviation = 12.44

Learn more about the addition visit:

https://brainly.com/question/25421984

#SPJ1

By calculating the distance we know that the PR measures 198.94 ft to the nearest foot.

Distance is the sum of an object's movements, regardless of direction.

The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively.

The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

So, the triangles PRE and POC appear to be comparable triangles in the diagram.

Let PR = x.

Utilizing the similarity theorem:

PR/RE = PR+RO/OC

x/135 = (x+140)/230

Now, cross multiply as follows:

230x = 135(x+ 140)

230x = 135x + 18,900

230x - 135x = 18,900

95x = 18900

x =18900/95

x = 198.94

Therefore, by calculating the distance we know that the PR measures 198.94 ft to the nearest foot.

Know more about the distance here:

https://brainly.com/question/26550516

#SPJ1

Correct question:

To indirectly measure the distance across a river, Nolan stands on one side of the river and uses sight lines to a landmark on the opposite bank. Nolan draws the diagram below to show the lengths and angles that he measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.

The lengths of a triangle must satisfy the triangle inequality which states that the sum of any two sides must be greater than the third side.

For option A:

5 + 9 = 14, which satisfies the triangle inequality. However, 5 + 14 = 19, which is not greater than 9. Therefore, this set of numbers does not satisfy the triangle inequality.

For option B:

7 + 7 = 14, which is less than 15. Therefore, this set of numbers does not satisfy the triangle inequality.

For option C:

1 + 2 = 3, which satisfies the triangle inequality. However, 1 + 4 = 5, which is not greater than 2. Therefore, this set of numbers does not satisfy the triangle inequality.

For option D:

3 + 6 = 9, which satisfies the triangle inequality. 3 + 8 = 11 and 6 + 8 = 14, both of which are greater than 8. Therefore, this set of numbers satisfies the triangle inequality.

So, the numbers 3, 6, and 8 could represent the lengths of a triangle. Therefore, the answer is option D.

Answer:

A and D

Step-by-step explanation:

you would have to test each option using the triangle inequality theorem

which is when the sum of any two sides of the triangle are greater than or equal to the third side

A)  5+9 [tex]\geq[/tex] 14  true

     5+14 [tex]\geq[/tex] 9  true

     14+9 [tex]\geq[/tex] 5  true

B)  7+7 [tex]\geq[/tex] 15  false    This answer can be eliminated

C)  1+2 [tex]\geq[/tex] 4    false     This answer can be eliminated

D)  3+6 [tex]\geq[/tex] 9  true

     3+8 [tex]\geq[/tex] 6   true

     6+9 [tex]\geq[/tex] 3   true      

Car B will catch up with Car A at 4:45pm, after travelling for 2 5/8 hours (3 hours minus 1 hour minus 3/8 of an hour).

Car A leaves the Grand Canyon at noon and travels at 80 mph. At 3 pm, it stops for an hour. Car B leaves the Grand Canyon at 2 pm and travels at 90 mph without stopping.To calculate when Car B will catch up with Car A, we need to find the time difference between their departure times and the difference in their speeds.Car A leaves one hour before Car B, so we can subtract 1 hour from the total travel time. The difference in their speeds is 10 mph, which is equivalent to 1/8 of an hour for every hour of travel. Therefore, we can subtract 1/8 of an hour from the total travel time for every hour of travel.We can use these two deductions to calculate the total travel time: 3 hours - 1 hour - 3/8 of an hour = 2 5/8 hours. Therefore, Car B will catch up with Car A at 4:45pm.

Learn more about travelling here

https://brainly.com/question/17235551
#SPJ4

A definite integral is an integral of a function over a closed interval. An improper integral is a definite integral that has at least one of its limits of integration set at infinity or an interval of integration that is infinite.

This can happen when the domain of the function is infinite or when one of the limits of integration is infinite. In this case, the integral can either diverge (no finite answer) or it may converge to a finite value. In either case, it is an improper integral.

A definite integral is an integral of a function over a closed interval, taking the form of the definite integral: ∫ a b f(x)dx. This means that the function is integrated from the lower limit of “a” to the upper limit “b”. An improper integral is a definite integral where either one of the limits of integration is set at infinity or the interval of integration is infinite. This can happen when the domain of the function is infinite, meaning that the function exists and is defined for all real numbers, or when one of the limits of integration is infinite. In this case, the integral can either diverge (no finite answer) or it may converge to a finite value. In either case, it is an improper integral, and it must be treated differently than a regular definite integral.

learn more about function here

https://brainly.com/question/12431044

#SPJ4

The length of EF= 15 cm.

As, the question states that the triangles are similar; their ratios are also equal.

AC/DF = AB/DE - CB/EF

Plug in the values

12/10 = AB/DE = 18/EF

If we isolate EF,

EF = 180/12

EF= 15cm

Read more about geometry here:

https://brainly.com/question/19241268

#SPJ1

Answer:

The vertical height above the runway to the nearest foot is 580 feet.

Step-by-step explanation:

The vertical height is opposite the angle 75 degrees, and the hypotenuse is 600 ft. The trigonometric function sine will be used since sine = opposite/hypotenuse and we're solving for the opposite side and have the hypotenuse.

Let x be the vertical height.

[tex]\frac{sin(75)}{1} = \frac{x}{600}[/tex]

x = sin(75) * 600

x = 579.555495773

The question is asking for the vertical height rounded to the nearest foot, which is 580.

Option (A): The height of the given ice cream cylindrical tubs is 7.35 inches.

What is a cylinder?

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. An infinite curvilinear surface is another way to describe a cylinder. A cylinder's surface area is the area that its surface takes up in three dimensions. A three-dimensional structure known as a cylinder has circular bases that are parallel to one another. There are no vertices on it. The area of three-dimensional shapes often refers to the surface area. Square units are used to denote the surface area.

Given,

 The total surface area of the given cylindrical tub = 387.79 in.²

The diameter of the tub = 2r =  10 inches

where r = radius

r = 10/2 = 5 inches

W are asked to find the height h of the tub

The formula for the total surface of a cylinder = 2πr² + 2 π rh

387.79 = 2 * 3.14 * 5*5 + 2 * 3.14 * 5 * h

387.79 - 157 = 31.4h

h = 7.35 inches

Therefore the height of the given ice cream cylindrical tubs is 7.35 inches.

To learn more about a cylinder, follow the link.

https://brainly.com/question/23935577

#SPJ1

Answer:

7.35 inches

Step-by-step explanation:

I took the test and got it right :)

The total marginal cost of using 8 bottles is $8.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Marginal utility of 1 bottle of Gatorade costs =  1$

Now,

The total marginal cost of using 8 bottles.

= 8 x $1

= $8

Thus,

The total marginal cost of using 8 bottles is $8.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The complete question:

Marginal utility of 1 bottle of Gatorade that costs 1$.

Find the total marginal cost for using 8 bottles of Gatorade.

Answer:

The exponential model that represents the population y of the city t years after 2014 is y = 471,000 * 1.04^t.

The estimated population in 2020 is about 591,000.

Answer:

x = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Solve for x

[tex]\frac{2}3}(3-6x)=-3(8x-4)[/tex]

Distribute [tex]\frac{2}{3}[/tex] and -3.

[tex]2-4x=-24x+12[/tex]

Simplify

[tex]-4x+2=-24x+12[/tex]

Subtract 2 on both sides

[tex]-4x=-24x+10[/tex]

Subtract -24x on both sides

[tex]20x=10[/tex]

Divide by 20

[tex]x=\frac{1}{2}[/tex] or 0.5

The required simplified value of the given expression [tex]\dfrac{2^{3x+1}-2^{3x}}{4*2^{3x - 1}}[/tex] is 1/2.

A rational expression is a mathematical expression that is the ratio of two polynomial expressions. That is, a rational expression is formed by dividing one polynomial expression by another polynomial expression.

Here,
Given expression,
[tex]=\dfrac{2^{3x+1}-2^{3x}}{4*2^{3x - 1}}[/tex]

Rewriting the equation by splitting the terms in numerator and denominator in order to take common terms out and make the expression more simple.

We can write [tex]2^{3x+1} = 2^{3x} * 2[/tex] and [tex]2^{3x-1} = 2^{3x} /2[/tex] so,

Given expression becomes, hence cancel the common terms.
[tex]=\dfrac{2^{3x}*2-2^{3x}}{4*2^{3x}/2}\\=1/2[/tex]

Thus, the required simplified value of the given expression [tex]\dfrac{2^{3x+1}-2^{3x}}{4*2^{3x - 1}}[/tex] is 1/2.

Learn more about rational expression here:

https://brainly.com/question/16906465
#SPJ9

Answer:

Exponential decay by 9% each cycle (n).

Step-by-step explanation:

The function y = 51(0.91)^n is an exponential decay function.  The term (0.91) is less than 1, so when multiplied by anything, the result will be less than the original number, by 9% [(100-91)/100].  The power n, represents the number of cycles (e.g., days, minutes, years, seconds, etc.).  Each succeeding cycle reduces the previous number by the same amount of (0.91).  

See the attached graph.

On 1 slice of pizza there will be 1/24th of the cheese and the constant of proportionality is 1/3.

Define Proportion.

The word "proportion" generally denotes a portion, share, or sum when contrasted to a total. When two ratios are equal, they are in proportion, as stated by the definition of proportion. Two ratios or fractions are equal when an equation is applied, or when a statement to that effect is made.

Two sets of supplied numbers are said to grow or fall in the same ratio in terms of proportion if they are directly proportionate to one another. For proportionality, use the symbols ":" or "=".

Given, 50lbs of cheese is used for 150 large pizzas.

For 1 pizza cheese used will be= 50/150

=1/3

So, the constant of proportionality here is 1/3.

Now, in 1 pizza there are 8 slices.

Cheese for each slice= 1/3 × 1/8

= 1/24.

Therefore, on 1 slice of pizza there will be 1/24th of the cheese.

To know more about proportions, visit:

https://brainly.com/question/30657439

#SPJ1

The mathematical phrase "e to the ipi" is composed of the imaginary unit i (the square root of -1 raised to the power of pi), which is symbolized by "pi," and the mathematical constant "e" (Euler's number).

The expression "e to the ipi" may be expressed as follows:

[tex]e^{(i*pi)}[/tex]

The following formula is known as Euler's formula:

[tex]e^{(ipi)}[/tex] = cos(pi) + isin(pi)

where "cos" and "sin" are the sine and cosine functions, respectively.

We may reduce this formula to using the cosine and sine trigonometric identities.

[tex]e^{(i*pi)}[/tex] = -1

"e to the ipi" hence equals a negative one. This startling and outstanding finding ties together various crucial mathematical ideas, including calculus, complex numbers, and trigonometry.

Learn more about Euler's number at

https://brainly.com/question/6459192

#SPJ4

220 lbs is approximately equal to 99.7903 kg  ( rounded to four decimal places )

The conversion factor to convert lbs to kilogram is 0.453592

1 lbs = 0.453592 kg

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in kg = The mass in lbs × conversion factor

Substitute the values in the equation

1 lbs = 0.453592 kg

220 lbs = 220 × 0.453592

Multiply the numbers

= 99.7903 kg ( rounded to four decimal places )

Therefore, 220 lbs is 99.7903 kg

Learn more about conversion factor here

brainly.com/question/5056146

#SPJ4

The transformations applied are: reflection about the x-axis, horizontal shift 10 units to the right, and vertical shift 400 units up.

A parabola is a symmetrical, U-shaped curve that can be formed by intersecting a plane with a cone. It is defined by the quadratic equation [tex]y = ax^2 + bx + c.[/tex]

Solution:

To identify the transformations that have been applied to the graph of [tex]f(x) = x^2[/tex]to produce the graph of [tex]g(x) = -5x^2 + 100x - 450[/tex] we can start by looking at the standard form equation for a parabola:

[tex]y = a(x - h)^2 + k[/tex]

where (h, k) is the vertex of the parabola and "a" determines the shape and direction of the parabola.

For[tex]f(x) = x^2[/tex], we have a = 1, h = 0, and k = 0, so the vertex is at (0, 0).

For [tex]g(x) = -5x^2 + 100x - 450[/tex], we can rewrite it as:

[tex]g(x) = -5(x^2 - 20x + 90)[/tex]

Completing the square inside the parentheses, we get:

[tex]g(x) = -5(x - 10)^2 + 400[/tex]

So the vertex of the parabola is (10, 400), and the "a" value is -5, which means the parabola is upside-down compared to[tex]f(x) = x^2.[/tex]

Therefore, the transformations that have been applied to f(x) to obtain g(x) are:

1. The graph is reflected vertically (flipped upside-down) due to the negative "a" value.

2. The graph is shifted 10 units to the right and 400 units up, which corresponds to a horizontal translation of 10 units and a vertical translation of 400 units.

In summary, the transformations applied are: reflection about the x-axis, horizontal shift 10 units to the right, and vertical shift 400 units up.

To learn more about Parabola from the given link

brainly.com/question/25651698

#SPJ1

nswer:

Step-by-step explanation:

6102.36 inches

Rember that you multiply the lentclength value by 39.37

To convert any number of meters to miles, you simply need to multiply the number of meters by this conversion factor 0.000621371192

The conversion factor from meter to miles is  0.000621371192

1 meter = 0.000621371192 miles

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

So, to convert meter to miles you can multiply the number of kilometers by 0.000621371192

The distance in miles = conversion factor × The distance in meters

Therefore, the steps to convert meter to miles has been explained

Learn more about conversion factor here

brainly.com/question/23718955

#SPJ4

The linear equation will be y=7000+4550n where n=no. of year greater than 1.

What is a linear equation, exactly?

When the greatest power of a variable is 1, the equation is said to be linear. Other term used for it is a one-degree equation. The standard form of a linear equation with one variable is Ax + B = 0. There are three variables in this equation: x, A, and B. A denotes a coefficient. A linear equation with only two variables is commonly written as Ax + By = C. There is three more constants added to the constant C: the variables x and y, the coefficients A and B, and the variables.

and general equation of line is y=mx+c

where m=slope=y2-y1/x2-x1

Now,

Given that no. of lionfish after a year=7000

and increment is 65% every year that means 65/100*7000

=4550 lionfish are added every year after 1 year

so the equation to represent lionfish in n years will be

Y=7000+4550n, where n>1 and n is no. of years.

hence,

          The linear equation will be y=7000+4550n.

To know about linear equations visit the link

https://brainly.com/question/29739212

#SPJ1

The conversion of 22 kg to lbs is 48.50164 lbs.

Kilogram (kg) and pound (lbs) are both units of mass or weight.

Kilogram is the base unit of mass in the International System of Units (SI). It is defined as the mass of the International Prototype of the Kilogram (IPK), a platinum-iridium cylinder kept at the International Bureau of Weights and Measures.

To convert 22 kilograms (kg) to pounds (lbs), we can use the conversion factor of 1 kg = 2.20462 lbs.

So, we can multiply 22 kg by 2.20462 lbs/kg to get the equivalent weight in pounds:

22 kg × 2.20462 lbs/kg = 48.50164 lbs (rounded to five decimal places)

Therefore, 22 kg is approximately equal to 48.50164 lbs.

To learn more about kg here:

https://brainly.com/question/17080950

#SPJ4

Answer:

[tex](x - 3)^2 + (y + 2)^2 = 41[/tex]

Step-by-step explanation:

The general shape of the equation is:

(x-a)² + (y-b)² = r²

Where (a,b) is the center and r is the radius.

(a,b) = (3,-2) is given.

To find the radius r, or even simpler, r², calculate the distance between (-3,2) and (8,2) using pythagoras.

r² = (8-3)² + (2--2)² = 41

Answer:

5. 2

15. 6

30. 12

Step-by-step explanation:

For every 5 miles walked, he walks for 2 hours each.

For example:

Miles. Hours

5. 2

10. 4

15. 6

20. 8

25. 10

30. 12

Answer:

Anything.

Step-by-step explanation:

The reason why I say " anything " is because the fraction, [tex]\frac{1}{1}[/tex] is bascially representing the number 1, nothing else so you can put whatever you want, tens, hundreds, thousands, millions, and so on.

So whatever number you want to put it will always equal, [tex]\frac{1}{1}[/tex], But just remember to always put the number that you choose on top or the numerator such as the following:

[tex]\frac{4}{1}[/tex].

Thus, you answer is, anything.

a) The coordinates of G are (3, -4)

b) The name of the line through G and E is y = (-3/2)x + 13/2

(a) Since the line x=1 is a line of symmetry for triangle EFG, we know that G must lie on the same line of symmetry, and hence its x-coordinate should be reflected across the line x=1 from the x-coordinate of E.

The x-coordinate of E is 5, so the x-coordinate of G should be 5-2=3. That is, G has an x-coordinate of 3.

Similarly, since the line x=1 is a line of symmetry, the y-coordinate of G should be the same as the y-coordinate of F, which is -4. Therefore, G has a y-coordinate of -4.

Thus, the coordinates of G are (3, -4).

(b) To find the name of the line through G and E, we can first calculate the slope of the line:

slope = (y2 - y1)/(x2 - x1) = (-4 - 2)/(3 - 5) = -3/2

The line through G and E has a slope of -3/2.

Next, we can use the point-slope form of the equation of a line to find the equation of the line. We can use either point E or point G to write the equation, but it might be easier to use point G since we have already calculated its coordinates.

Using point-slope form with point G and the slope -3/2, we get:

y - (-4) = (-3/2)(x - 3)

Simplifying and rearranging, we get:

y = (-3/2)x + 13/2

Learn more about coordinates here

brainly.com/question/14778438

#SPJ4

Table A is representing  a function, and Table B does not represent a function.

What is function?

Function, can be stated as an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

When a Table needs to be a function, it need to satisfy following conditions (look at the .jpeg image attached with this answer):

1. condition: every image has its pre-image,

in other words, In first circle, EVERY element has to be connected with SOME of the elements in second circle

2. condition: every image has only on pre-image.

in other words, In first circle, there MUSTN'T be an element that has MORE THAN ONE connection with elements in second circle

Table A satisfies BOTH of these conditions; that is why table A is indeed a function.

Table B satisfies FIRST condition but it does not satisfy the SECOND condition, that is why it is NOT a function.

To learn more on function click:

brainly.com/question/21145944

#SPJ9

57 kilograms is approximately equal to 125.66334 pounds.

A kilogram (symbol: kg) is the base unit of mass in the International System of Units (SI).

A pound (symbol: lb) is a unit of mass used in the imperial and US customary systems of measurement.

1 kg = 2.2046226218 lbs

1 lbs = 0.45359237 kg

To convert 57 kg to pounds, we need to multiply the value in kilograms by 2.20462,

Since one kilogram is approximately equal to 2.20462 pounds.

Therefore,

57 kg multiplied by 2.20462 gives us:

57 kg x 2.20462 = 125.66334 pounds (rounded to five decimal places)

So 57 kilograms is approximately equal to 125.66334 pounds.

For similar questions on conversion of kilogram to pounds,

https://brainly.com/question/24757786

#SPJ4

The required solutions to the equation are x = 2 or x = -14.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Starting with the equation:

(x + 6)² = 64

Taking the square root of both sides, we get:

x + 6 = ±8

Solving for x, we have two cases:

Case 1:
x + 6 = 8

x = 8 - 6

x = 2

Case 2:
x + 6 = -8

x = -8 - 6

x = -14

Therefore, the solutions to the equation are x = 2 or x = -14.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ1

The numerator of the z-score test statistic measures the difference between the sample mean and the population mean (or the hypothesized population mean, depending on the context) in terms of the standard error of the mean.

It can use z- test only if the population standard deviation is known (or given) and the sample is large (more than 30 units)

If the mean and standard deviation is known, then the z-score is calculated using the formula.

z = (x - μ) / σ

where x is data;

μ is the mean and σ is the standard deviation.

Thus, the actual distance between a sample mean x and a population mean µ is measured by the numerator of z- score test statistic.

To know more about hypothesis here

https://brainly.com/question/29996729

#SPJ4