Measures of Relative Position
Calculate the five-number summary of the given data. 13,4,20,2,14,18,22,12,22,12,20,12,22,23,12
Enter your answers in ascending order, separating each answer with a comma.

The equation of the tangent line is:
y = 12x - 47.25
where the slope m is 12 and the y-intercept b is -47.25.

To find the slope of the tangent line to the curve y at the point (4, 0.75), we first need to find the derivative of y with respect to x. Let's assume that the equation of the curve y is given by:

y = f(x)

Then, the derivative of y with respect to x is given by:

dy/dx = f'(x)

where f'(x) is the derivative of f(x).

Once we have the derivative, we can evaluate it at x = 4 to find the slope of the tangent line at the point (4, 0.75). So, let's find the derivative of y:

y = f(x) = x^3 - 12x^2 + 36x - 25

Taking the derivative with respect to x, we get:

dy/dx = 3x^2 - 24x + 36

Now, we can evaluate this derivative at x = 4 to get the slope of the tangent line:

dy/dx = 3(4)^2 - 24(4) + 36 = 12

So, the slope of the tangent line at the point (4, 0.75) is 12.

To write the equation of the tangent line in the form y = mx + b, we need to find the y-intercept b. We know that the point (4, 0.75) lies on the tangent line, so we can use this point and the slope we just found to find b:

y = mx + b
0.75 = 12(4) + b
b = -47.25

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Answer: the answer is 0.5 inch(es)

Step-by-step explanation:

correct me if i’m wrong

The depth in inches just before snow begins to melt is 7 inches. The correct option is B.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the depth of snow melting on a sidewalk changes over time. The equation below represents the depth (d) in inch(es) as time (t) passes is d = -0.5t +7.

The depth at the beginning is calculated by putting the value of t = 0. At the initial period, the time is zero.

d = -0.5t +7.

d = ( 0.5 x 0 ) + 7

d = 7 inches

Therefore, the depth in inches just before snow begins to melt is 7 inches. The correct option is B.

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RMSE =  (nΣt=1 (At-Ft)²/n is the formula .

What is Root Mean Square Error (RMSE)?

What makes a good RMSE?

Identify the formula used to calculate the root mean square error over a range of forecasted values, if the actual value of the time series at time t and the forecast value for time t are denoted by A t and F t respectively.

RMSE = [ (nΣt=1 (At-Ft)2) / n ]0.5

MSE = (nΣt=1 (At-Ft)²/n

RMSE = Root of MSE

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The mistake Jadyn made in the long division is

Long division refers to a way of dividing large numbers

performing the long division correctly gives

divisor    dividend     quotient     multiplication    subtraction  new dividend

8             335              40               8 * 40 = 320     335 - 320       15          

8             15                 1                   8 * 1 = 8            15 - 8                7  

8             70                0.8               8 * 8 = 64      70 - 64                6

8             60                0.07             8 * 7 = 56       60 - 56               4

8             40                0.005           8 * 5 = 40       40 - 40               0

The quotient is then added as

40 + 1 + 0.8 + 0.07 + 0.005 = 41.875

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The claim that there is not much difference between qualitative and quantitative data is incorrect.

Qualitative and quantitative data are two distinct types of data that serve different purposes and have different characteristics.

Qualitative data refers to non-numerical information that is typically obtained through observations, interviews, or surveys. It provides insights into opinions, attitudes, behaviors, and subjective experiences. Qualitative data is often descriptive in nature, expressed in words, narratives, or themes. It allows researchers to explore complex phenomena, understand contextual factors, and capture the richness of human experiences. Examples of qualitative data include interview transcripts, field notes, and open-ended survey responses.

On the other hand, quantitative data is numerical in nature and involves the collection and analysis of measurable variables. It focuses on quantities, statistical analysis, and mathematical modeling. Quantitative data allows researchers to quantify relationships, make predictions, and conduct statistical tests. It is often collected through surveys, experiments, or structured observations. Examples of quantitative data include numerical measurements, survey responses on a Likert scale, and statistical values such as means and standard deviations.

In conclusion, qualitative and quantitative data are distinct in their characteristics, purpose, and analytical approaches. The claim that there is not much difference between them is incorrect.

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The value of standard normal variable z is - 1.31 when z satisfies p( -z < z < z) = 0. 8788.

A normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution. The standard normal distribution is centered at zero, and the standard deviation indicates how much a measurement deviates from the mean.

p( -z < z < z) = 0. 8788

According to the standard normal distribution table

p( -z < z < z) = - 2.91 + 1.16

                  = - 1.31

Therefore the value of standard normal variable z is - 1.31

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Sorry, but this problem cannot be simplified.

It stays how it is.

Answer:

4 1/2

Step-by-step explanation:

Step 1:

1/2 + 2/3 ÷ 1/6     Equation

Step 2:

1/2 + 2/3 × 6/1      Flip the Fraction

Step 3:

1/2 + 2/1 × 2/1    Simplify

Step 4:

1/2 + 4      Multiply

Answer:

4 1/2     Add

Hope This Helps :)

Answer:

0.625

Step-by-step explanation:

5 out of 8 of the sections in the circle are yellow. This means that there is a 5/8 chance of the spinner landing in a yellow section.

5/8 written as a decimal is 0.625

The answer is 0.625

Some of the groups of cards that have the same sum are:

Group 1               Group 2                    Sum

{8, 1}                      {7, 2}                         9

{8, 2}                     {7, 3}                         10

{8, 3}                     {7, 3, 1}                      11

{8, 1, 3}                  {7, 3, 2}                     12

From the question, we have the following parameters that can be used in our computation:

Numbers: 8 7 6 2 1 3.​

In the above group of numbers, we have

Highest = 8

Least = 1

When these are added, we have

8 + 1 = 9

Another set of numbers that have a sum of 9 is (7, 2)

There are several other numbers that can be created

Some of these numbers are

And several others

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the answer is A ;)))))

Answer:

2 months

Step-by-step explanation:

$80 x 0.5 = $40

$80 + $40 = $120

$120 * 0.25 = $30

1st month - $120-$30 = $90

2nd month - $90-$22.5 = $67.5

Answer:

AFTER 2 MONTHS

Step-by-step explanation:

Answer:

cannot be determined

Step-by-step explanation:

you know they are similar triangles because their angles are congruent, but you cannot determine if they are the same because you are not given that any of their sides are congruent

Answer:

The slope of the graph is -3

Step-by-step explanation:

do rise over run.

3 down, 1 right

Answer:

0 (as you already know)

Step-by-step explanation:

First we will simplify both sides of this equation:

5f = -125 + 175 + -35 + -15

Now we are going to Combine Like Terms:

5f = (-125 + 175 + -35 + -15)

5f = 0

Divide both sides by 5

5f / 5 = 0 / 5

F = 0

Hope this helps

\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

Let's find the Radius ~

\(\qquad \sf  \dashrightarrow \: area = \frac{ \theta}{360} \times \pi {r}^{2} \)

\(\qquad \sf  \dashrightarrow \: 80= \frac{ 72}{360} \times \pi {r}^{2} \)

\(\qquad \sf  \dashrightarrow \: {r}^{2} = \frac{80 \times 360}{72 \times \pi} \)

\(\qquad \sf  \dashrightarrow \: {r}^{2} = \frac{80 \times 5}{ \pi} \)

\(\qquad \sf  \dashrightarrow \: {r}^{} = \sqrt\frac{400}{ \pi} \)

\(\qquad \sf  \dashrightarrow \:r = \frac{20}{ \sqrt{\pi} } \)

or

\(\qquad \sf  \dashrightarrow \:r \approx 11.28 \: ft\)

I hope you understood the whole procedure, let me know if you have doubts ~

➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

Answer:

43°

Step-by-step explanation:

-the interior angle of a triangle always adds up to 180°

- angles that form a straight line always adds up to 180°

- the angle at 75° has the angle of 105° to add up to 180°

- the triangle needs a full degree of 180, but only affs up to 137° (105° + 32°) so you have to subtract the 137° from the total amount you need(180°) which gives you the answer of 43°

Answer:

Step-by-step explanation:

it cant be 73° then it would look about the same size as 75°

and it cant be 15° cause it would look smaller than 32°.

so in my Opinion it looks like it would be 43°.

sorry if its wrong

Answer:Points, Lines, and Ang. A midpoint is a point that bisects, or divides, a line segment into two congruent pi. Point B is the midpoint of AC

Step-by-step explanation:

Answer:

if you make the 3.5 equal 7/2

and the 1.40 equal 7/5 its will be more easier

so7/5 × 7/2 its 4.9

sorry guys its not 4.9 i made mistake with 3.25 i was thinking that it was 3.50 any wwy

i have good method too

we can make 3.25 equal 13/4 and 1.40 equal 7/5 the multiply it

we will find 91/20 but we have problem its The 10 dont worry we can take the 10 from the both number and we will get 9.1/2 and We can devide easily now and the answer is 4.55

sorry iam trying so hard to speak engilish well sorry if u cannot understand me big respet for all the students

A student need a raw score of 36.

We can find the raw score (R) of the student by substituting A = 60 into the the formula and then solve for R. That is:

A = 10√R

√R = 60/10

√R = 6

R = 6²

R = 36

Thus, a student need a raw score of 36 to get a passing grade after her score is adjusted.

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The measure of angle PQR is given as follows:

To obtain the measure of angle PQR, first we verify if the triangle PQR is a right triangle or not.

To verify if the triangle is a right triangle we apply the Pythagorean Theorem, which states that the length of the hypotenuse squared is equals to the sum of the lengths of each side squared, in the case of a right triangle.

Hence, for this problem, considering the side lengths, we have that:

10² = 6² + 8²

100 = 36 + 64

100 = 100.

Which is true, hence this is in fact a right triangle and the measure of angle PQR is of 90º.

The problem asks for the measure of angle PQR.

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An engineer is designing a fuel tank in the shape of a cylinder, the approximate radius of the cylinder is 8.2 inches.

Volume:

V = πr²h

Height:

h = 2r

V = πr²h

V= πr²(2r)

V= 2πr³

And we know that the volume must be 3,500 in³, now we can replace that and solve for R, we will get:

V= πr²h

3500 = 3.14 x 2 x (r)³

r = 8.2 inch

The cylinder's approximate radius must be 8.2 inches.

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. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterised as an infinitely curved surface.

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Answer:

2.)-1,5/2 is your answer

Step-by-step explanation:

2x2 - 3x = 5

2x²-3x-5=0

do ing middle term factorization

2x²-5x+2x-5=0

x(2x-5)+1(2x-5)=0

(2x-5)(x+1)=0

either

x=5/2

or

x=-1

Answer:

\( \displaystyle \: 2) - 1,\frac{5}{2} \)

Step-by-step explanation:

we are given a quadratic equation

\( \displaystyle \: {2x}^{2} - 3x = 5\)

we have to determine the roots

to do so first bring it to standard form i.e

ax²+bx+c=0

move left hand side expression to right hand side and change its sign:

\( \displaystyle \: {2x}^{2} - 3x - 5 =0\)

since we moved left hand side expression to right hand side there's only 0 left to the left hand side

we'll use factoring method to solve the quadratic

first, we need to express the middle term as a sum or subtraction of two different terms

to do so

rewrite -3x as 2x-5x:

\( \displaystyle \: {2x}^{2} + 2x - 5x- 5 =0\)

now we have two common factors 2x and -5 so

factor them out:

\( \displaystyle \: 2x ({x} + 1 )- 5(x + 1) =0\)

group:

\( \displaystyle \: (2x - 5) (x + 1) =0\)

since 2x-5 and x+1 both equal 0

separate the equation as two different equation:

\( \displaystyle \: \begin{cases}2x - 5=0 \\ x + 1 = 0\end{cases}\)

let's work with the first equation:

add 5 to both sides:

\( \displaystyle \: 2x - 5 + 5 = 0 + 5 \\ 2x = 5\)

divide both sides by 2:

\( \displaystyle \: \frac{2x}{2} = \frac{5}{2} \\ \therefore \: x_{} = \frac{5}{2} \)

let's work with the second one

cancel 1 from both sides:

\( \displaystyle \: x + 1 - 1 = 1 - 1 \\ \therefore \: x = - 1\)

hence,

our answer choice is \(\text{option 2}\)

The shaded area under the probability curve for X = female wrist girth (cm) represents the probability of certain events related to the wrist girth. The interpretation of the shaded area depends on its location and the given statements.

         The shaded area under a probability curve represents the probability of an event occurring within a specific range. In this case, we are considering the female wrist girth (X) and its associated probability curve.

If the shaded area is to the right of 16 cm, we interpret it as the probability that a woman has a wrist girth larger than 16 cm.

If the shaded area represents a single point exactly at 16 cm, we interpret it as the probability that a woman has a wrist girth of exactly 16 cm.

If the shaded area is to the left of 16 cm, we interpret it as the probability that a woman has a wrist girth less than 16 cm.

However, without further information or a visual representation, it is difficult to determine the exact interpretation of the shaded area. The context and the specific statements provided would help clarify the intended meaning of the shaded area.

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Answer: A , C and F

Step-by-step explanation:

Answer: 3a

Step-by-step explanation:

(4a*6a)/8a

24a^2/8a

3a

\(4a\times6a\)

\(4\times6=24\\4a\times6a=24a\)

\(\dfrac{24a}{8a}\)

\(=\fbox{3a}\)

a) Draw the process flow sheet for the enriching column.

b) Calculate the mole fraction of acetone in the sidestream (Xs).

c) Calculate the mole fraction of acetone in the bottoms (X3).

d) Determine the number of equilibrium stages required.

a) To draw the process flow sheet for the enriching column, we start with the feed stream at the bottom of the column. This stream contains a mixture of acetone and ethanol, with a flow rate of 100.0 mol/min and a composition of 60.0 mol% acetone. The feed stream is a saturated vapor. The liquid side product is withdrawn from the third stage below the total condenser at a flow rate of 15.0 mol/min. Reflux is returned as a saturated liquid. The distillate, which is the top product, has a composition of 91.0 mol% acetone. The column operates at a pressure of 1.0 atm and is adiabatic.

b) To find the mole fraction of acetone in the sidestream (Xs), we need to consider the material balance. The total number of moles entering the column is 100.0 mol/min, and the sidestream flow rate is 15.0 mol/min. Since the sidestream is a liquid, we can assume that it is in equilibrium with the vapor phase at the third stage. Using the equilibrium relationship, we can calculate the mole fraction of acetone in the sidestream.

c) To find the mole fraction of acetone in the bottoms (X3), we need to consider the material balance again. The total number of moles entering the column is 100.0 mol/min, and the sidestream flow rate is 15.0 mol/min. Therefore, the flow rate of the bottoms is 100.0 - 15.0 = 85.0 mol/min. Using the equilibrium relationship, we can calculate the mole fraction of acetone in the bottoms.

d) To determine the number of equilibrium stages required, we need to use the concept of equilibrium stages. Each equilibrium stage represents the separation achieved by the column. The reflux ratio (L/D) is given as 7/2, which means that for every 2 moles of distillate (acetone-rich), 7 moles of liquid reflux (saturated liquid) are returned to the column. By using the equilibrium relationship and the given compositions, we can calculate the number of equilibrium stages required for the desired separation.

In summary, to answer the given questions:

a) Draw the process flow sheet for the enriching column.

b) Calculate the mole fraction of acetone in the sidestream (Xs).

c) Calculate the mole fraction of acetone in the bottoms (X3).

d) Determine the number of equilibrium stages required.

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Answer:

\(a_n=4n-11\)

Step-by-step explanation:

The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:

\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)

Answer:

2 20/69

Step-by-step explanation:

Answer:

2 12/11

Step-by-step explanation:

7 9/6 / 2 3/4

34/11