1/4 (20x−28) <2(x−3)+2

If the best fit line is nearly horizontal, it suggests no significant relationship between height and head circumference.

In this scenario, the explanatory variable is the child's height, as it is being used to predict the head circumference.

The response variable is the head circumference itself, as it is the variable being predicted or explained by the height.

To draw a scatter diagram of the data, you would plot the child's height on the x-axis and the corresponding head circumference on the y-axis. Each data point would represent a child's measurement pair.

Once all the data points are plotted, you can then draw the best fit line, also known as the regression line, that represents the overall trend or relationship between height and head circumference.

By observing the scatter diagram and the best fit line, you can determine the relationship between a child's height and head circumference.

If the best fit line has a positive slope, it indicates a positive relationship, meaning that as height increases, head circumference tends to increase as well.

If the best fit line has a negative slope, it indicates a negative relationship, meaning that as height increases, head circumference tends to decrease.

By assessing the slope of the best fit line in the scatter diagram, you can determine whether the relationship between height and head circumference is positive, negative, or nonexistent.

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The velocity of the ball when it is 384 ft above the ground on its way down is 0 ft/s.

(a) The maximum height is found at the vertex of the quadratic equation s = 160t - 16t². By using the formula t = -b/2a (where a = -16 and b = 160), we determine the time t = 5 seconds. Substituting this into the equation, we find the maximum height: s = 160(5) - 16(5)² = 400 ft.

(b) The velocity function v(t) is obtained by differentiating the position equation: v(t) = 160 - 32t.

When the ball is 384 ft above the ground on its way up (t = 2 seconds), we find v(2) = 96 ft/s.

When the ball is 384 ft above the ground on its way down (t = 5 seconds, maximum height), we find v(5) = 0 ft/s.

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The fourth vertex's coordinates are as follows: ( 2.1, -3.6)

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

So, let the missing coordinates be (a,b).

Let's now utilize the midpoint formula to locate the erroneous coordinate.

Let the reference point be (-2.3, 3.6) A.

Let point B be (2.3, 2.2).

(2.1, 2.2) Let C be the point.

The center of AC should be at BD.

Step 1: Locating the AC's midpoint

Middle pint of AC:

(-2.3 + 2.1/2), (-3.6 + 2.2/2)

(0.2/2), (1.4/2)

(-0.1, -0.7)

Let's equate the midpoints in step two.

The BD mid-point:

(a + -2.3/2), (b + 2.2/2) =  (-0.1, -0.7)

(a + -2.3/2) = -0.1

(a -2.3/2) = -0.1*2

a = -0.2+2.3

a = 2.1

(b + 2.2/2) = -0.7

b + 2.2 = -0.7*2

b + 2.2 = -1.4

b = -1.4 -2.2

b = -3.6

Therefore, the fourth vertex's coordinates are as follows: ( 2.1, -3.6)

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Complete question:

Freddy drew a plan for a rectangular piece of material that hehe will use for a blanket. Three of the vertices are ​( -2.3 and −3.6​), ​(−2.3​, and 2.2​), and ​(2.1​, and 2.2​). What are the coordinates of the fourth​ vertex?

Answer:

A) there are no outliers in this distribution.

Answer:

16-(4*x)-(4*x^2)+x^3

Step-by-step explanation:

(x+2)(x-2)(x-4)

16-(4*x)-(4*x^2)+x^3

Answer:

x= 8

Step-by-step explanation:

The graph of the reflected function: g(x) = 3^(-x) can be seen in the image at the end.

First, for any function y = f(x), a reflection across the y-axis is written as:

g(x) = f(-x)

So we only change the sign of the argument of the function.

The graphed function is the parent function:

f(x) = 3^x

A reflection across the y-axis, will give the new function:

g(x) = f(x) = 3^(-x)

The graph of this will be like the graph of f(x) but reflected across the y-axis, like the graph below.

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Answer:

(c+3b)/8 = a

Step-by-step explanation:

c = 8a -3b

Add 3b to each side

c +3b = 8a-3b+3b

c +3b = 8a

Divide each side by 8

(c+3b)/8 = 8a/8

(c+3b)/8 = a

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

\(\stackrel{f(x)}{y}~~ = ~~2x^2+4x\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~2y^2+4y} \\\\\\ x=2(y^2+2y)\implies \cfrac{x}{2}=y^2+2y\impliedby \begin{array}{llll} \textit{now let's complete the square}\\ \textit{to make it a perfect square trinomial}\\ \textit{by using our good friend, Mr "0"} \end{array} \\\\\\ \cfrac{x}{2}=y^2+2y(+1^2-1^2)\implies \cfrac{x}{2}=y^2+2y+1-1\implies \cfrac{x}{2}=(y^2+2y+1)-1\)

\(\cfrac{x}{2}+1=(y^2+2y+1^2)\implies \cfrac{x}{2}+1=(y+1)^2\implies \sqrt{\cfrac{x}{2}+1}=y+1 \\\\\\ \sqrt{\cfrac{x+2}{2}}=y+1\implies \sqrt{\cfrac{x+2}{2}}-1=y~~ = ~~f^{-1}(x)\)

Answer:i think its 115 degres

Step-by-step explanation:

We have

As we can see in order to find the shaded area of the figure, we only need to calculate the area of a square.

the shaded area is 400 mm^2

Answer:

He is correct

Step-by-step explanation:

Put the first equation into y = mx + b by isolating y:

4x + 2y = 10

2y = -4x + 10

Divide each side by 2:

y = -2x + 5

So, putting the first equation into y = mx + b got us the same equation as the second one, y = -2x + 5.

Since they are the same, the equations are equivalent.

Atticus is correct.

The given statement, "We can use the normal distribution to approximate the sampling distribution of the average (\(\bar X\)) for a small sample (n<30) even if our sample has clear outliers." is false.

Several random samples of a predetermined size are taken from the same population to generate a sampling distribution, which is a sort of probability distribution. You can better understand how a sample statistic fluctuates from sample to sample by using these distributions.

The given statement is false because when the sample size is small (n < 30) and the data have clear outliers, the normal distribution may not be a suitable approximation for the sampling distribution of the average (\(\bar X\)). In such cases, the presence of outliers can significantly affect the distribution, causing it to deviate from a normal distribution.

For small samples with outliers, it is generally recommended to use alternative methods or non-parametric tests that do not assume a specific distribution. These methods take into account the non-normal nature of the data and provide more robust and reliable results.

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Answer:

2.25 ft^2

Step-by-step explanation:

area of kite = half of the product of diagonals

A = (3 ft)(0.75 ft + 0.75 ft)/2

A = 2.25 ft^2

Answer: 8x^2 + xy - 15y^2

Step-by-step explanation:

first do the FOIL method than add 3xy to the equation after

Answer:

\(8x^2+xy-15y^2\)

Step-by-step explanation:

\((4x+5y)(2x-3y)+3xy\\\\=(4x)(2x)+(4x)(-3y)+(5y)(2x)+(5y)(-3y)+3xy\\\\=8x^2-12xy+10xy-15y^2+3xy\\\\=8x^2+xy-15y^2\)

Complete question :

WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in:

a. More than 20 minutes? b. For 20 minutes or less

Answer: 0.0764 ; 0.9236

Step-by-step explanation:

Mean (m) = 15 minutes

Standard deviation (sd) = 3.5

Z - score :

Z = (x - m) / sd

A) more than 20 minutes

P(X > 20) ; x = 20

Z > (20 - 15) / 3.5 = 5/3.5 = 1.429

P(z > 1.429) = 0.5 - P(0<z<1.43)

Using the z-table: 1.43 = 0.4236

0.5 - 0.4236 = 0.0764

2) 20 minutes or less :

P(X <= 20) ; x = 20

Z < (20 - 15) / 3.5 = 5/3.5 = 1.429

P(z < 1.429) = 0.5 + P(0<z<1.43)

Using the z-table: 1.43 = 0.4236

0.5 + 0.4236 = 0.9236

Answer:

24/25

Step-by-step explanation:

sin 2 θ = 3÷25/8 =24/25

from web2calc

Answer:

24/25

Step-by-step explanation:

P(u, v) = (3, 4) describes a triangle:  One vertex is at the origin (0, 0) and the other at (3, 4).  According to the Pythagorean Theorem, 3^2 + 4^2 = 5^2, so we know the hypotenuse length is 5 units.

Recall that the sine function is defined as opp/hyp, which here is 4/5, and that the cosine function as adj/hyp, which here is 3/5.  

Finally, we'll apply the double angle formula sin 2x = 2 sinx cos x.

Substituting the values found above,              sin 2x = 2(4/5)(3/5) = 24/25.

The sine of 2x (where x is the smaller acute angle whose vertex is (0, 0) ) is 24/25.

The speed of the train with time is given on a speed time graph

obtained from a past questions website drawn and attached here.

Correct response:

Given:

Length of the train = 220 m

Time at which the train crossed the bridge = 9:30

Length of the bridge = 1,400 m

The plot of the graph of the motion of the train obtained from a past papers website and created with MS Excel is attached;

From the attached graph, we have;

The speed of the train at 9:30 = 126 km/h

Required:

The time it took the train to completely cross the bridge.

Solution:

\(126 \, km/h = 126 \, km/hr \times \dfrac{1,000 \, m}{1 \, km} \times \dfrac{1 \ hr}{3,600 \, s} = \mathbf{ 35 \, m/s}\)

Therefore, the time it took the train to completely cross the bridge is given as follows;

Distance traveled = 1,400 m + 220 m = 1,620 m

The time it took the train to completely cross the bridge is t ≈ 46.29 s

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The value(s) of k that make the function continuous over the given interval are k ≥ 0.

To determine the values of k that make the function f(x) continuous over the interval [0, 5] and (5, 10], we need to ensure that the function is defined and has no discontinuities at the endpoints and the transition point.

For the function f(x) = √(kx), the square root function is defined for non-negative values of its argument. Therefore, for the interval [0, 5], we require that kx ≥ 0 for all x in the interval. Since x is non-negative, it follows that k must also be non-negative or k ≥ 0.

For the interval (5, 10], the function is given by f(x) = x + 2, which is a linear function and is continuous for all real values of x. In this case, the value of k does not affect the continuity of the function.

In summary, for the function f(x) = √(kx) to be continuous over the interval [0, 5] and (5, 10], we need k to be non-negative or k ≥ 0.

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The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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Step-by-step explanation:

holaaaaaaaaaaaaaaaaaaa22zz

Answer:

5800

Step-by-step explanation:

thank me

c:

Answer: 24

Step-by-step explanation:

The length of the QR is 16 cm when PQR ~MNO

In the given question, it is given that two similar triangles as PQR ~MNO

Then, the corresponding sides will be in equal proportion to each other as follows

PQ / MN = PR / MO = QR / NO

We need to find the length of the side QR

As above relations are given,

\(\frac{PQ}{MN}\) = \(\frac{PR}{MO}\) = \(\frac{QR}{NO}\)

\(\frac{30}{10}\) = \(\frac{5x + 7}{x+5}\) = \(\frac{4x}{\frac{16}{3} }\)

Equating all the fractions, equal to each we'll find

\(\frac{5x + 7}{x+5}\) = \(\frac{30}{10}\)

5x + 7 = 3(x +5)

5x + 7 = 3x + 15

2x = 8

x = 4

We know that, the length of the QR = 4x cm = 4 x 4 cm = 16 cm

Therefore, the length of the QR is 16 cm when PQR ~MNO

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To draw the graph of the function f(x) = 2 - x^2 using a graphing calculator, follow these steps: Turn on your graphing calculator and enter the function f(x) = 2 - x^2 into the calculator's equation editor.

Set the viewing window of the calculator to a suitable range, such as -5 ≤ x ≤ 5 and -5 ≤ y ≤ 5, to capture the shape of the graph. Press the "Graph" button to plot the graph of f(x). The graph of f(x) = 2 - x^2 should appear on the screen as a downward-opening parabola centered at the point (0, 2). You can use the arrow keys on the calculator to move around and explore different parts of the graph.

The graph of f(x) = 2 - x^2 will show a symmetric curve that opens downwards. The highest point on the graph will be at (0, 2), and the curve will extend infinitely in both the positive and negative x-directions.

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4.8 packages will need for the use of one year.

No. of used packages of printer paper during 10 months = 4 Packages

As we know that there is 12 months in a year,

To determine the number of packages need for the year, first we have to find the number of package is being use in one month.

S0,  No. of used package in 1 month = 4/10 = 0.4 Package

Now, we will determine the number of packages for the use of one year, by multiplying the No. of used package in 1 month with 12.

No. of packages for the use of one year = 12 × 0.4

                                                                   = 4.8 Packages

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Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

To dilate a point at a point, you start by selecting a center of dilation and a scale factor.

Then, for each point that you want to dilate, you do the following:

For example, if you wanted to dilate point P by a scale factor of 2, with the center of dilation at O, you would draw a line segment from O to P, double its length, and then draw a new line segment from O to the new point, using the new length that you calculated. The new point would be the point that you arrive at when you complete this line segment.

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