Explain why it is likely that the distributions of the
following variables will be normal:
a) the volume of soft drinks in cans
b) the diameter of bolts immediately after manufacture.l

An equation that represents the same relationship include the following: D. y = -3x + 1.5.

In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁) or [tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]

Where:

At data point (-3.5, 10.5), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - 10.5 = \frac{(3- 10.5)}{(-0.5 +3)}(x +3)[/tex]

y - 10.5 = -3(x + 3)

y = -3x - 9 + 10.5.

y = -3x + 1.5

In this context, we can reasonably infer and logically deduce that a linear function of the line that represents this table in slope-intercept form is y = -3x + 1.5.

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The volume of the solid bounded below by the cone z = √(x^2 + y^2) and bounded above by the sphere x^2 + y^2 + z^2 = 18 is 192π/3 cubic units

To find the volume of the solid bounded below by the cone z = √(x^2 + y^2) and bounded above by the sphere x^2 + y^2 + z^2 = 18, we can use a triple integral.

First, we need to determine the limits of integration. Since the solid is symmetric about the z-axis, we can use cylindrical coordinates.

The cone is given by z = √(x^2 + y^2), which in cylindrical coordinates becomes z = r. The sphere is given by x^2 + y^2 + z^2 = 18, which in cylindrical coordinates becomes r^2 + z^2 = 18.

Thus, the limits of integration are

0 ≤ r ≤ √(18 - z^2)

0 ≤ θ ≤ 2π

0 ≤ z ≤ √(r^2)

The integral to find the volume is

V = ∭ dV = ∫∫∫ dV

Using cylindrical coordinates, dV = r dz dr dθ, so the integral becomes

V = ∫₀²π ∫₀ᵣ√(18 - z²) ∫₀ᵣ r dz dr dθ

We can simplify this integral by first integrating with respect to z:

V = ∫₀²π ∫₀ᵣ√(18 - z²) r dz dr dθ

Using a trigonometric substitution u = z/√(18 - z²), we can simplify this to

V = ∫₀²π ∫₀¹ r√(18 - u²(18)) 18du dr dθ

V = 18∫₀²π ∫₀¹ r√(18(1 - u²)) du dr dθ

Using another substitution u = sin(θ), we can simplify this to:

V = 36∫₀²π ∫₀¹ r√(1 - u²) du dr dθ

This integral can be evaluated using the formula for the volume of a sphere of radius R

V = 36(4/3 π(√2)³)

V = 192π/3 cubic units

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The given question is incomplete, the complete question is:

Use a triple integral to find the volume of the solid bounded below by the cone z = √(x^2 + y^2 ) and bounded above by the sphere x^2 + y^2 + z^2 = 18

Answer:

the answer is $10

Step-by-step explanation:

trust that

Answer: t = 1.8 seconds

Step-by-step explanation:

The function h(t) = 25t^2 - 81 gives the height of the rock (in feet) at time t seconds after it was dropped.

When the rock lands, its height is 0. So we can set h(t) = 0 and solve for t:

25t^2 - 81 = 0

Solving for t, we get:

t = ±√(81/25) = ±(9/5)

Since we are only interested in the time after the rock was dropped, we take the positive value:

t = 9/5 = 1.8 seconds

Therefore, the time between when the rock was dropped and when it landed is 1.8 seconds.

So the answer is: t = 1.8 seconds

Answer: $27.98

Step-by-step explanation:

22.00 × .2= 4.40

22 + 4.40 = 26.40

26.40 × .06 = 1.584

26.40 + 1.584 = 27.984

Round to the nearest hundred so the total paid by the customer would be 27.98

Answer:0.40

Step-by-step explanation:

the experimental probability of winning the contest is 0.4 or 40%.

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 denotes the impossibility of the occurrence and 1 denotes its certainty. An occurrence is more likely to occur the higher its probability.

Players: 123 + 155 + 172, or 450 total

52 plus 63 plus 65 winners make up the total of 180.

Experimental probability of winning the contest = Total number of winners / Total number of players

Experimental probability of winning the contest = 180 / 450 = 0.4

Hence, the experimental probability of winning the contest is 0.4 or 40%

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Step 1: Rearrange the equation √x +2y^2 = 15 to get x = (15 - 2y^2)^2.

Step 2: Substitute x = (15 - 2y^2)^2 in the equation √4x - 4y^2=6.

Step 3: Simplify the equation to get 4(15 - 2y^2)^2 - 4y^2 = 6.

Step 4: Solve for y^2 by rearranging the equation to get y^2 = (6 + 4(15 - 2y^2)^2)/8.

Step 5: Substitute y^2 = (6 + 4(15 - 2y^2)^2)/8 in the equation x = (15 - 2y^2)^2.

Step 6: Solve for x by rearranging the equation to get x = (15 - (6 + 4(15 - 2y^2)^2)/4)^2.

Step 7: Substitute y^2 = (6 + 4(15 - 2y^2)^2)/8 in the equation x = (15 - (6 + 4(15 - 2y^2)^2)/4)^2.

Step 8: Simplify the equation to get x = (15 - (6 + 60 - 8y^

Answer:

Step-by-step explanation:

$75.06×2%=$75.06×0.02=$1.50

The finance charge is the product of the unpaid balance and the periodic rate.

Selection bias can creep into a study if subjects are picked (intentionally or not) according to some criterion and not randomly.

Selection bias occurs when the selection of study participants is not random and is instead influenced by certain criteria. This can result in a non-representative sample that does not accurately reflect the population being studied, leading to inaccurate conclusions. For example, if a study on the effectiveness of a medication only enrolls participants who are already known to respond well to that medication, the results may overestimate its effectiveness in the general population. To minimize selection bias, researchers should use random sampling techniques and carefully consider the inclusion and exclusion criteria .

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Solution In the Attachment Above

Answer: x = 2, y = 0

Step-by-step explanation:

Assuming you need help solving for x or y, and the capital Y is y, we have the system of equations:

3x + y = 6

y + 2 = x

Substituting x for y + 2 gives us

3(y + 2) + y = 6

3y + 6 + y = 6

4y = 0

y = 0

Plugging y = 0 in for the second equation gives us

x = 0 + 2, or x = 2

Answer:

Relating SSE to Other Statistical Data



The claims under "Regression" are as follows: 1. can be described by the l

Regression is a statistical technique that connects one or more independent (explanatory) variables to a dependent variable. If there is a relationship between changes in one or more of the explanatory factors and changes in the dependent variable, it can be shown using a regression model.

Y = mx + b is how the slope-intercept form of the equation for a straight line is expressed.

In the equation y = mx + b, m denotes the slope of the line and b its intercept. The distance between the line and the x- and y-axes is denoted by the letters x and y, respectively.

The first of the following claims, "Is used to assess the fit of a model," is true.

b) By including more factors, the result may be overstated.

called the coefficient of determination.

d.) Indicates the proportion of the variation in y that the model can account for.

e.) It is equivalent to the correlation coefficient r2 in basic linear regression.

What is Regression Analysis?

A collection of statistical procedures known as regression analysis is used to estimate the correlations between a dependent variable and one or more independent variables.

SS(res) + SS(reg) = SS, R2 1 - SS(res) / SS(tot) (tot)

R2 is defined as (SS(reg)/SS(tot) = (SS(reg)/n)/(SS(tot)/n)

Where SS(tot) = (y - y(bar)), the total sum of squares (proportional to the variance of the data), 2 • The explained sum of squares, also known as the regression sum of squares, is SS(reg) = (f(i)-y(bar)). SS(res) = (y(i) - f(i))2 = e2 is the sum of squares of residuals, often known as the residual sum of squares (i)

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Answer:

Step-by-step explanation:

Answer:

[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&AB&BC&AC\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&3.61&4&3.61\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&4.47&5.39&3.61\\\cline{1-4}\end{array}[/tex]

[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&m \angle A&m \angle B&m \angle C\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&67.38^{\circ}&56.31^{\circ}&56.31^{\circ}\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&82.87^{\circ}&41.63^{\circ}&55.49^{\circ}\\\cline{1-4}\end{array}[/tex]

Step-by-step explanation:

Place points A, B and C on the coordinate grid.

Alternatively, type the following into the input field as 3 separate inputs:

Triangle 1

Triangle 2

Use the Segment tool to join each pair of points.

Alternatively, type Segment( <Point>, <Point> ) into the input field (replacing <Point> with the letter name of the point) to create a segment between two points.

Record the length of each side.

[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&AB&BC&AC\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&3.61&4&3.61\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&4.47&5.39&3.61\\\cline{1-4}\end{array}[/tex]

Use the Angle tool to measure each angle in the resulting triangle.

Alternatively, type Angle(Polygon(A, B, C)) into the input field to create all interior angles.

Record the measure of each angle.

[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&m \angle A&m \angle B&m \angle C\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&67.38^{\circ}&56.31^{\circ}&56.31^{\circ}\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&82.87^{\circ}&41.63^{\circ}&55.49^{\circ}\\\cline{1-4}\end{array}[/tex]

Note: All measurements have been given to the nearest hundredth (2 decimal places).

Step-by-step explanation:

All of the EXTERNAL angles of a polygon sum to 360 °

95 + 44 + 42 + 78 + p = 360°

   p =101°

  then   q + p  form a straight line = 180 °

     so q =  79 °

The graph is of the given equation is represented in the figure below.

The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic.

By dividing the price change by the fluctuation in the amount of deli meat, one may calculate the slope. The magnitude indicates that the price per pound of deli meat has changed by 3.5 units.

Given linear equation represents the cost measured in dollars, as a function of the amount of deli meat, measured in pounds:

[tex]y = 3.5x[/tex]

The graph is of that linear equation as plotted below diagram.

By dividing the price change by the fluctuation in the amount of deli meat, one may calculate the slope. The magnitude denotes a change in the price per pound of deli meat of 3.5 units.

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The graph is of the given equation is represented in the figure below linear line: Y = 3.5x

The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic.

By dividing the price change by the fluctuation in the amount of deli meat, one may calculate the slope. The magnitude indicates that the price per pound of deli meat has changed by 3.5 units.
Given linear equation represents the cost measured in dollars, as a function of the amount of deli meat, measured in pounds:
Linear line: Y = 3.5x

The graph is of that linear equation as plotted below diagram.
By dividing the price change by the fluctuation in the amount of deli meat, one may calculate the slope. The magnitude denotes a change in the price per pound of deli meat of 3.5 units.

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Answer:

she payed 78% of the origional price

Step-by-step explanation: ok so boom right 20% of 3200 is 640  so that would make 2% 64 which would be the discount voucher ( 20% = 640 take a away a 0 on both and it shows u) so u do the 20% plus the 2% and that would make 22% and 22-100 is 78%. :)

The coordinate of fourth point of a parallelogram is (2,0)

We need to remember that the diagonals of a parallelogram intersect each other at a halfway point and the midpoint of each diagonal is the same.

A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram's adjacent angles add up to 180 degrees.

The midpoint formula

[tex]M=\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}[/tex]

AC=BD

We can find the coordinates of the fourth vertex  (x,y) through this procedure:

For x

[tex]\frac{5-2}{2}=\frac{0+x}{2}\\\\x=2\\\\for\ y \\\frac{2-2}{2}=\frac{y+2}{2}\\\\y=0[/tex]

Hence the coordinate of fourth point is (2,0)

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Answer:

y = -5x + 5

Step-by-step explanation:

y = mx + b

y = __x + __

To write the equation we need the slope (m) and the y-intercept (b).

Slope:

The is the change in y over the change in x.  As the y is decreeing by 5, the x is increasing by 1. This gives us the slope -5/1 = -5

y-intercept:

The y intercept is the point (0,b).  It is when x equals zero. If we start at 1 and go back to 0.  That mean that the y increase by 5, so the intercept is at the point (0,5) which makes the y-intercept 5.

y = -5x + 5

Helping in the name of Jesus.

Answer:

J   29%

Step-by-step explanation:

Monthly rent: $600.

There are 12 months in 1 year, so the total rent she pays in 1 year is

12 × $600 = $7200

We need to find what percent $7200 is of $25,000.

percent = part/whole × 100%

percent = 7200/25000 × 100%

percent = 28.8%

Rounded to the nearest percent, the answer is 29%.

Answer:

10 binders ........... .......... .....

Answer:

For this one I assigned y as the missing number

We know that $6 magazine plus $9 times a specific amount would equal $78

so 6 + 9(y) = 78

6 + 9(8) = 78

9(8)=72

72+6=78

So there were 8 binders bought at $9 each and a 1 magazine bought for $6.

Step-by-step explanation:

Solving for CI in terms of the given lengths, we get: [tex]Cl=\frac{\sqrt{BG^{2} -IM^{2} } }{\sqrt{2} }[/tex]

Substituting this expression for CI and the given value for CG into the expression for BI, we get:  [tex]BI=CG-\frac{\sqrt{BG^{2} -IM^{2} } }{\sqrt{2} }[/tex].

A triangle is a three-sided polygon, which is a closed two-dimensional shape with straight sides. In a triangle, the three sides connect three vertices, or corners, and the angles formed by these sides are called the interior angles of the triangle. The sum of the interior angles of a triangle is always 180 degrees. Triangles can be classified by their side lengths and angle measurements. For example, an equilateral triangle has three sides of equal length, and all of its angles are 60 degrees; an isosceles triangle has two sides of equal length, and its base angles are also equal; a scalene triangle has three sides of different lengths, and all of its angles are also different. Triangles are a fundamental shape in mathematics and geometry, and they have numerous applications in fields such as architecture, engineering, physics, and more.

Given by the question.

Based on the given information, we can start by drawing a diagram of triangle ABC and the segments AH, BJ, CI, CJ, and BI as described.

Since CG = BG, we can draw the perpendicular bisector of side AC passing through point G, which will intersect side AB at its midpoint M.

Now, we can see that triangle CGB is isosceles with CG = BG, so the perpendicular bisector of side CB also passes through point G. This means that G is the circumcenter of triangle ABC, and therefore, the distance from G to any vertex of the triangle is equal to the radius of the circumcircle.

Next, we can use the fact that AJ and BJ are congruent to draw the altitude from point J to side AB, which we will call JN. Similarly, we can draw the altitude from point I to side BC, which we will call IM.

Since AJ and BJ are congruent, the altitude JN will also be the perpendicular bisector of side AB, so it will pass through point M. Similarly, the altitude IM will pass through point G, which is the circumcenter of triangle ABC.

Now, we can use the Pythagorean theorem to find the lengths of JN and IM in terms of the given lengths:

[tex]JN^{2}= AJ^{2} -AN^{2} \\ = ( AH+HN)^{2} - AN^{2} \\=AH^{2} +2AH*HN+HN^{2}-AN^{2} \\[/tex]

[tex]IM^{2}= CI^{2} -CM^{2} \\=( CG-GM)^{2} -CM^{2} \\CG^{2}-2CG*GM+GM^{2} -CM^{2}[/tex]

Since CG = BG and GM = BM (since M is the midpoint of AB), we can simplify the expression for IM^2 as follows:

[tex]IM^{2}[/tex] = [tex]BG^{2}[/tex] - 2BG * BM + [tex]BM^{2}[/tex] - [tex]CM^{2}[/tex]

= [tex]BG^{2}[/tex] - [tex]BM^{2}[/tex] - [tex]CM^{2}[/tex]

Now, we can use the fact that BJ and CI intersect at point K to find the length of KJ:

KJ = BJ - BJ * (CK/CI)

= BJ * (1 - CK/CI)

= BJ * (1 - BM/CM)

To find BM/CM, we can use the fact that triangle BCI is isosceles with BI = CI, so the altitude IM is also a median of the triangle. This means that CM = 2/3 * BI. Similarly, we can find BJ in terms of JN using the fact that triangle ABJ is isosceles with AJ = BJ:

BJ = 2 * JN

Substituting these expressions into the equation for KJ, we get:

KJ = 2 * JN * (1 - 2/3 * BI/CM)

Now, we just need to find BI/CM in terms of the given lengths. Using the fact that triangle BCI is isosceles with BI = CI, we can find BI in terms of CG:

BI = CG - CI

Substituting this expression into the equation for [tex]IM^{2}[/tex]and simplifying, we get:

[tex]IM^{2}[/tex] =[tex]BG^{2}[/tex] - CG * CI

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360000 acres

Step-by-step explanation:

12000 x 30= 360000

An equation of the line that goes through the point (-1, -3) and (3, 5) is y = 2x - 1.

An equation of the line in slope-intercept form that is perpendicular to the equation for obstacle 1 is y = -x/2 + 3.

In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁) or [tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]

Where:

At data point (-1, -3), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - (-3) = \frac{(5- (-3))}{(3-(-1))}(x -(-1))\\\\y +3 = \frac{(5+3)}{(3+1)}(x +1)[/tex]

y + 3 = 2(x + 1)

y = 2x + 2 - 3

y = 2x - 1

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

2 × m₂ = -1

m₂ = -1/2.

At point (-4, 5), an equation of the line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x + 4)

y = -x/2 - 2 + 5

y = -x/2 + 3

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There are 352 square inches in the triangle's surface area. Hence, O 352 sq. inches is 's correct response.

The correct answer is  352 sq. inches

The triangle has the following characteristics: There are 180 angles in a triangle, thus they all sum up to 180. The lengths of the two sides of a triangle are greater than the length of the third side. Similar to this, the third side of a triangle has a shorter length than the angle between its 2 sides.

In this instance, the triangle's height is 22 inches, while its base is 32 inches. These values are substituted into the calculation to produce the following result: A = (1/2)(32)(22) A Equals 352 square inches

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V is 5.92 centimetres above the pyramid's base at its highest point.

A pyramid is a 3D pοlyhedrοn with the base οf a pοlygοn alοng with three οr mοre triangle-shaped faces that meet at a pοint abοve the base. The triangular sides are called faces and the pοint abοve the base is called the apex. A pyramid is made by cοnnecting the base tο the apex. Sοmetimes, the triangular sides are alsο called lateral faces tο distinguish them frοm the base. In a pyramid, each edge οf the base is cοnnected tο the apex that fοrms the triangular face.

Give the altitude the letter h. Next, we have:

tan(60) = h/2

Simplifying, we get:

h = 2 tan(60) = 2 √(3)

The Pythagorean theorem yields the following:

[tex]$\begin{align}{{V O^{2}+O F^{2}=V F^{2}}}\\ {{V O^{2}+1^{2}=6^{2}}}\\ {{V O^{2}=35}}\end{align}$[/tex]

Taking the square root of both sides, we get:

VO ≈ 5.92 cm

Rounding to three significant figures, we get:

VO ≈ 5.92 cm

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The median wait time for Speed Slide is 2 minutes longer than the median wait time for Wave Machine and the IQR for both rides is 6 minutes.

A box plot, also known as a box and whisker plot, is a graphical representation of a data set that shows the distribution of the data along a number line.

In the box plots show a random sample of wait times for two rides at a water park is shown in figure.

If we compare the wait times in the box plots,

then for, Speed Slide: Median = 11

IQR= Q1 - Q3           (Calculation formula of IQR)

      = 12 - 6

IQR = 6 minutes

for wave slide: median: 9

IQR= Q1 - Q3           (Calculation formula of IQR)

      = 11 - 9

IQR = 2 minutes

The median wait time for Speed Slide is 2 minutes longer than the median wait time for Wave Machine and the IQR for both rides is 6 minutes.

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Answer:

x = 0.8

Step-by-step explanation:

5x+6/1/3=3x/0.4

5x + 2 = 3x/0.4

2x + 0.8 = 3x

x = 0.8

The product of the number 3/4 and 8 1/2 is 51/8.

A mixed number is one that has a fraction and a whole number, separated by a space. An example of a mixed number is 8 1/2. Contrarily, an improper fraction is one in which the numerator exceeds or is equal to the denominator. For instance, 17/2 is a bad fraction. An improper fraction is a fraction in which the numerator is more than or equal to the denominator, as opposed to a mixed number, which combines a whole number with a proper fraction.

The given numbers are 3/4 and 8 1/2.

Convert the mixed number to an improper fraction:

8 1/2 = (8 x 2 + 1) / 2 = 17/2

Then, we can multiply the fractions:

3/4 x 17/2 = (3 x 17) / (4 x 2) = 51/8

Hence, the product of 3/4 and 8 1/2 is 51/8.

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