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

Explain Why It Is Likely That The Distributions Of Thefollowing Variables Will Be Normal:a) The Volume

Answers

Answer 1

After answering the provided question, we can conclude that  This expression process frequently results in bolt diameters that are normally distributed, with minor random variations around the target diameter.

what is expression ?

In mathematics, an expression is a collection of symbols, digits, and companies that portray a statistical correlation or formula. An expression can be a single number, a mutable, or a combination of both of them. Addition, subtraction, proliferation, division, and exponentiation are examples of mathematical operators.  Expressions are used extensively in mathematics, including arithmetic, calculus, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.

a) Because of the central limit theorem, the volume of soft drinks in cans is likely to follow a normal distribution. Because soft drink manufacturers typically produce a large number of cans filled with the same volume of liquid, the sample size is large.

b) The diameter of bolts immediately after manufacture is also likely to be distributed normally. Bolt manufacturing typically involves a large number of measurements and adjustments to ensure that the bolts are manufactured to exact specifications. This process frequently results in bolt diameters that are normally distributed, with minor random variations around the target diameter.

To know more about expression visit :-

https://brainly.com/question/14083225

#SPJ1


Related Questions

write the equation for the relationship between x and y. x=1,2,4 y= 0,-5,-15

Answers

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.

Fredericka Smith's account statement. Unpaid balance of $75.06. Periodic rate of 2 percent. What is the finance charge? New purchases of $432.11. What is the new balance?

Answers

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.

3x + y = 6
Y + 2 = x

Answers

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

The box plots show a random sample of wait times for two rides at a water park

Answers

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.

Define the term box plot?

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.

To know more about median, visit:

https://brainly.com/question/14532771

#SPJ1

How do you compute the sum of squared errors

Answers

Answer:

Relating SSE to Other Statistical Data

Variance = SSE/n, if you are calculating the variance of a full population.Variance = SSE/(n-1), if you are calculating the variance of a sample set of data.



3.
h
b=32 inches
h = 22 inches
Find the area of the triangle above.
O242 sq. inches
O125 sq. inches
O 300 sq. inches
O 352 sq. inches

Answers

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

Which fundamental principle of a triangle is this?

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.

A = (1/2)bh if b is the quadrilateral base and h is its height.

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

To know more about triangle  visit:

https://brainly.com/question/2773823

#SPJ1

PLEASE HELP AND SHOW THE WORK

Answers

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.

How to determine an equation of this line?

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:

m represent the slope.x and y represent the points.

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

Read more on point-slope here: brainly.com/question/24907633

#SPJ1

The cost white in dollars for X pounds of deli meat is represented by the equation Y equals 3.5 X graph the equation and interpret the slope

Answers

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

Define the term graph?

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.

To know more about graph equation, visit:

https://brainly.com/question/29464771

#SPJ1

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

Define the term graph?

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.

To know more about graph equation, visit:
brainly.com/question/29464771
#SPJ1

Keekee bought a magazine for $6 and some binders for $9 each. She spent a total of $78. How
many binders did she buy? Step by step Please!!

Answers

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:

7. Hal records the numbers of winners
of a contest in which the player
chooses a marble from a bag.
DA G
Game 1
Game 2
Game 3
Number of Number of
Players
Winners
123
52
155
63
172
65
Based on the data for all three
games, what is the experimental
probability of winning the contest?
Express the answer as a decimal.

Answers

Answer:0.40

Step-by-step explanation:

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

Define probability

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%

To know more about occurrence, visit:

https://brainly.com/question/28953812

#SPJ1

Part A
Use GeoGebra to graph points A, B, and C to the locations shown by the ordered pairs in the table. Then join each pair of
points using the segment tool. Record the length of each side and the measure of each angle for the resulting triangle.

Location
A(3,4), B(1,1).
C(5.1)
A(4.5), B(2.1).
C(7.3)
—————-
AB=
BC=
AC=

Answers

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:

Step 1

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

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

Triangle 1

A = (3, 4)B = (1, 1)C = (5, 1)

Triangle 2

A = (4, 5)B = (2, 1)C = (7, 3)

Step 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]

Step 3

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).

Graph the system of linear equations.
4x + 3y = 24
-2x + 6y = 18

Use the Line tool to graph the lines.

Answers

To graph a line requires two pieces of information that can be extracted from the line's equation.
A line can be defined by two points, this is how standard form equations are graphed. The points are the x-intercept, (C/B, 0), and the y-intercept, (0, C/A).
A line can also be defined by a point and the slope, this is how slope-intercept equations are graphed. The -intercept, b, is the point (0,b), and the slope, m, gives the rise and the run to calculate another point on the graph.

Classify each statement according to whether it describes a regression or a coefficient of determination Regression Coefficient of determination represented as R models the relationship between two variables describes how well data points fit a line values range from 0 to 1 can be positive or negative can be described by the linear equation YmX + b

Answers

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)

To know more about Regression, click the below link

https://brainly.com/question/29855763

#SPJ4

FILL IN THE BLANK ______ can creep into a study if subjects are picked (intentionally or not) according to some criterion and not randomly.

Answers

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 .

To know more about Selection bias, here

brainly.com/question/30355124

#SPJ4

PLS HELP 40 POINTS AND BRAINLIEST!!

Answers

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 °

A store purchased a stylus for $22.00 and sold it to a customer for 20% more than the purchase price. The customer was charged a 6% tax when the stylus was sold. What was the customer’s total cost for the stylus?

Answers

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

Estimate the product. Then find each product 3/4 8 1/2
PLEASE HELP

Answers

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

What is mixed fraction and improper fraction?

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.

Learn more about improper fraction here:

https://brainly.com/question/21449807

#SPJ1

Q6) The diagram shows a pyramid. The apex of the pyramid is V.
Each of the sloping edges is of length 6 cm.
A
6 cm
2 cm
B
2 cm с
F
6 cm
The base of the pyramid is a regular hexagon with sides of length 2 cm.
O is the centre of the base.
B
2 cm
E
2 cm C
Calculate the height of V above the base of the pyramid.
Give your answer correct to 3 significant figures.

Answers

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

What is pyramid?

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

To know more about pyramid's base visit:-

brainly.com/question/19567818

#SPJ1

Michelle and Robert constructed a wooden bridge for ATVs over a deep creek on the edge of their property. To recuperate the cost of the materials, they decided to charge an annual toll of $8 to each of the 120 members of a local club. A survey showed that for every $1 the toll is increased, 4 members wouldn't use the bridge anymore. What is the best toll charge to allow them to recuperate the cost of the materials the fastest?

Answers

Answer:

the answer is $10

Step-by-step explanation:

trust that

5x+6/1/3=3x/0.4 HELP RSM.

Answers

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

question content area top part 1 use a triple integral to find the volume of the solid bounded below by the cone z

Answers

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

Learn more about volume here

brainly.com/question/14527107

#SPJ4

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

You are buying 30 acres of farm land at $12000 per acre. What is total cost?

Answers

the total cost will be $360,000

360000 acres

Step-by-step explanation:

12000 x 30= 360000

ges saved
1. A rock is dropped from a height of 100 feet. Calculate the time between when the rock was dropped and when it landed. If we choose "down" as positive and ignore air friction, the function is
h(t)=25²-81.
O t=3.24 seconds
O t=9 seconds
O t=1.8 seconds
O t=6.48 seconds

Answers

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

Helpp with these questions please

Answers

Solution In the Attachment Above

Hope It Helps :)

The coordinates of three vertices of a parallelogram are (3,-2), (5,2) and (0,2). What are the coordinates of the fourth vertex?

Answers

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)

learn more about The midpoint formula ,

https://brainly.com/question/13200165

#SPJ4

10. Audry spends $600 per month on rent. She makes $25,000 per year. To the nearest percent, what percent of her income does she spend on rent? F 28% G 21% H 20% J 29%​

Answers

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%.

helps asap !!!!!

if the original price of a refrigerator is $3200 tiana buys the refrigerator at a sale for 20% off the original price she has a discount voucher that gives her a further $64 off the sale price

what percentage of the original price does tiana pay for the refrigerator ?

(can somebody show me how to do this step by step)

Answers

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%. :)

Find x, if √x +2y^2 = 15 and √4x - 4y^2=6

pls help soon

Answers

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^

In △ △ ABC, CJ = 18. If CG = BG, what is KJ? Triangle A B C is divided by 4 segments. A H is the height. C J extends from C to side A B. B I extends from B to side A C. H I extends from the height on B C to I on A C. C J and B I intersect at point K. A J and B J are congruent. A I and C I are congruent.

Answers

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].

What is triangle?

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

To learn more about Pythagorean theorem:

https://brainly.com/question/28361847

#SPJ1

The table represents some points on the graph of a linear function.

Which equation represents the same relationship?
y= -1.5x+3
y = 3x - 1.5
y= 1.5x -3
y= -3x+1.5

Answers

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

How to determine an equation of this line?

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:

m represent the slope.x and y represent the points.

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.

Read more on slope here: brainly.com/question/3493733

#SPJ1

Other Questions
you want to prevent users in your domain from running a common game on their machines. This application does not have a digital signature. You want to prevent the game from running even if the executable file is moved or renamed. You decide to create an Applocker rule to protect your computer. Which type of condition should you use in creating this rule? Two problems with advertising in ________ are the lack of accountability and ROI measurements and the increasing public concern about environmental impact. HELP ASAP WILL GIVE BRAINLYEST AND 100 POINTSIF YOU DON"T TRY TO ANSWER THE QUESTION RIGHT I WILL REPORT YOU CA 20233.4(60 minutes)This question tests the definition of a 'resident'. It also tests the concept of 'carrying on business'.It tests sections 10(1)(A), 10(1)(), 10(1)(A) and the judgments from Cohen v CIR (1946 AD 173, 13SATC 362), CIR v Kuttel (1992 (3) SA 242 (A), 54 SATC 298) and ITC 1501 ((1989) 53 SATC314).Hunter Jackal sold his coal-mining business 23 years ago. The enormous capital profit he madeprovided him with a life-long wealth. Despite never needing to work again he became a farmer - hebreeds racehorses. He loves horse-racing. And as a 'hobby, or a sport, he has raced horses for thepast 23 years. He has never raced horses as a business.Three years ago Hunter Jackal emigrated from South Africa. Prior to emigrating he sold his studfarm (the farm on which he bred racehorses) and ceased farming operations. He now breedsracehorses in the country in which he resides. He lives in a homestead on this stud farm. He hasnot, however, ceased racing horses in South Africa and is still one of South Africa's leadingracehorse owners. Horses owned by him often compete in South Africa's feature horse races. Theseare always the 'richest horse races in South Africa. He often visits South Africa to watch hishorses run in these horse racesWhen Hunter Jackal emigrated he invested his blocked funds in local dividend-yielding shares,local interest-bearing securities and local rent-producing propertiesSince Hunter Jackal's emigration his horses have not performed as well in horse races as was thesituation prior to his emigration. Over the past two years this horse-racing 'hobby" or "sport" hascost him a lot of money in that the expenses of his horse-racing sport have way exceeded the stakemoney won by his racehorses. A friend has suggested to him that he should 'convert' this "hobby'or 'sport' into a business. The friend claims that the loss from this business will be deductible in thedetermination of his South African taxable income thereby reducing his South African normal taxhability.Due to Hunter Jackal's numerous visits to South Africa he spends almost half the year in SouthAfrica Another friend has warned him that should he end up spending more than half a year ofassessment in South Africa this could have adverse tax consequences in South Africa.Hunter Jackal owns luxury town houses in Cape Town, Durban and Johannesburg. He does not letthese town houses. He occupies them himself when he visits Cape Town, Durban andJohannesburg to watch his racehorses run at the race courses situated in, or near, these townsA third friend of Hunter Jackal is of the view that due to the ownership of these three 'homes' inSouth Africa, and because of his regular visits to South Africa, that he could be regarded as beingordinanly resident in South AfricaYet another friend of Hunter Jackal, a fourth friend, has informed him that even if the third friend'sview is Incorrect that he may be a resident of the Republic resulting from the time he spends inSouth AfricaHunter Jackal, who is at present 63 years old, would like to know if the view or concerns of any ofhis four friends as detailed above are validYou are required to state whether the opinions of Hunter Jackal's friends are correct. calculate suppose an object has a mass of 15 g and a volume of 5 cm^3. what is the density of the object? a 30.00-ml sample of 0.125 m hcooh is being titrated with 0.175 m naoh. what is the ph after 21.4 ml of naoh has been added? ka of hcooh Consider the mesh analysis solution method for this circuit. Which one equation describes the loop on the right? O-IZ (Z2 + Z3) - I1Z2 = E2 -12(22 + Z3) + 1122 = E2 O 12 (Z2 + Z3) - Iz Z2 = E2 12(Z2 + Z3) + 1122 = E2 - each level of organization in an ecosystem is made up of parts. which of the following is an example of the population level of organization in a coral reef ecosystem? The data in the table below shows the average temperature in Northern Latitudes: The line of best fit for the data is approximately y=-1.07x+92.87.a) Trueb) False Un robot salta sobre una recta numrica iniciando en el cero. Las reglas del juego sonlas siguientes si mira hacia tu mano derecha, la longitud de cada salto se expresacon un nmero positivo y, si mira hacia tu mano izquierda, con un nmero negativo. Tambin: si salta de frente (o sea, en la direccin que est mirando), el nmerode saltos se expresa con un nmero positivo, y si salta de espaldas (es decir, enla direccin contraria a la que est mirando), el nmero de saltos se considera conun nmero negativo. Observa los siguientes saltos del robot, su posicin final en cada caso y contesta en tucuaderno las preguntas In 3 to 5 sentences, explain why enslaving the indigenous peoples of the Americas was largely unsuccessful in filling the need of the plantations. Support your answer by using one piece of qualitative, and one piece of quantitative information from La casas writing. Your uncle has invited you to visit a city in his country. Write a letter to uncle telling about your favorite city and why you want to go there. Please figure out #3. Ill mark brainliest for right answer. a business that buys large quantities of merchandise from several different manufacturers and then resells this merchandise to many different retailers is a: multiple choice question. retailer. manufacturer. wholesaler. service business. For an enzyme-catalyzed reaction, the initial velocity was determined at two different concentrations of the substrate. Which of the following would be closest to the value of Km?[S] (mM) Vo(mM/min)1.0 2.04.0 2.8A. 2.7 mMB. 5.7 mMC. 0.17 mMD. 0.60 mM John Deere engaged in ______ when it developed an inexpensive tractor for farmers in India and then found a market for the tractor in the United States. A. Disruptive innovation B. reverse innovation C. an ambidextrous approach which type of volcanism is often found far from plate boundaries? choose mechanisms that remove neurotransmitters in the synaptic cleft. which muscle is a superficial anterior flexor muscle? which structure of the ear converts sound waves into vibrations?