the formula for the test statistic used for a two sample test of means where the population variances are unknown and unequal is: t = x1−x2√s12/n1 s22/n2 match the variables to their description.

Using PEMDAS to solve the mathematical expression, the result is -637.947

The mathematical operation refers to calculating a value using operands and a math operator. The symbol of the math operator has predefined rules to be applied to the given operands or numbers.

In this kind of problem, we need to use the PEDMAS rule which is

Parenthesis, Exponents, Division, Multiplication, Addition and Subtraction.

The order in which this must be prioritized is from parenthesis and the least is subtraction.

Applying PEMDAS to this mathematical operation, we would have

19.42 - 34.89(19.3) + 10.23 + 5.78

Using a calculator which follows this rule, we would have;

19.42 - 34.89(19.3) + 10.23 + 5.78 = -637.947

Learn more on mathematical operation here;

https://brainly.com/question/550188

#SPJ1

The total revenue function if the revenue from 115 devices $2116 is 200 when R'(x)=4x(x²+25000[tex])^{2/3}[/tex].

Given that,

The following function calculates the marginal revenue (in thousands of dollars) from the sale of a portable gaming system.

R'(x)=4x(x²+25000[tex])^{2/3}[/tex]

We have to find the total revenue function if the revenue from 115 devices $2116.

We know that,

R'(x)=4x(x²+25000[tex])^{2/3}[/tex]

Integrating on both sides

R(x)= [tex]\int {4x(x^{2} +25000)^{2/3} } \, dx[/tex]

Let x²+25000=t

=> 2xdx=dt

=> 4xdx=2dt

We get,

R(x)= [tex]\int {2t^{-2/3} } \, dt[/tex]

R(x)= [tex]6t^{1/3}[/tex]+C

By Substitution then

R(x)= 6(x²+25000[tex])^{1/3}[/tex]+C

We get

Given R(115)=$2,116 or 2.116 (in thousands of dollars) and x=115 units

Then total revenue function(in thousands of dollars)

2.116= 6(115²+25000[tex])^{1/3}[/tex]+C

C=200

Therefore, The total revenue function if the revenue from 115 devices $2116 is 200.

To learn more about function visit: https://brainly.com/question/5975436

#SPJ4

The cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.

A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value.

From the question , we are given that the laptop costs $350 more than the desktop, therefore,

let x represent the cost of the laptop thus, x-350 will be the cost of the desktop .

The total finance charge of $388 is equal to 8% of the cost of the laptop and 7.5% of the cost of the desktop, we solve as;

388 = 0.08(x) + 0.075(x - 350)

252 = 0.08x + 0.075x - 26.25

278.75 = 0.155x

x = 278.75/0.155

x = 1798

Recall that the cost of desktop = x -350

therefore:

1,798- 350 = 1448

The cost of laptop = $1798

The cost of desktop = $1448

Thus, the cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.

Read more about mathematics operations at:

brainly.com/question/17869111

#SPJ1

An equation in slope-intercept form that represents the situation is y = 3x - 208.

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided, we have the following points:

Points on x-axis = (103, 105).

Points on y-axis = (101, 107).

Substituting the given points into the formula, we have;

Slope, m = (107 - 101)/(105 - 103)

Slope, m = 6/2

Slope, m = 3

Mathematically, the slope-intercept form of a straight line is given by;

y = mx + c

Where:

At point (103, 101), an equation in slope-intercept form is given by:

y - y₁ = m(x - x₁)

y - 101 = 3(x - 103)

y - 101 = 3x - 309

y = 3x - 309 + 101

y = 3x - 208.

Read more on slope-intercept form here: brainly.com/question/1884491

#SPJ1

The single trigonometric function form of the expression is 2sin(3π/8) cos(3π/8).

Trigonometric function:

In math, trigonometric functions are the periodic functions which denote the relationship between angle and sides of a right-angled triangle.

Given,

Here we need to write the given expression as a single trigonometric function. 2 sine (start fraction 3 pi over 8 end fraction) cosine (start fraction 3 pi over 8 end fraction)

Here we have the expression,

2 sine (start fraction 3 pi over 8 end fraction) cosine (start fraction 3 pi over 8 end fraction)

Now, we have to convert this into the form of trigonometric function,

For that we have to rewrite the given expression based on the arithmetic operators, then we get the resulting function as,

=> 2sin(3π/8) cos(3π/8).

To know more about trigonometric function here.

https://brainly.com/question/6904750

#SPJ4

Answer:C

Step-by-step explanation:

did it on edge

The solution to the equation represented by One-fourth x minus one-eighth = Start Fraction 7 Over 8 End Fraction + one-half x is (b) x = negative 4

The statement in the question is given as

One-fourth x minus one-eighth = Start Fraction 7 Over 8 End Fraction + one-half x

Mathematically, this statement can be represented as

1/4x - 1/8 = 7/8 + 1/2x

Multiply through the equation by 8

So, we have:

2x - 1 = 7 + 4x

Collect the like terms

4x - 2x = -1 - 7

Evaluate the like terms

2x = -8

Divide both sides by 2

x = -4

Hence, the solution is -4

Read more about equation at

https://brainly.com/question/2476251

#SPJ1

Answer: Side of an empty cubicle carton = 9 cm.

Now as we know that volume of the cube is the cube of its side.

So the volume of an empty cubicle carton having side 9 cm, V = (9)3=729 cm3.

Now we have to find out can 1000 cubes of side 1cm fit in it.

So the volume of the cube of side 1 cm is, V’ = (1)3=1 cm3

So the volume of the 1000 such cubes = 1000 (1) = 1000 cubic centimeters.

Now if the ratio of the volume of the empty cubicle carton to the volume of 1000 cubes of 1 cm is greater than 1 then we can will 1000 cubes of side 1 cm into an empty cubicle carton otherwise not.

So the ratio of the volume of the empty cubicle carton to the volume of the 1000 cubes is,

⇒VV′=7291000=0.729 < 1

So as we see that the ratio is less than one so we cannot fit 1000 cubes of side 1 cm into an empty cubicle carton of side 9 cm.

Step-by-step explanation:

I really hope this works!

                                      Hope you Have a Great Day!! :)

The test statistic for the given test is t = 2.59.

What is a standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.

Given data:

                    [tex]\bar D[/tex] = 4.1, Sd = 5, n = 10, μd = 0

Now the test statistic can be computed as

                [tex]t=\frac{\bar D-\mu_d}{S_d/\sqrt{n} }[/tex]

                [tex]t=\frac{4.10-0}{5/\sqrt{10}} \\\\t=2.59[/tex]

Hence, the test statistic for the given test would be t = 2.59.

To learn more about standard deviation, visit:

https://brainly.com/question/475676

#SPJ4

Answer:

[tex]7\sqrt{5}[/tex]

Step-by-step explanation:

Using the geometric mean theorem, [tex]n=\sqrt{28 \cdot 7}=14[/tex].

Using the Pythagorean theorem, [tex]m=\sqrt{7^2+14^2}=7\sqrt{5}[/tex]

The rational equation with the desired asymptotes and intercepts is given by: f(x) = [-20(x²-5x-6)] / [3(x² 7x + 10)].

Vertical asymptotes are x values that are outside the domain and, in a fraction, are the denominator zeroes.

As long as this value differs from infinity, the horizontal asymptote is the value of f(x) as x approaches infinity.

The vertical asymptotes are related to the denominator roots, so:

f(x) = a / ( x + 5)( x + 2 )

f(x) = a / ( x² + 7x + 10 )

The x-intercepts are related to the function's numerator, so:

f(x) = [a( x + 1 )( x - 6) ] / [x² + 7x  + 10 ]

The y-intercept is to find a, hence, when x = 0, y = 5, thus:

4 = a(-6)/ 10

a = (-40/6)

a = -20 / 3

The equation will be written as,

f(x) = [-20(x²-5x-6)] / [3(x² 7x + 10)].

To know more about asymptotes follow

https://brainly.com/question/28184934

#SPJ1

2.5(cos 5π/6  + i sin 5π/6) is the polar form  of the complex number

Complex numbers are numbers that are expressed in the form of a+ib, where a and b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1)

Given: the complex number (5√3)/4 - 5/4 i

In polar form:

(5√3)/4 - 5/4 i = r(cosθ + isinθ)

θ  = tan⁻¹( (-5/4) / (5√3 /4) )

θ = -30°

θ = -30+180 = 150°

θ = 5π/6

r = √( (5√3)/4)² +(- 5/4)²) = 2.5

Thus,

(5√3)/4 - 5/4 i = r(cosθ + isinθ)

r(cosθ + isinθ) = 2.5(cos 5π/6  + i sin 5π/6 )

Therefore, the polar form  of the complex number is 2.5(cos 5π/6  + i sin 5π/6)

Learn more about complex number on:

https://brainly.com/question/27844433

#SPJ1

Answer:

16.(a)  24

16.(b)  See attachment.

Step-by-step explanation:

Cumulative frequency means ‘running total’. A cumulative frequency diagram plots this running total so you can estimate the median and the quartiles easily.

According to the given cumulative frequency graph, the number of necklaces that have a mass 21 g or less is 16.

Therefore, an estimate of the number of necklaces with a mass of 21 g or greater is:

[tex]\implies 40-16=24[/tex]

To draw a box plot to represent the data, estimate the median and quartiles from the graph.  

Calculate the position of the median and quartiles, then go to the position on the vertical scale of the graph and read off the value from the horizontal axis.  (See attached annotated graph).

[tex]\sf Median \; position=\dfrac{40}{2}=20[/tex]

So the median = 22

[tex]\sf Q_1 \; position = \dfrac{1}{4} \times 40=10[/tex]

So Q₁ = 18

[tex]\sf Q_3 \; position = \dfrac{3}{4} \times 40=30[/tex]

So Q₃ = 24

Draw the box plot with the calculated median and quartiles, and the given lowest and highest values.  (See second attachment).

The equation of the line which passing through the point and parallel to the line which has undefined slope is y=0(x)-6

Given that,

The point is (1/2,-6)

We have to find the equation of the line which passing through the point and parallel to the line which has undefined slope.

We know that,

The equation of the line has a formula that is y=mx+b

m is the slope of the line

b is the intercept

m is slope that is undefined means

m is 0.

Now, b is

y=0(x)+b

y=b

Here y is from the point -6

b is -6

So, we get equation has

y=0(x)-6

Therefore, The equation of the line which passing through the point and parallel to the line which has undefined slope is y=0(x)-6

To learn more about equation visit: https://brainly.com/question/29538993

#SPJ1

The largest possible area of rectangle with base on the x-axis and upper vertices on the curve [tex]y = 8 -x^{2}[/tex] is [tex]\frac{64\sqrt{6} }{9}[/tex].

It is given to us that -

The rectangle has the base on x-axis

The rectangle has its upper vertices on the curve [tex]y = 8 -x^{2}[/tex] ----- (1)

We have to find out the largest possible area for the rectangle with given specifications.

We know that the area of a rectangle can be represented as -

[tex]A = xy[/tex] ---- (2)

where,

[tex]x =[/tex] length of the base of the rectangle

[tex]y =[/tex] vertices of the curve = width of the rectangle

Since it is given to us that the rectangle has it base on the x-axis, therefore the length of the base of the rectangle = [tex]2x[/tex] ---- (3)

Substituting equations (1) and (3) in equation (2), we have

[tex]A = xy\\= > A = (2x)(8-x^{2}) \\= > A = 16x-2x^{3}[/tex]----- (4)

For the largest possible area, we know that -

[tex]\frac{dA}{dx}=0[/tex] ---- (5)

Substituting equation (4) in equation (5), we have

[tex]\frac{dA}{dx}=0\\= > \frac{d}{dx}(16x-2x^{3}) =0\\ = > \frac{d}{dx}(16x)-\frac{d}{dx}(2x^{3} )=0\\= > 16-6x^{2} =0\\= > 6x^{2} =16\\= > x^{2} =\frac{16}{6} \\= > x=\frac{4}{\sqrt{6} }[/tex]------ (6)

To find out the largest possible area, we have to put the value of x from equation (6) in the area of the rectangle in equation (4). So, we have

[tex]A = 16x-2x^{3}\\= > A = (16*\frac{4}{\sqrt{6} }) -[2(\frac{4}{\sqrt{6} } )^{3} ]\\= > A = \frac{16*4}{\sqrt{6} } -\frac{2*4*4*4}{\sqrt{6}*\sqrt{6}*\sqrt{6} } \\= > A = \frac{64\sqrt{6} }{9}[/tex]

Therefore, the largest possible area of rectangle with base on the x-axis and upper vertices on the curve [tex]y = 8 -x^{2}[/tex] is [tex]\frac{64\sqrt{6} }{9}[/tex].

To learn more about rectangle area visit https://brainly.com/question/20693059

#SPJ4

Answer: 11 14/15

Step-by-step explanation:

A null hypothesis is a particular kind of statistical hypothesis that asserts that no statistical significance can be found in a given set of observations.

A null hypothesis is a particular kind of statistical hypothesis that asserts that no statistical significance can be found in a given set of observations. The use of sample data in hypothesis testing allows one to judge a hypothesis' veracity.

The null hypothesis states that the estimate is only based on chance. If the observed data (in the sample) do not differ from what would be predicted solely by chance, then the null hypothesis is true. The alternative hypothesis is what the null hypothesis has as its counterpart.

Two population parameters, such as an independent variable and a dependent variable, are said to be unrelated under the null hypothesis. It's possible that an experimental or sampling error caused the result if the hypothesis indicates a relationship between the two parameters.

To learn more about null hypothesis refer to:

https://brainly.com/question/4436370

#SPJ4

If the car's speed is 65 kilometres per hour, then the bus' speed may be 75 kilometres per hour.

How to find the distance travelled by an object?

The distance travelled by an object in a specified direction is velocity×time.

if the car's speed is 65 kilometres per hour then in 2 hours it will travel a distance of 65×2 kilometres.

65×2=130 kilometres

if the bus' speed is 75 kilometres per hour then in 2 hours it will travel a distance of 75×2 kilometres.

75×2=150 kilometres

So, after 2 hours the distance between the two vehicles will be 130+150= 280 kilometres

which is less than 350 kilometres.

Hence, it is possible that if the car's speed is 65 kilometres per hour then the bus' speed is 75 kilometres per hour.

Read more about the velocity and speed relationship at https://brainly.com/question/14850956

#SPJ9

Answer:

Is that all

_______

_______

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{4 +3}{3 +1} \implies {\Large \begin{array}{llll} \cfrac{7 }{ 4 } \end{array}}[/tex]

The equivalent expression of (6x² - 9x) - (2x -3) is 6x² - 11x + 3

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

In other words, equivalent expressions are expressions that have similar value or worth but do not look the same.

To find equivalent expression we can simplify the expression.

Therefore,

(6x² - 9x) - (2x -3)

open the brackets

6x² - 9x - 2x + 3

combine like terms

Therefore,

(6x² - 9x) - (2x -3) = 6x² - 11x + 3

learn more on equivalent expression here: https://brainly.com/question/6997280

#SPJ1

The composition of the function are as follows:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10

What is a Composite Function?
If we are given two functions, we can compose one function into the other to produce a third function. The steps needed to complete this operation are the same as those needed to solve any function for any given value. These are referred to as composite functions.

We have,

i] f(x) = 8x  and
g(x) = (2x+8)

(g ∘ g) (x) = g[g(x)]
Substitute x with (2x+8) in the function g(x) = (2x+8).
= 2((2x+8))+8
= 4x + 16

(f ∘ g) (x) = f [g (x)]
Substitute x with (2x+8) in the function f(x) =  8x.
(f ∘ g) (x) = 8(2x+8)  
= 16x + 64

ii]  f(x) = 6x + 2 and g(x) = x -5
f [g(7)] = 6(x-5) + 2  
= 6x - 28

g [f(3)] = (6x + 2 ) - 5
= -30x - 10

Hence, the composition of the function is:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10

To learn more about the composition of the function visit,

https://brainly.com/question/10687170

#SPJ1

a) Probability that Meteor will release between 1 and 4 megatons of energy: 0.304

b) Probability that Meteor will release between 9 and 10.5 megatons of energy: 0.029

c) Probability that Meteor will release at least 6 megatons of energy: 0.613

What is histogram?

The spread and size of the data are measured using histograms. We can virtually analyse the data based on the histogram.

From the Histogram we get:

a) Probability that Meteor will release between 1 and 4 megatons of energy= P [X=1 to X=4]

           = [0.156+0.088+0.060]

            =0.304

b) Probability that Meteor will release between 9 and 10.5 megatons of energy= P [X=9 to X=10.5]

           = [0.020+0.009]

           =0.029

c) Probability that Meteor will release at least 6 megatons of energy         = 1- P[X≤5]

= 1-P [X=1 to X=5]

= 1- [0.156+0.088+0.060+ 0.046+0.037]

= 0.613

To know more about histogram:

https://brainly.com/question/29586631

#SPJ4

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

760% can be written in fraction form as 38/5.

760% can be written in mixed form as 7(3/5).

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

760%

This can be written as a fraction.

760/100

= 76/10

= 38/5

or

= 7(3/5)

Thus,

760% can be written in fraction form as 38/5.

760% can be written in mixed form as 7(3/5).

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ1

The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.

What is linear equation?

Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable.

Given, the equation y = 2x -4

Which is linear function and have y a dependent variable and x be the independent variable,

because value of y depends upon the value of x.

Hence, a is the correct answer.

To know more about linear equation, visit:

https://brainly.com/question/11367265

#SPJ1

Answer: A

Step-by-step explanation: Trust me

The average rate of change in median age per year from 1950 to 1990 is 0.085 years of age per year.

The median is the mid-value in a set of data. to find it we first arrange the data set from smallest to largest, then pick the middle value which divides the data set in half.

From the given table,

The median age at the time of the first marriage in 1950 = 22.8 years,

While the median age in 1990 = 26.1 years,

Hence, the average rate of change in median age per year from 1950 to 1990

= (22.8-26.1)/(1950-1990)

= (-3.3)/(-40)

= 0.0825 years of age per year.

Read more about Median:

brainly.com/question/26177250

#SPJ4

The three statements about his solution that are true include the following:

1. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.

2. He did not multiply the numerator and denominator by the correct number to equal 1,500.

5. He should have multiplied the numerator and denominator by 75, not 30,  because 20 × 75 = 1,500.

Based on the information provided, a mathematical expression which models the number of songs of each genre on Josiah's MP3 player to be 300 songs:

10/20 = x/1500

Multiplying the mathematical expression by 75, we have the following:

75 × (10/20) = x/1,500

750/1500 = x/1500

1,500x = (750 × 1,500)

x = (750 × 1,500)/1,500

x = 750.

Read more on expression here: https://brainly.com/question/12368420

#SPJ1

The best fitting line is one where the intercept of the regression equationrResidual sum of squares is closest to zero. So the option c is correct.

In the given question,

The best fitting line is one where the intercept of the regression equation:

As we know that;

The slope of the line of best fit is the coefficient in a simple regression with a single independent variable. The slope is a mixture of the two coefficients in this example and in any regression with two independent variables. The y-intercept of the line of best fit is constant C.

So, the best fitting line is one where the intercept of the regression equationrResidual sum of squares is closest to zero. So the option c is correct.

To learn more about best fitting line link is here

brainly.com/question/14279419

#SPJ4

The number of sides in the polygon that has 1,260° as the sum of the interior angles, found using the formula for the sum of the interior angles in the polygon, S = 180·(n - 2) is 9 sides

A polygon is a figure consisting of a specified number of straight sides such that they form a closed loop. The number of sides in a polygon are three or more.

The formula for the sum of the interior angles of a polygon, S, can be be used to find the number of sides in the polygon as follows;

S = 180·(n - 2)

Where;

n = The number of sides the polygon has

The sum of the interior angles in the specified polygon = 1,260°

The number of sides in the polygon can be found by equating the formula for S to 1,260° as follows;

When S = 1.260°, we get;

1,260 = 180·(n - 2)

Which indicates;

n - 2 = 1,260 ÷ 180 = 7

Therefore; n - 2 + 2 = 7 + 2 = 9

n = 9

Learn more about polygons here:

https://brainly.com/question/12291395

#SPJ1

Answer:

4 x^3 + 24 x^2 = 4 (x^3 + 6 x^2) = 4 x^2 (x + 6)

4 x^2 (x + 6)        seems to be the lowest factor