What must be true in order to find a sum for an infinite geometric series?

The munimum value is, at x = 3/10, y = 5 and 10x+3y/5 = 6.

To find the minimum value of 10x (3y/5):

Given - y = 3/(2x)

So, we want the bare minimum of,

Take the derivative to obtain:

When you set it to zero, you get:

So, at x = 3/10, y = 5 and 10x + 3y/5 = 3 + 3 = 6.

Therefore, the munimum value is, at x = 3/10, y = 5 and 10x+3y/5 = 6.

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Answer:

-8

Step-by-step explanation:

y=(1/3)x

4 = (1/3)12

y=(1/3)(-24)

y= -8

Answer:

11.7647%

Hope this helps!

The given expression is equivalent to the expression (B) [tex](x-1)^{2} -3[/tex].

To complete the square to transform the expression:

Therefore, the given expression is equivalent to the expression (B) [tex](x-1)^{2} -3[/tex].

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The correct question is shown below:

Complete the square to transform the expression x^2− 2x − 2 into the form a(x − h)^2+ k.

(A) (x − 1)2 + 3

(B) (x − 1)2 − 3

(C) (x − 2)2 − 3

(D) (x − 2)2 + 3

Answer:

The first option:

[tex]x^2-5x+9[/tex]

Step-by-step explanation:

Trust me I am right.

If you need work please ask!

Have a nice day!

Alpha level. the minimum P-value at which we reject the null hypothesis

That two options are identical is the null hypothesis. According to the null hypothesis, the observed difference is solely the result of chance. The probability that the null hypothesis is correct can be determined via statistical testing.

The "significance level," often known as the alpha level, must be established before performing any statistical test. The likelihood of rejecting the null hypothesis when it is true is what is meant by the term "alpha level" in statistics. The likelihood of making a poor decision is what this phrase means.

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The circumference of the given circle is 25.1 cm.

According to the statement

we have given that the the radius of circle which is 4cm.

And we have to find the circumference of the circle.

So, For this purpose

The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center.To calculate the circumference of a circle, multiply the diameter of the circle with π (pi).

The formula to calculate it is

C = 2(pi)r

So, substitute the values in it then

Here use pi value is 3.14

C = 2 *3.14*4

C = 25.12.

The circumference of the given circle is according to one decimal place is 25.12 cm.

So, The circumference of the given circle is 25.1 cm.

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Answer:

4112

Step-by-step explanation:

When you plug in 3 for x you get 6.

Then you just do 4^6 which is 4096.

Then add 16 which gets you 4112.

Answer:

A

Step-by-step explanation:

the side opposite of the angle is related to the size of this angle. Smaller angles have less space for the line to "spread out," so it will be shorter. Vice versa, bigger angles will have opposite sides longer because of more space.

A given linear equation has infinitely many solutions.

Given: −3y 3y 4 = 4

            3y+4=3y+4

The given linear equation satisfies any value of 'y'.

So, A given linear equation has infinitely many solutions.

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Answer:

96 and 192

Step-by-step explanation:

This is a geometric sequence with a common ratio of 2 :

3 × 2 = 6

6 × 2 = 12

12 × 2 = 24

24 × 2 = 48

48 × 2 = 96

96 × 2 = 192

Therefore our final answers are 96 and 192

Hope this helped and have a good day

Answer:

No,

Step-by-step explanation:

X^-2 is equal to 1/X^2. so any number or letter to negative power, is the same as 1 divided by that number or letter to the positive power..(power remains with denominator

The perimeter of inside of the track is 536.44m

The perimeter of a circle is also known as the circumference of the circle. The formula for calculating the circumference is expressed as:

C = 2πr

where

r is the radius

From the given diagram

r = 46/2 = 23m

C = 2(3.14)(23)
C = 144.44m

Find the perimeter of the rectangle

P = 2(l+w)

p = 2(46+150)
P = 2(196)
P =392m

The perimeter of the inside track = 144.44 + 392

The perimeter of the inside track = 536.44m

Hence the perimeter of inside of the track is 536.44m

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Here is the five-number summary, range and interquartile range:

Minimum: 9

Lower quartile:   11

Median: 24

Upper quartile:  34

Maximum: 45

Interquartile range: 23

The minimum number is the smallest number in the data. The  minimum number is 9. The maximum number is the biggest number in the dataset. The maximum number is 45.

The first quartile, third quartile and the interquartile range are used to measure dispersion.

The first quartile : 1/4(n + 1)

1/4 x (12) = 3rd term = 11

The third quartile : 3/4 x (n + 1)

3/4 x (12) = 9th term = 34

Interquartile range = third quartile - first quartile

34 - 11 = 23

Median can be described as the number that is at the center of the dataset when the number is arranged in either ascending or descending order.

Median = 25

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Answer:

(4 , -3)

Step-by-step explanation:

the points (3 , 5) and (3 , 7) ​have the same x-coordinates 3

then ,the line D joining them has the equation  

D : x = 3

the image of the point A(2 , -3) under reflecting about The line D ,

lie on the line ∆ perpendicular to D and passes through A.

∆ perpendicular to D then the equation of ∆ is :

∆ : y = a   ,where a is a real number.

Calculating ‘a’ :

∆ passes through A

Then

-3 = a

Therefore

the final equation of ∆ is :

∆ : y = -3

Obviously, the lines D and ∆ intersect at the point M(3 , -3)

FINAL STEP :

Calculating the coordinates of the point B(x , y) image of the point A(2 , -3)

M is the midpoint of the line segment AB :

Then

3 = (2 + x)/2 and -3 = (-3 + y)/2

Then

x = 4 and y = -3.

The surface area of the prism is 256in².

Given that the sides of the prism is 5in, 12in and 4in.

The total area occupied by the surfaces of an object is called the area.

Here, l=12in, b=5in and h=4in

Firstly, we will find the area of the base, we get

B=l×b

B=12×5

B=60in²

Now, we will find the perimeter of the base, we get

P=2(l+b)

P=2(12+5)

P=2×17

P=34in

Further, we will find the surface area of the prism by using the formula SA=2B+Ph.

Here, we will substitute the values from above, we get

SA=2×60in²+34in×4in

SA=120in²+136in²

SA=256in²

Hence, the surface area of the prism where the sides of the prism is 5in, 12in and 4in is 256in².

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The end behavior of a polynomial function is as x tends to infinity, f(x) tends to negative infinity.

In this question,

The power function is f(x) =-2x^3

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

The graph below shows the behavior of the function f(x).

The above equation has the degree of 3, which is odd and the leading coefficient has the negative coefficient.

Then the end behavior is

As x -> ∞,

[tex]\lim_{x \to \infty} f(x)[/tex]

⇒ [tex]\lim_{x \to \infty} -2x^{3}[/tex]

⇒ [tex]-2(\infty)^3[/tex]

⇒ - ∞

Hence we can conclude that the end behavior of a polynomial function is as x tends to infinity, f(x) tends to negative infinity.

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Answer: 8π mm (in terms of π)

Step-by-step explanation:

1) The formulas for solving the circumference of a circle is πd (π times diameter).

2) 8 times π equals 8π mm.

Hopes this helps!

Answer:

12.56 [tex]mm^{2}[/tex]

Step-by-step explanation:

c = 2[tex]\pi[/tex]r

or c =[tex]\pi[/tex]D

The diameter is the measure of a line segment going from one side the circle to the other and going through the middle of the circle.  A radius is a line 1/2 a diameter.  It is a line segment that goes from the center of a circle to a point on the edge of the circle.

C = (3.14)(4)

C = 12.56

The amount of space (volume) that is in the larger spherical ball than the smaller = 1,084.8 in.³

To find the volume of a sphere, which is the amount of space the solid contains, the formula used is given as: 4/3 πr³, where r is the radius of the sphere, which is half the measure of the diameter. Volume of sphere (V) = 4/3 πr³.

Diameter of the smaller spherical ball = 5 inches

Radius of the smaller spherical ball = 5/2 = 2.5 inches

Volume of the smaller spherical ball = 4/3 πr³ = 4/3 × π × 2.5³

Volume of the smaller spherical ball ≈ 65.5 in.³

Diameter of the larger spherical ball = 13 inches

Radius of the larger spherical ball = 13/2 = 6.5 inches

Volume of the larger spherical ball = 4/3 πr³ = 4/3 × π × 6.5³

Volume of the larger spherical ball ≈ 1,150.3 in.³

The amount of space (volume) that is in the larger spherical ball than the smaller = 1,150.3  - 65.5

The amount of space (volume) that is in the larger spherical ball than the smaller = 1,084.8 in.³

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The vertex of the function f(x) exists (1, 5), the vertex of the function g(x) exists (-2, -3), and the vertex of the function f(x) exists maximum and the vertex of the function g(x) exists minimum.

Given:

[tex]$\mathrm{f}(\mathrm{x})=-(\mathrm{x}-1)^{2}+5$[/tex] and

[tex]$\mathrm{g}(\mathrm{x})=(\mathrm{x}-2)^{2}-3$[/tex]

The generalized equation of a parabola in the vertex form exists

[tex]$y=a(x-h)^{2}+k[/tex]

Vertex of the function f(x) exists (1, 5).

Vertex of the function g(x) exists (-2, -3).

Now, if (a > 0) then the vertex of the function exists minimum, and if (a < 0) then the vertex of the function exists maximum.

The vertex of the function f(x) exists at a maximum and the vertex of the function g(x) exists at a minimum.

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Answer:

- For the function f(x) = -(x - 1)^2/5, the vertex is a maximum point.

- For the function g(x) = x^4 - 3, the vertex is a minimum point.

Step-by-step explanation:

To determine if the vertex for each function is a minimum or a maximum, we need to analyze the leading coefficient of each function.

Let's start with the function f(x) = -(x - 1)^2/5. This function is already in vertex form, where the vertex is (1, 0).

Since the leading coefficient is negative (-1/5), the graph of f(x) opens downward. In this case, the vertex is a maximum point. You can visualize it as a peak on a graph.

Now, let's move on to the function g(x) = (x^2)^2 - 3. This function can be rewritten in vertex form as g(x) = x^4 - 3.

The leading coefficient is positive (1), so the graph of g(x) opens upward. In this case, the vertex is a minimum point. You can visualize it as a valley on a graph.

In summary:

- For the function f(x) = -(x - 1)^2/5, the vertex is a maximum point.

- For the function g(x) = x^4 - 3, the vertex is a minimum point.

Remember, the sign of the leading coefficient determines whether the vertex is a minimum or maximum point.

Given the point U and point V, the midpoint between of the line segment UV is ( 0, -5/2 ).

The midpoint formula is used to find the midpoint of a line segment.

It is expressed as;

[ (x₁ + x₂ )/2 , (y₁ + y₂ )/2 ]

Given the data in the graph,

Point U = ( 3, -1 ) and Point V = ( -3, -4 )

We substitute into the formular above.

[ (x₁ + x₂ )/2 , (y₁ + y₂ )/2 ]

[ (3 + (-3) )/2 , ( (-1) + (-4) )/2 ]

[ 0/2, (-1-4)/2 ]

[ 0/2, -5 /2 ]

( 0, -5/2 )

Given the point U and point V, the midpoint between of the line segment UV is ( 0, -5/2 ).

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Step-by-step explanation:

sin∅=-3/4 in 4 quadrant which sine is negative there

using soh cah toa

sin=opp/hyp

where our opp=-3 and our hyp=4

using pythagoras theorem

hyp²=opp²+adj²

(4)²=(-3)²+adj²

16=9+adj²

16-9=adj²

adj²=7

adj=√7

from soh cah toa

cos∅=adj/hyp

cos∅=√7/4

The surface area of the cylinder with the given height and radius is 835.2 square inches

The given parameters are

The surface area is then calculated using the following formula

A = 2πr² + 2πrh

Substitute the given values in the above equation

So, we have:

A = 2 * 3.14 * 7^2 + 2 * 3.14 * 7 * 12

Evaluate the exponents

A = 2 * 3.14 * 49 + 2 * 3.14 * 7 * 12

Evaluate the products

A = 307.72 + 527.52

Evaluate the sum

A = 835.2

Hence, the surface area of the cylinder with the given height and radius is 835.2 square inches

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89% of pebbles weigh more than 2.1 grams.

What is a percentage?

Given,

         Mean = 2.6

           SD = 0.4

As we have to find the percentage of pebbles weighing more than 2.1, we have to find the z-score for 2.1 first.

             [tex]z = \frac{x- mean}{SD}[/tex]

             [tex]z = \frac{2.1 - 2.6}{0.4}[/tex]

             [tex]z = -1.25[/tex]

Now we have to use the z-score table to find the percentage of pebbles weighing less than 2.1

So,

   [tex]P ( x < 1.25 ) = 0.10565[/tex]

This gives us the probability of P(z<-1.25) or P(x<2.1)

To find the probability of pebbles weighing more than 2.1

[tex]P ( x > 2.1 ) = 1 - P( x < 2.1 ) = 1 - 0.10565 = 0.89435[/tex]

Converting into percentage

0.89435 × 100 = 89.435 %

Rounding off to nearest percent   =89%

Therefore, 89% of pebbles weigh more than 2.1 grams.

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The value of x if a, b, and c are collinear points and b is between a and c : 7

Collinear points are those that are situated on the same line of sight or within a single line. In Euclidean geometry, two or more points are said to be collinear if they are located on a line either close to or far from one another.

According to the given information:

if A, B, and C are col-linear points and B is between A and C

then

AB+BC=AC

AB=x+6

BC=3x-5

AC=36-x

(x+6)+(3x-5)=36-x

(x+3x)+(6-5)=36-x

4x+1=36-x

4x+x=36-1

5x=35

x=35/5

x=7

The value of x is 7

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The critical values of the function are x = 0 and x = 64

The critical values of a function f(x) are the values of x for which f'(x) = 0.

Given,

f(x) = [tex]\frac{x^{4} }{5(x-8)^{2} }[/tex]

The derivative is found as follows, applying the quotient rule:

f'(x) = [tex]\frac{[5(x^{4} )(x-8)^{2}-5x^{4} [(x-8)^{2} ]' }{[5(x-8)^{2} ]^{2} }[/tex]

     = [tex]\frac{2x^{3}(x-64) }{5(x-8)^{3} }[/tex]

The zeros of the function are the zeros of the numerator, thus:

[tex]2x^{3} (x-64) =0\\2x^{3} =0-------- > x =0\\[/tex]

x - 64 = 0------------->x = 64

The critical values are x = 0 and x = 64

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The formula for Observed Score is; Observed score (X) = True score (T) + measurement error (e)

The formula for Observed Score is;

Observed score (X) = True score (T) + measurement error (e)

1) True score is the score that would be obtained if an individual took a test an infinite amount of times and those test scores were averaged. The concept of true score is theoretical because you can't give someone something an infinite number of times.

2) Standard error of measurement is the standard deviation of multiple test scores (how far the sample mean of the data is likely to be from the true population mean).

The less random error (e) in the measure, the more the observed score X approximates the true score T.

Thus;

Observed score = True Score + Error

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The total surface area of the shape is 10053 cm²

From the question, we are to determine the surface area of the shape

The surface area of the shape = Surface area of hemispherical part + Surface are of the cylindrical part

∴ Surface area of the shape = 2πr² + 2πrh + πr²

Where r is the radius

and h is the height of the cylindrical part

From the given information.

r = 20

h = 50

Putting the parameters into the equation, we get

Surface area of the shape = 2π(20)² + 2π(20)(50) + π(20)²

Surface area of the shape = 2π×400+ 2π×1000 + π×400

Surface area of the shape = 800π+ 2000π + 400π

Surface area of the shape = 3200π cm²

Surface area of the shape = 10053.096 cm²

Surface area of the shape ≈ 10053 cm²

Hence, the total surface area of the shape is 10053 cm²

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