Which expression is equivalent to RootIndex 4 StartRoot StartFraction 24 x Superscript 6 Baseline y Over 128 x Superscript 4 Baseline y Superscript 5 Baseline EndFraction EndRoot? Assume x not-equals 0 and y

Answer: Option 1

Step-by-step explanation:

The graphs intersect at x=0 and x=2.

The answer that represents the point where f(x) = g(x) is; A: f(2) = g(2) and f(0) = g(0)

A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math.

Given is a graph we need to find the point of intersection where f(x) = g(x)

How to find the coordinates of Intersection :-

From the attached graph, we see that is represents the relationship between the functions f(x) and g(x).

Now, the coordinates of the points where f(x) = g(x) will be the coordinates of the points where both graphs intersect.

The first point of intersection, we see that;

f(0) = g(0) = 4

Second point shows;

f(2) = g(2) = 0

Thus, we can conclude that;

f(2) = g(2) and f(0) = g(0)

Hence, the answer that represents the point where f(x) = g(x) is; A: f(2) = g(2) and f(0) = g(0)

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The variable that you would have to plot on the y axis (height) is the dependent variable while the variable that is on the x axis (arm span) is the independent or the explanatory variable.

The slope was gotten through the use of the points  (37,39) and (19,25)

This gave the slope of 7/9. This tells us that  height of the person got to be raised by 7/9 inches when arm span increases by 1 inch.

From the given model, a person that has the arm span of 66 would have the height of

12 + 7/9 * 66

= 63.3 inches

A person who is  74 inches height the arm span of = 62*9/7

= 79. 71 inches.

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The order that will result in a final output of -31 when the first input is 0 is as follows; Third → Second → Fourth → First

First gives;

y = -2·x + 34 = 18

Second gives;

y = -x/3 - 10 = -38/3

Third gives;

= -24

Fourth gives;

y = (x - 2)² = 36

We have after several iterations;

Third gives,

= -24

Next we input into the second to get,

y = -(-24)/3 - 10 = 24/3 - 10 = 8 - 10 = -2

Next we input into the fourth to get,

y = ((-2) - 2)² =  (-4)² = 16

Next we input into the first to get,

y = -2×16 + 34 = -32 + 34 = 2

Which gives the order as follows;

Third → Second → Fourth → First

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The probability of winning exactly 21 times is:-0.32

Given,

The probability of winning on an arcade game, p = 0.659

Number of times you play arcade game, n = 30

By assuming this as a normal distribution, we get

Mean=μ=30×0.659 =19.77

Standard deviation, σ = [tex]\sqrt{np(1-p)}[/tex]

= [tex]\sqrt{30(0.659)(1-0.659)}[/tex]

≈ 2.60

Let X be a binomial variable

Then, the z score for x = 21 will be:

z = (x - μ) / σ = [tex]\frac{21-19.77}{2.60}[/tex]

≈ 0.47

Now, the probability of winning exactly 21 times

P (x ≥ z) = P (21 ≥ 0.47) = 0.32

Hence the probability of winning exactly 21 times is 0.32

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The volume of the 0.3% concentration of sodium fluoride required to mix with 100mL of a strong toothpaste with a 1.1% concentration of sodium fluoride to create a blend with a 0.8% concentration of sodium fluoride is 60 mL.

Mixtures refers to substances which are composed of two or more substances physically combined together.

The 1.1% concentration of sodium fluoride will form a mixture with the 0.3% concentration sodium fluoride.

Let the volume of the 0.3 % concentration toothpaste required be x.

Final volume of toothpaste = (100 + x) mL

Amount of mixture = 0.8 * (100 + x)

100 ml * 1.1 + x * 0.3 = 0.8 * (100 + x)

solving for x

110 + 0.3x = 80 + 0.8x

110 - 80 = 0.8x - 0.3x

30 = 0.5x

x = 60

Therefore, 60 mL of the 0.3% concentration of sodium fluoride is required.

In conclusion, the volume of the weaker solution of the sodium fluoride solution required is obtained from the method of mixtures.

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The cross section of a right circular cone parallel to its base is a circle.

A three dimensional shape is a shape that has length, width and height. Examples of three dimensional shapes are cone, cylinder, prism and pyramid.

A two dimensional shape is a shape that have both length and width. Examples of two dimensional shape are circle, rectangle, square.

A cone is a three-dimensional solid geometric shape having a circular base and a pointed edge at the top

The cross section of a right circular cone parallel to its base is a circle.

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Using it's formula, it is found that the monthly payment should be of $688.49 in order to pay off the debt in 15 years.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

For this problem, the parameters are given as follows:

A = 90000, r = 0.045, n = 15 x 12 = 180.

Hence:

r/12 = 0.045/12 = 0.00375.

Then we solve for A to find the monthly payment, as follows.

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 90000(0.00375)\frac{(1.00375)^{180}}{(1.00375)^{180} - 1}[/tex]

A = $688.49

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Kathy has 22 more Euros than British pounds.

Linear equation is an algebraic equation that is a representation of the straight line. Linear equations are composed of variables and constants. These equations are of first-order, that is, the highest power of any of the involved variables i.e. 1. It can also be considered as a polynomial of degree 1. Linear equations containing only one variable are called homogeneous equations. The corresponding variable is called the homogeneous variables.

For instance,

300 / 2 = 150 dollars.

150 /1.64 = 91.46 British pounds

150 /1.32 =113.64 Euros

113.64 - 91.46 =22.18 ≅ 22

Thus Kathy has 22 more Euros than British pounds.

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Answer:

x(x-1)^2

Step-by-step explanation:

x(x^2-2x+1)

x(x-1)(x-1)

(x-1)(x-1)=(x-1)^2

The quantity of meat and cheese sold by the deli according to the description accounts in the task content are; 4.5 and 2.5 pounds respectively.

The quantity of meat sold by the deli as represented by the variable X in the task content can be calculated by solving the systems of equations.

The quantity of cheese sold by the deli as represented by the variable y in the task content can be calculated by solving the systems of equations.

Consequently, solving the system of equations by means of substitution, we have;

y = (30.50-4x)/5

Hence, we have;

11x + 14((30.50-4x)/5) = 84.50

x = 4.5 pounds of meat and

y = 2.5 pounds of cheese.

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Step-by-step explanation:

solution

here

15×5

=75inches

The number that could represent the number of students in class is = X + 2x

Let us take the number of boys to be = X

Then the number of girls is twice that of the boys. That is, y = 2x

Therefore the total number of students in the class z = X + 2x

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If (x+5) is a factor of f(x) then the condition that will be true is f(-5)=0.

Given that (x+5) is a factor the polynomial f(x) and we are required to be the condition that will be true.

Polynomial is combination of algebraic terms may be in addition, subtraction, multiplication and division. If the highest power of variable in polynomial is one then it is said to be monomial ,If the highest power of variable in polynomial is two then it is said to be binomial,If the highest power of variable in polynomial is three then it is said to be trinomial and many more polynomials.

Factors are the numbers which when multiplied gives the number whose factors they are.

It is given that (x+5) is a factor of f(x).

Put (x+5)=0

x=-5

means when we are putting x=-5 then we will get 0.

Hence if (x+5) is a factor of f(x) then the condition that will be true is f(-5)=0.

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The volume of a solid is  [tex]\frac{26}{3} \pi[/tex].

Given

The given curves about the specified line. y = x + 1, y = 0, x = 0, x = 2; about the x-axis

Curve is y = x + 1

Line is y = 0

We have to find out the volume v of the solid obtained by rotating the region bounded by these curves.

If the region bounded above by the graph of f, below by the x-axis, and on the sides by x=a and x=b is revolved about the x-axis, the volume V of the generated solid is given by [tex]V = \pi \int\limits^b_a {(f(x))^{2} } \, dx[/tex]. We can also obtain solids by revolving curves about the y-axis.

Volume of a solid:

According to washer method:

[tex]V = \pi \int\limits^b_a {(f(x))^{2} } \, dx[/tex]

Using washer method, where a=0 and b=2, we get

V = [tex]\pi \int\limits^2_0 {(x+1)^{2} } \, dx[/tex]

= [tex]\pi[ \frac{(x+1)^{3} }{3} ]0 \ to \ 2[/tex]

= [tex]\pi [\frac{(3+1)^{3} }{3} -\frac{(0+1)^{3} }{3}][/tex]

= [tex]\pi [\frac{27}{3} -\frac{1}{3} ][/tex]

= [tex]\pi [\frac{26}{3}][/tex]

= [tex]\frac{26}{3} \pi[/tex]

Therefore the volume of a solid is  [tex]\frac{26}{3} \pi[/tex].

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Answer:

Mean:36

Median:27

Mode:27

Range:50

Step-by-step explanation:

Mean: 19+26+27+27+30+53+69/7=36

Median: The middle number in the sequence when arranged in ascending order which is 27

Mode: The number that appeared more than others which is 27

Range: This is the difference between the largest number and the lowest number in the sequence which is 50.

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Answer:

  a = 144

  b = 67

Step-by-step explanation:

Where a transversal meets parallel lines, consecutive interior angles are supplementary.

  a° +36° = 180° . . . . . . consecutive angles are supplementary

  a = 144 . . . . . . . . . . divide by ° and subtract 36

  b° +113° = 180° . . . . . . consecutive angles are supplementary

  b = 67 . . . . . . . . . . divide by ° and subtract 113

The question given is incomplete. Completed question is given below the answer.

The set,  {(x, y)|9<x2+y2<25} is open and connected.

The following set, {(x, y)|9<x2+y2<25} is:

A. is open (all points of the set are interior)

B. is connected (since it can not be divided into parts)

C. it is not simply connected (it has holes)

D. False, according to the previous answers

Open Set:

In mathematical terms, a set is said to be open if all its points are interior.

That is to say, no point that belongs to the border of the set or is isolated belongs to the set.

Determine the qualities of the given set. (Select all that apply.)

{(x, y)|9<x2+y2<25}

A. open

B. connected

C. simply connected

D. none of the above

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to find the fraction of losses, we need to divide the total amount of losses by the total amount of games played.

if we know that the Rangers won 14 games but they played 25, we can write an equation to find the amount of games lost.

14 + n = 25, where n equals the amount of losses.

now we isolate by moving the 14 to the other side. to do this, we must subtract 14 from both sides, leaving us with n = 11. now we know they lost 11 games.

to find the fraction of lost games, all we need to do is divide 11 by 25 without completing the division. that leaves us with 11/25.

the Rangers lost 11/25 games during the season

hope this helped!!

Volume=80cubic feet

Length×Width×Height =80cubic feet

Base area×Height =80cubic feet

25square feet×Height =80cubic feet

Height =80÷25

=3.2feet

The height of the rectangular prism is 3.2 feet.

To determine the height of a rectangular prism with a volume of 80 cubic feet and a base area of 25 square feet,

The volume of a rectangular prism, that is V = lwh, where l is the length, w is the width, and h is the height of the prism.

Given:

Volume (V) = 80 cubic feet

Base area (A) = 25 square feet

We know that the base area is equal to the product of the length and width:

A = lw.

Calculate the length (l) and width (w) from the given base area:

We know that A = lw, and A = 25 square feet.

If we assume the length to be greater than the width, we can express the base area as lw = 25.

We need to find two factors of 25 that have a difference as small as possible. The factors of 25 are 1, 5, and 25.

We can choose l = 5 feet and w = 5 feet.

V = lwh.

80 = 5 * 5 * h

Divide both sides of the equation by 25:

80/25 = h.

h = 16/5 = 3.2 feet.

Therefore, the height of the rectangular prism is 3.2 feet.

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When a detailed scoring guide or rubric is used to score open-ended questions, the result is scored.

The scoring guide assign points to special degrees of student performance. Instructors use them when a scholar's response can earn a number of the full possible factors, commonly for built-reaction items and performance responsibilities.

Rubrics and scoring guides were implemented into cutting-edge classrooms to offer college students higher know-how of what's being assessed, what standards grades are primarily based upon, and what clean and compelling product standards are addressed.

Even as scoring guides illustrate how college students can earn a certain amount of points for precise questions and responses, rubrics assign ratings primarily based on how well a pupil's reaction meets a degree of overall performance.

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Anja is correct that the histogram is skewed to the right

According to the statement

we have given that the anja collected the data and created the histogram and after analyzing we  have to tell that her claim is correct or not.

So, she collected the data:

A graph shows number of dogs labeled 0 to 2 on the horizontal axis and frequency on the vertical axis. 0 dogs at frequency 20. 1 dog at frequency 15. 2 dogs at frequency 12.

we know that the

Histogram is is an approximate representation of the distribution of numerical data.

and after making the histogram we see that

The histogram is skewed to the right because there is less data on the right side.

So, Anja is correct that the histogram is skewed to the right.

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Answer:

D: She is correct; the histogram is skewed to the right because there is less data on the right side.

Answer: Statistical

Step-by-step explanation:

I think its statistical because its quantitative data, meaning you can count it.

Answer:

5/10

Step-by-step explanation:

0.5 is 5/10 as a decimal. Any number that can be written as a fraction or a ratio is a rational number, so, since 0.5 can be written as 5/10, it’s a rational number.

7.1 cm  long is the arc intersected by a central angle .

What is length of an arc?

Given,

Central angle = π / 2

radius = 4.5 cm

we apply formula of length of arc.

length of the arc = angle ×  radius

                              = (π/2) × (4.5 cm)

Now put value of π = 3.14

length of the arc = (3.14 / 2) × (4.5) cm

                            = 7.065 cm ≈ 7.1 cm

Therefore, 7.1 cm  long is the arc intersected by a central angle .

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The smallest surface area of cubic rectangular boxes = 96 ft²

An object with three dimensions is solid and has both height and depth. A sphere and a cube, for instance, have three dimensions, whereas a circle and a square do not.

A three-dimensional shape's total surface area equals the sum of its side's surface areas. The measured area of all surfaces of three-dimensional solids, such as cubes, spheres, prisms, and pyramids, is expressed in square units.

Since it is a closed rectangular box so, there will be two equal sides.

Volume = 64 ft³

Volume of rectangular cube = hx²

Surface area of rectangular cube = 2x²+4hx

Equating the above equation we get, hx² = 64

                                                               h=64/x²

Put the value of h in surface area formula,

S = 2x² + 4(64/x²)*x

S = 2x² + 256/x

For the surface area to be minimum,

ds/dx = 0

4x - (256/x²) = 0

4x³ = 256

x³ = 64

x = 4 ft

Therefore, the smallest surface area

= 2(4)² + (256/4)

S = 32 + 64

= 96 ft²

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Answer:

9

Step-by-step explanation:

We can tackle the individual parts and combine

1/5 of the sum of 9 and 6 means 1/5 * (9 + 6)

The quotient of 18 divided by the sum of 2 and 4 is 18 / (2 + 4)

Combing everything gives us (1/5 * (9 +6)) * (18 / (2 + 4)

(1/5 * 15) * 18/6

3 * 3 = 9

The power series  is

g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....

To deduce the power series of g(x) from the power series for f(x) and identify its radius of convergence

The power series for f(x) is just the geometric series derived from 1/1-y ,setting y=2x.

Its radius of convergence is 0.5

Let,

f(x)= 1/1-2x = 1+ (2x) + (2x)2 + .........+(2x)n......+....

The power series expansion (geometric series),

valid for I2xI < 1 , IxI < 0.5

so, radius of convergence = 0.5

The power series for g(x) is found by integrating term by term the power series of f(x) (upto a constant). The radius of converngence of g(d) is the same as that of f(x) (from general theory) =0.5

Now, g(x) = ln(1-2x)

= -2 [tex]\int\limits^a_b {(1/1-2x)} \, dx = -2 \int\limits^a_b {f(x)} \, dx[/tex]

=-2 [tex]\int\limits^a_b {[1+(2x)+ (2x)2 +........+ (2x)n+.......]} \, dx[/tex]

g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....

is the power series expansion for g(x).

radius of convergence =0.5

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Answer:

7.

Step-by-step explanation:

Calculate the means for each group:

mean of 0-4 is 2

mean of 5-9 is 7

mean of 10-14 is 12

Mean = (Sum of frequencies * mean) / sum of frequencies

= required mean = [ (2(2) + 1(7) + 2(12)] / (2+1+2)

=  35/ 5

= 7.

It exists not linear the curve indicates that the rate of change exists not constant.

Linear functions exist as those whose graph exists as a straight line. A linear function exists that can be characterized by the equation

y = mx + c, Where m exists the slope and c exists the intercept on the

y-axis. A linear function contains one independent variable and one dependent variable.

Therefore, the correct answer is option c) No, because the curve indicates that the rate of change is not constant.

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