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The sum of geometric series is 12.34 and the series is converges

According to the question,

Geometric series is  100/81 + 10/9 + 1 + 9/10 + 81/100 + 729/1000 + . . .

The given series looks like to be in geometric progression with constant ratio r

r = 2nd term/1st term = a2/a1

= (10/9) / (100/81)

=> 9/10

We know that if the ‘r’ is less than 1 then it is convergent

Here 9/10 < 1, it is convergent.

Clearly, this is the sum of an infinite geometric series.

Sum of infinite series in GP = a/(1 - r)

Where a is the first term, 9/10 is the common ratio.

Sum of the geometric series = (100/81) / (1 - 9/10)

=> (100 / 81) / ( 1 / 10)

=> 100 / 8.1

=> 12.34

Therefore, the given series is convergent and its sum is 12.34

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The lengths of the sides of the quadrilateral are:

WX = 7 units

XY = 11 units

YZ = 7 units

WZ = 11 units

A quadrilateral is any polygon that has four sides and four interior angles.

Part A: The quadrilateral WXYZ has the following vertices,

W(-4, 5)

X(3, 5)

Y(3, -6)

Z(-4, -6)

Each of these vertices of quadrilateral WXYZ have been plotted in the graph that is attached below (see attachment).

Part B: To find the length of each of the sides of the quadrilateral, count the number of square boxes between two points on the graph, given that a square is equal to 1 unit.

Length of WX = 7 boxes = 7 units

Length of XY = 11 boxes = 11 units

Length of YZ = 7 boxes = 7 units

Length of WZ = 11 boxes = 11 units

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We calculated 3-month weight moving average forecast = 0.417

It is a statistical expression of calculating average forecast that allows to keep heavier weight with the most recent data.

Given, weights for the 3 months are 0.6, 0.3 and 0.1 where the first weight is used for the most recent month and the last weight is used for the least recent month.

the weighing factor will be n, n-1 and n-2

n is the number of periods and n=3

now, weight moving average = [W1 × n +W2 × (n-1) × W3 × (n-2)]/ [n+(n-1)+(n-2)]

         [0.6 x 3 +0.3 x 2 + 0.1 x 1]/ [3+2+1] = 0.417

hence, weight moving average is 0.417

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The value of c in the interval (-4 , -3) is -√12 such that f'(c) = 0 as

f'(-√12) = 0, so c = -√12.

Given, the function below satisfies Rolle's Theorem on the specified interval.

we have to find the value of c in the interval (-4 , -3) such that

f'(c) = 0.

the function given is,

f(x) = x + 12/x

First we have to find the derivative of the given function f(x).

f(x) = x + 12/x

f'(x) = 1 - 12/x²

Now, equating the derivative with 0 we get

f'(x) = 0

1 - 12/x² = 0

1 = 12/x²

x² = 12

x² - 12 = 0

(x + √12)(x - √12) = 0

x = √12 or x = -√12

we have two values of x be, ±√12.

but only -√12 lie in the interval (-4 , -3).

So, the value of c be -√12.

Hence, the value of c be -√12.

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Differential formula that estimates the change in the surface area S=6x2 of a cube when the edge lengths change from [tex]x_{0}[/tex] to [tex]x_{0}[/tex] + dx is [tex]$$d S=\left(12 x_0\right) d x$$[/tex]

As per the given data:

The surface area is given by

[tex]$$S = 6 x^2$$[/tex]

Differentiate both sides with respect to  f(x)

[tex]$$S^{\prime}(x)=\frac{d}{d x}\left(6 x^2\right)\\\\=6(2) x^{2-1}$$[/tex]

= 12 x

The estimated change in surface area is given by

[tex]$$d S=S^{\prime}(x) d x= > d S\\\\$$[/tex]

= (12 x) dx

The change in surface area at [tex]$x=x_{0} $[/tex] is

[tex]$$d S=\left(12 x_0\right) d x$$[/tex]

Therefore the answer is [tex]$$d S=\left(12 x_0\right) d x$$[/tex]

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Write a differential formula that estimates the change in the surface area S=6x2 of a cube when the edge lengths change from [tex]x_{0}[/tex] to [tex]x_{0}[/tex] + dx

For the given height and distance  the answer of the following questions are:

a. Change in distance between the camera to the rocket at that moment is equal to 540ft/sec.

b. Change in the angle of elevation is equal to 0.144rad/sec.

As given in the question,

Let 'α' be the angle of elevation

'h' be the height of the rocket

'x' be the distance between the camera and the rising rocket.

a. Relation between x , h, and 4000 ft during launching pad is given by Pythagoras theorem:

x² = h² + 4000²

Differentiate with respect to time 't' we get,

2xdx/dt = 2hdh/dt + 0 __(1)

When h = 3000ft

x² = 3000² + 4000²

⇒x = 5000ft

dh/dt = 900ft/s

Substitute all values in (1) we get,

2(5000)dx/dt= 2(3000)(900)

⇒dx/dt = 5,400,000/ 10,000

⇒dx/dt = 540ft/sec.

b. tanα = h/4000 __(2)

when h = 3000ft

tanα = 3/4

⇒α = 0.6435

Differentiate (2) with respect to t we get,

sec²α dα/dt = (1/4000) dh/dt

⇒sec²(0.6435) dα/dt = (1/4000)(900)

⇒dα/dt = (0.225)/ 1.5625

⇒dα/dt = 0.144 rad/ sec.

Therefore, for the given height and distance the answer of the following questions are:

a. Change in distance between the camera to the rocket at that moment is equal to 540ft/sec.

b. Change in the angle of elevation is equal to 0.144rad/sec.

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The slope of the line between these two points is $.06 / lb which is defined as the ratio of vertical extrade among points, the rise, to the horizontal extrade.

The slope is described because the ratio of the vertical extrade among points, the rise, to the horizontal extrade among the equal  points, the run. . A slope with a extra absolute price shows a steeper line. The course of a line is both increasing, decreasing, horizontal or vertical. If a line is horizontal the slope is zero.

Let X1 = 2.1 pounds, Y1 = $3.4 and

X2 = 70 pounds, Y2 = $7.5

ΔX = 70 - 2.1 = 67.9

ΔY = 7.5 - 3.4 = 4.1

Slope (m) = ΔY / ΔX

= 4.1 / 67.9

= 0.060382916053019

= 0.06 (Rounded)

Therefore, answer is Option $.06 / lb.

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Linda enrolls in two semesters for a total of 20 credits at a cost of $550 per credit hour (tuition and fees), plus $350 for each semester's textbooks. $488 is the total cost for one month. The right response in this case is option A.

In economics, the total cost is the total of all expenses a company incurs in order to produce a particular level of production.

The total cost is the sum of all the expenses a firm has expended to create a specific level of output. Product managers can assess their overall profit margin by adding together their fixed and variable costs. The sum of the fixed and variable expenses is the total cost.

The total cost for one semester = 10(550) + 350

= 5850

Total cost for one month = 5850/12

= 487.5 = $488

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The Time taken for David and Amy to be exactly 23 miles apart is 1.014 Hours.

Let [tex]t[/tex] be the time taken to reach 23 miles apart from a single point.

David and Amy start at same point and move towards different directions, making them move at perpendicular to each other.

According to Pythagoras theorem, and distance = Speed x time.

[tex](17t)^2 + (15t)^2 = 23^2[/tex]

[tex]289t^2 + 225t^2 = 529[/tex]

[tex]\therefore 514t^2 = 529[/tex]

[tex]t^2 = \frac{529}{514}[/tex]

[tex]t^2 = 1.029[/tex]

[tex]\therefore t = \sqrt{1.029} = 1.014 \text{ hours}[/tex]

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We have to find a problem at the 5% significance level.

Sample size = 10.

If the Significant value is between five and ten, we lose one till the test. W. C. has a critical value of 44. We must perform a one-tailed analysis of the test. What tail is that?

If one is more efficient than the other, we are asked.

Here, almost everything is positive, and we discover what our values are. Mhm. The following data set, High bromide, was employed to get more sleep for 10 patients who used love level high school.

That's the control group minus the other one.

The control group is made up of people. I'm not sure if it's a left or right tail, so we'll just calculate the two ends.

The right tail will be 44, the other tail will be divided by two, and 55 minutes will equal 44. It's extremely useful. Okay. It won't reject if it's less than 11, and it will if it's more than 44. Is the music good? There were 10 pupils in our class, and their scores were 1.9 plus 0.8 plus 1.1 plus 0.1. The value of our nut is 23.4. Okay. Critical value takes us directly to the center. This was only a right tail test because we were unable to rule out the null hypothesis. The results would change to 50 if we ran it again at the 1% significance threshold. ten tons and eleven

We failed to reject the hypothesis again.

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The value of x in the kite is 32 (option B)

Polygons are defined as plane (two-dimensional) and closed shapes that are formed by joining three or more line segments with each other.

A polygon can be categorized as regular and irregular polygon based on the length of its sides.

Given figure of kite is a polygon,

Three angles of kite are given as 100° , 101° and (4 + 3x)°

It is given that sides opposite sides are equal to each other

Therefore, opposite angles are also equal

=> 4 + 3x = 100

=> 3x = 96

=> x = 96 / 3

=> x = 32

Hence , Value of x in the kite is 32

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Answer:

[tex]7.6 \times 10^7[/tex]

Step-by-step explanation:

[tex]1.5 \times 10^8-7.4 \times 10^7 \\ \\ =10^7 (15-7.4) \\ \\ =7.6 \times 10^7[/tex]

The difference between (1.5 x 10⁸) and (7.4 x 10⁷) is 7.6 x 10⁷.

The mathematical operation is subtraction. It is employed to eliminate words or expression's objects.

To find the difference between (1.5 x 10⁸) and (7.4 x 10⁷) :

We subtract both the numbers,

(1.5 x 10⁸) - (7.4 x 10⁷)

To solve further, we take the common term outside the bracket.

(1.5 x 10⁸) - (7.4 x 10⁷)

= 10⁷ (15 - 7.4)

= 7.6 x 10⁷

Therefore, the difference is 7.6 x 10⁷.

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After simplification of the given stock of steel bar , 1-21/64 inches of available stock are wasted.

As given in the question,
Length of the steel bar in stock = 9 7/16 inches

Length of one punch = 4 1/64 inches

Length of other punch = 4 3/32 inches

Simplification of the given data,

Length of steel bar - length of one punch

= 9 7/16 - 4 1/64

= 144/16 - 256/64

= (576 - 256)/64

= 320/64

=5 27/64 inches

Now,

subtract 4 3/32 from 5 27/64

= 5 27/64 - 4 3/32

= 347/64 - 131/32

=347/64 - 262/64

=(347-262)/64

=85/64

= 1 21/64inches

It means about "1 21/64" inches of the steel beam was wasted.

Therefore, after simplification the length of 1 21/64 inches of stock get wasted.

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Answer:

Step-by-step explanation:

Answer: In the below pic attached

The LCD of the given number set is; B: 108

The least common denominator (LCD) is defined as  the smallest number that is a common denominator for a given set of fractions or numbers.

Now, we are given the number set as;

27, 54, 9, 108

Let us break down these into their respective products in terms of the prime numbers to get;

27 = 3 * 3 * 3

54 = 2 * 3 * 3 * 3

9 = 3 * 3

108 = 3 * 3 * 3 * 2 * 2

Thus, the LCD = 3 * 3 * 3 * 2 * 2 = 108

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To model the data with a linear function, we can use the two data points for ages 32 and 35 to find the slope and y-intercept of the line. Since the cost of life insurance for a female non-smoker at age 32 is $172 and the cost at age 35 is $182, the slope of the line is given by the formula:

$m = \frac{\text{cost at age 35} - \text{cost at age 32}}{\text{age 35} - \text{age 32}} = \frac{182 - 172}{35 - 32} = \frac{10}{3} = 3.33$

We can then use the point-slope formula to find the y-intercept of the line:

$y - y_1 = m(x - x_1)$

$y - 172 = 3.33(x - 32)$

To find the y-intercept, we can set $x = 0$ and solve for $y$:

$y - 172 = 3.33(0 - 32)$

$y - 172 = -105.76$

$y = 66.24$

Therefore, the equation of the line that models the data is given by:

$y = 3.33x + 66.24$

To predict the cost of life insurance for a female non-smoker of age 40, we can substitute 40 for $x$ in the equation above:

$y = 3.33(40) + 66.24$

$y = \boxed{239.44}$

Therefore, the predicted cost of life insurance for a female non-smoker of age 40 is $239.44.

A psychologist selects a random sample of 25 handicapped students and measures their manual dexterity scores, then if she wants to improve her precision she should use a larger sample size.  

Each sample has an equal chance of being chosen as part of the sampling procedure known as random sampling. A randomly selected sample is intended to be a fair reflection of the entire population. By increasing sample size, you can improve the accuracy of your estimates, which means that the result will be more "statistically significant" for any given estimate or size of effect. The accuracy of the average results will increase with sample quantity. Smaller error margins and the identification of outliers in the data are two further benefits of larger sample sizes.

If they observe an effect that is almost significant, some researchers decide to increase their sample size. This is done rather than concluding that there is no effect because the researcher believes he is short on samples. Because the standard error is reduced as sample size increases, confidence intervals are narrower. c) The statement "there is a 95% likelihood that the population mean is between 350 and 400" is similar to the statement "there is a 95% confidence interval for the population mean is (350, 400)".

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Correct Question:

A psychologist selects a random sample of 25 handicapped students and measures their manual dexterity scores. she uses this data to test the hypothesis that the mean dexterity score is different than 45. What would you advise her?

Answer:

40.8 miles.

Step-by-step explanation:

To solve this problem, we need to know the distance that the airplane traveled in the air from the point of descent until it touched the ground. This distance is determined by the glide angle and the altitude of the airplane.

In general, the distance traveled in the air is equal to the altitude of the airplane divided by the sine of the glide angle. In this case, we are given the altitude and the glide angle, so we can calculate the distance traveled in the air as follows:

Distance = Altitude / sin(glide angle)

Plugging in the values from the problem, we have:

Distance = 20.42 miles / sin(30 degrees)

The sine of 30 degrees is 0.5, so the distance traveled in the air is:

Distance = 20.42 miles / 0.5

This simplifies to:

Distance = 40.84 miles

Rounded to the nearest tenth mile, the distance traveled in the air is 40.8 miles. This is the answer to the problem.

There are four possible  values of C if there exist distinct complex numbers.

A complex number is an element of a number system that extends the real numbers with a specific element denoted i is called the imaginary unit . the equation every complex number can be expressed as,

             a + bi

where a and b are real numbers.

Let p(z) denote the cubic on the left-hand side; the right-hand side is then c3p(z/c). Write p(z)=z3+Az2+Bz+C so

z3 + Az2 + Bz + C ≡  z3+ cAz2 + c2Bz + c3C

⟹ (c−1)A =  (c2−1)B = (c3−1)C = 0.

Solving this we can find the possible values of C.

A real number can be said as a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. continuous means that values can have arbitrarily small variations. Every real number can be almost uniquely represented by an infinite decimal expansion.

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Question is incomplete. The complete question is:

Let c be a complex number. Suppose there exist distinct complex numbers r, s, and t such that for every complex number z, we have

    (z−r) (z−s) (z−t) = (z−c r) (z−c s) (z−c t).

Compute the number of distinct possible values of c.

Answer:

2(x + 1)

Step-by-step explanation:

x is the unknow number.  Add 1 to that and then take that expression (x+1) and multiply it by 2.

Answer:

the answer that ur looking for is Aisha she has read more than David

Step-by-step explanation:

55% of 240=132

Answer:

Step-by-step explanation:

Ashia read more

The mother will give the child $3 for each dot on the upside of the die. the greater expected value is Mother's Offer

The expected value of father's offer is $10, since the probability of getting heads is 50% and the reward for getting heads is $20.

The expected value of mother's offer is $3, since the probability of getting any number is 1/6 and the reward for getting any number is $3.

Therefore, the mother's offer has a greater expected value than the father's offer.

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Answer: 27/100

Step-by-step explanation:

A number line is a visual representation of real numbers in elementary mathematics. It is an image of a magnitude line.

What is number line

A number line is a visual representation of real numbers in elementary mathematics. It is an image of a magnitude line. It is assumed that each real number on the number line corresponds to a point on the number line, and vice versa.

Pencil. Edges of a ruler Edges of a paper

Pencil.

Edges of a ruler.

Edges of a paper.

Horizontal Line, Vertical Line, Perpendicular line, Intersecting lines.

Oblique Lines, Divergent lines, Convergent Lines, and Parallel Lines.

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Answer:

answer on the picture.........

The variance of the number of hurricanes in a randomly selected year is 12.5 .

Mean number of hurricanes in a randomly selected year =

0.1 × 20 + 0.3 × 15 + 0.6 × 10 = 12.5

Now, since the sum of independent Poisson random variables also follows Poisson distribution.

Thus, the variance of the number of hurricanes in a randomly selected year = Mean = 12.5

In both statistics and probability theory, variance is the predicted squared deviation of a binomial distribution from its sample proportion or sample mean.

Dispersion, or how far apart from the mean a set of data are from one another, is measured by variance. A few ideas that involve variance are descriptive research, statistical inference, testing hypotheses, goodness of fit, and Monte Carlo sampling.

The variance of a set of uncorrelated explanatory variables is equal to the sum of their variances, making it easier to manipulate mathematically than other measures of dispersion like anticipated absolute deviation.

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Answer:

The width of the rectangle is 32cm and the length is 37cm.

Step-by-step explanation:

Answer:

(10 * 312) + (10 * 612) + (10 * 812)

Step-by-step explanation:

To find the total amount of shampoo that Christa purchased in ounces, we can use the expression (10 * 312) + (10 * 612) + (10 * 812), which is equivalent to the expression that Christa used. This expression is also equivalent to 3120 + 6120 + 8120, which can be simplified to 3120 + 6120 + 8120 = 3120 + 6150 + 8100 = 9280 + 6150 = 15,430. Therefore, the expression (10 * 312) + (10 * 612) + (10 * 812) is equivalent to 15,430.

Answer:GIVE A BETTER DETAILED QUESTION sorry for caps

Step-by-step explanation: