(SAT Prep) Find the value of x.

Answer:

c

Step-by-step explanation:

The radius of convergence,R, of the series \(\[ \sum_{n=1}^{\infty} ~9(-1)^n~ nx^n \]\) is (1, ∞)

We know that for a power series ∑an (x - p)^n

if |x - p| < R then the series converges,

and if |x - p| > R then the series diverges.

Here, the number R is called the radius of convergence.

We have been given a series \(\[ \sum_{n=1}^{\infty} ~9(-1)^n~ nx^n \]\)

We need find the radius of convergence.

We use ratio test.

We know for \($\lim_{x\to\infty}~ | \frac{a_{n+1}}{a_n}|=L\)

if L < 1, then the series converges

and If \($\lim_{x\to\infty}~a_n \neq 0\) then \(\sum a_n\) diverges.

Using ratio test for given series,

\($\lim_{x\to\infty}~ | \frac{9(-1)^{n+1}~ (n+1)x^{n+1}}{9(-1)^n~ nx^n}|\\\\\\\)

= \($\lim_{x\to\infty}~ | \frac{(n+1)x^{n+1}}{nx^n}|\)

= \($\lim_{x\to\infty}~ | \frac{(n+1)x}{n}|\)

\(=|x| $\lim_{x\to\infty}~ | \frac{n+1}{n}|\)

= |x|

This means, the series is convergent for |x| < 1.

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Answer:

x≤−9

Step-by-step explanation:

Answer:

64.44cm^2

Step-by-step explanation:

11×7 -pi ×2^2=77-31.4×4=77-12.56= 64.44 cm^2

Answer:

55%

Step-by-step explanation:

99+121=220

121/220 x 100= 55

For the value of L = 144.48, the probability of having L greater than the mean glucose level of Shelia is 0.02.

Here it is given that Sheila's glucose level follows a normal distribution with a mean of 128 mg/dl and a standard deviation of 8 mg/dl

L is the patient's blood test level.

It is given that the probability that the mean glucose level i.e 128 mg/dl is above L is 0.02.

We need to find L

We know

P(128>L) = 0.02

or, 1 - P(128 ≤ L) = 0.02

or, P(128 ≤ L) = 0.98

We know that for any Normal distribution we find the probability by converting it to standard form and then checking the p-value.

P(X < x) = Φ[(x - μ)/σ]

where,

μ = mean

σ = standard deviation

Therefore,

Φ[(L - 128)/8] = 0.98

we see that for a Z score of 2.06,

Therefore we get

(L - 128)/8 = 2.06

or, L - 128 = 16.48

or, L = 128 + 16.48

= 144.48

Therefore, the value of L would be 144.48

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Complete Question

Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 milligrams per deciliter one hour after a sugary drink is ingested. Shelia's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with a mean of 128 mg/dl and a standard deviation of 8 mg/dl. Let L denote a patient's glucose level.

If measurements are made on four different days, find level L such that there is a probability of only 0.02 that the mean glucose level of four test results falls above L for Shelia's glucose level distribution. What is the value of L?

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Answer:

I think it's A/the first one

Step-by-step explanation:

The total return over the year is 15.46%. The dividend yield is 7.21%, and the capital gain rate is 15.46%.

The price of a stock is equal to the current dividend plus the present value of all future dividends plus the price in one year. As a result, the share price of SPCC after a year will be:$112 = $7 + $105 + PV$PV = $0

Using the formula of the total return of an asset, which is equal to its capital gain plus dividend yield, we have;Total Return = Capital Gain + Dividend YieldCapital Gain = (Ending Price - Initial Price) / Initial PriceCapital Gain = ($112 - $97) / $97 = 0.1546 or 15.46%Dividend Yield = Annual Dividend per Share / Initial PriceDividend Yield = $7 / $97 = 0.0721 or 7.21%

Therefore, the total return over the year is 15.46%. The dividend yield is 7.21%, and the capital gain rate is 15.46%.

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Answer:

420

Step-by-step explanation:

Answer:

420

Step-by-step explanation:

vnhfuurrttjnnnnnbh

Answer: The given statement "if every column of an augmented matrix contains a pivot then the corresponding system is consistent" is true. This is because when every column of an augmented matrix contains a pivot, it implies that there are no free variables in the system of equations represented by the matrix.

Step-by-step explanation: Since every variable has a pivot in the augmented matrix, there is a unique solution to the system of equations. This is the definition of a consistent system - one that has at least one solution.                                                                                                                  In summary, the statement is true because the presence of a pivot in every column of an augmented matrix guarantees a unique solution to the system of equations, which is the definition of a consistent system.

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Answer:

Step-by-step explanation:

Required condition for SSS is three sides congruence.

We have:

We observe:

We need:

TW must be congruent or equal to XY

Because

It's sss i e side-side-side

Here

Hence only one more side is required

Answer:

35x+40y

Step-by-step explanation:

1. expand the terms by multiplying 5 by what's inside the parenthesis, so multiply by 7x and 8y and add them. So you get 35x+40y

Answer:

35x +40y

Step-by-step explanation:

5(7x+8y)

Distribute

5*7x + 5*8y

35x +40y

B. save time in arriving at solutions to problems. Heuristics are problem-solving shortcuts or rules of thumb that can save time when arriving at solutions to problems.

The use of heuristics rather than algorithms is most likely to save time in arriving at solutions to problems. Heuristics are mental shortcuts or rules of thumb that are used to solve problems quickly and efficiently, whereas algorithms are step-by-step procedures for solving problems. While algorithms may produce more accurate solutions, they can be time-consuming to apply. Heuristics, on the other hand, allow for quick problem-solving and are often based on our language skills and prior knowledge. However, relying too heavily on heuristics can sometimes lead to errors or the overconfidence phenomenon.

They might not always yield the most accurate solutions compared to algorithms, which are step-by-step, systematic procedures that guarantee a correct solution. Heuristics usually rely less on language skills and do not necessarily minimize the overconfidence phenomenon.

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Heuristics are mental shortcuts or rules of thumb that people use to make decisions or solve problems quickly and efficiently.

B. save time in arriving at solutions to problems . The correct answer is:

Heuristics are mental shortcuts or rules of thumb that people use to make decisions or solve problems quickly and efficiently. They are simple and often automatic strategies that allow individuals to make judgments or decisions without engaging in a lengthy, deliberate, and systematic process of problem-solving.

One of the main advantages of using heuristics is that they can save time in arriving at solutions to problems. Instead of analyzing all available information and considering all possible alternatives, heuristics allow individuals to quickly narrow down options and make decisions based on simplified cognitive processes. This can be especially useful in situations where time is limited or when individuals need to make decisions on the spot.

However, heuristics are not always foolproof and can sometimes lead to errors or biases in decision-making.

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Answer:

\(x = -3\)

Step-by-step explanation:

\(\frac{-3(2x + 1)}4 = 3(x + 4) + \frac34 \text{ // Distribute}\\\\\frac{-6x - 3}4 = 3x + 12 + \frac34 \text{ // Multiply by 4}\\\\-6x - 3 = 12x + 48 + 3\\-6x - 3 = 12x + 51 \text{ // Add 6x and subtract 51}\\-54 = 18x \text{ // Divide by 18}\\-3 = x\)

Answer: x=-3

\(\frac{-3(3x+1)}{4} = 3(x+4) +3/4\\\frac{-3x-3}{4} = 3x+12+3/4\\\frac{-3x-3}{4}=3x+15/4\\4*\frac{-3x-3}{4}= 3x+15/4\\ *4\\-3x-3= 3x+15\\+3 +3\\-3x=3x+18\\-3x -3x\\-6x=18\\/-6 -/6 \\x= -3 \\\\\)

I think i did this right for you, hopefully this helped

The height of the cone needs to be approximately 4.5 inches to have the same volume as the cup, which has a width of 3 inches and a height of 2 inches.

To determine the required height of the cone, we can use the formula for the volume of a cone, which is \(\frac 13 * \pi * r^2 * h\), where r is the radius and h is the height of the cone.

Given that the cup has a width of 3 inches, we can calculate the radius of the cup by dividing the width by 2, which gives us 1.5 inches. Therefore, the radius of the cup is 1.5 inches.

Since we want the cone to have the same width as the cup, the radius of the cone should also be 1.5 inches.

Now, let's substitute the values into the volume formula for the cup: \(\frac 13 * \pi * (1.5)^2 * 2\). The volume of the cup is approximately 7.07 cubic inches.

To find the required height of the cone, we can rearrange the volume formula and solve for h:

\(h = \frac {3 * volume} {\pi * r^2}\).

Plugging in the values, we get \(h = \frac {3 * 7.07}{\pi * (1.5)^2}\), which simplifies to h = 4.5 inches.

Therefore, the height of the cone needs to be approximately 4.5 inches to hold the same amount of ice cream as the cup with a width of 3 inches and a height of 2 inches.

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Using proportions, the costs are given as follows:

a) Total Labor Cost: $2,505,600.

b) Total Product Cost: $1,950,000.

c) Total Cost = $4,455,600.

d) Cost per home = $461.77.

e) Cost per week = $99,013.33.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For item a, the labor cost is found using the earnings of the workers, as follows:

45 weeks x 5 days x 8 hours x 58 per hour x (12 + 8 + 4 workers)

Hence:

Total Labor Cost = 45 x 5 x 8 x 58 x 24 = $2,505,600.

For item b, the product cost is the cost of the boards, hence:

(175 + 150 + 50 boards) x 5,200

Total Product Cost = 375 x 5,200 = $1,950,000.

For item c, the total cost is the sum of the product cost and the labor cost, hence:

Total Cost = 2,505,600 + 1,950,000 = $4,455,600.

For item d, the cost per home is found dividing the total cost by the 9,649 homes, hence:

Cost per home = 4455600/9649 = $461.77.

For item e, the cost per week is found dividing the total cost by the 45 weeks, hence:

Cost per week = 4455600/45 = $99,013.33.

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x=-.7+1.8734994i  and x=-.7-1.8734994i

Step-by-step explanation:

2x+5x² +7x+10+6+4+-2x=(5x²)+(2x+7x-2x)+(10+6+4)=5x²+7x+20

quadratic equation

x=(-b±√(b²-4ac))/2a

where a=5, b=7, c=20

x=(-7±√(7²-4(5)(20)))/(2(5))

x=(-7±√((49-400))/10

x=(-7±√(-351))/10

x=(-7±18.734994i)/10

x=-.7+1.8734994i  and x=-.7-1.8734994i

Answer:

y= - 3/2x + 7 hope this helps you out :)

Answer:

orange

Step-by-step explanation:

Answer: A. Orange Graph.

Step-by-step explanation: I put A, and it was the perfect answer.

Answer:

Darryl's TV is larger by 200 inches2

Step-by-step explanation:

Darryl's tv is 30*40 = 1200 inches2

Terrence's tv is 20*50 = 1000 inches2.

==========================================================

Explanation:

We simply multiply the two values given to us

600*(1/12) = 600/12 = 50

We expect about 50 bulbs to be defective.

Note how if we had 50 bad bulbs, then 50/600 = (1*50)/(12*50) = 1/12 of the batch of 600 bulbs is defective.

Answer:

R and s are parallel as they are the same size and length

i would think 2 and 5 or 2 and 6

hope this helps! (:

A function is a function that represents the area under a curve. In this case, f is the curve being considered. The function a(x) represents the area under the curve of f from x=0 up to x.

So, if we want to find the area under the curve of f from x=0 up to x=3, we would evaluate a(3) - a(0). This would give us the total area under the curve of f from x=0 to x=3. Similarly, if we have another area function, say b(x), that represents the area under the curve of f from some other starting point (e.g. from x=1), we would use b(x) to find the area under the curve of f from x=1 up to some other x value.
The graph of f, displayed in the figure to the right, represents a function that can be analyzed using various mathematical concepts. In this case, we can consider two area functions for f, denoted as A(x) and B(x), which would allow us to evaluate the areas under the curve of the graph with respect to the x-axis. These area functions can be used to understand properties and behaviors of the function f in different regions of the graph.

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Answer:

LN = 37

Step-by-step explanation:

The Segment Addition Postulate tells us that LM+MN = LN

The maximum and minimum values of f(x,y,z) = 2xyz are \(\frac{2}{\sqrt{3} } and \frac{-2}{\sqrt{3} }\)

The value of the function at a maximum point is called the maximum value of the function and the value of the function at a minimum point is called the minimum value of the function. Differentiate the given function.

f(x,y,z)=2xyz

Computation:

Differentiating the given equation up to second order

\(\begin{gathered}f_x=2yz\Rightarrow 2yz=0 either y=0 or z=0\\f_y=0\Rightarrow 2xz=0 either x=0 or z=0\\f_z=0\Rightarrow 2xy=0 either x=0 or y=0\end{gathered}\)

So, the critical point is (0,0,0)

Now, using the Lagrange's on the boundary,

\(\begin{gathered}g(x,y,z)=x^2+y^2+z^2-1=0\\g_x=2x\\g_y=2y\\g_z=2z\end{gathered}\)

\(So, \bigtriangledown f=\lambda \bigtriangledown g\left < 5yz,5xz,5xy \right > =\lambda \left < 2x,2y,2z )\)

By solving we get,

\(x^2=y^2=z^2\) then,

\(\begin{gathered}x^2+y^2+z^2=1\\3z^2=1\\z=\pm \frac{1}{\sqrt{3} } \\y=\pm \frac{1}{\sqrt{3} } \\\\x=\pm \frac{1}{\sqrt{3} } \\\end{gathered} x 2+y 2+z 2=13z 2=1z=± 31\)

\(So, the critical points are (0,0,0),(\frac{1}{\sqrt{3} } ,\frac{1}{\sqrt{3} } ,\frac{1}{\sqrt{3} } )and (\frac{-1}{\sqrt{3} }, \frac{-1}{\sqrt{3} },\frac{-1}{\sqrt{3} })\)

So, by substituting the critical points we get,

\(\begin{gathered}f(0,0,0)=0\\f(\frac{1}{\sqrt{3} }, \frac{1}{\sqrt{3} },\frac{1}{\sqrt{3} })=2(\frac{1}{\sqrt{3} })(\frac{1}{\sqrt{3} })(\frac{1}{\sqrt{3} })\\=\frac{2}{3\sqrt{3} } \\f(-\frac{1}{\sqrt{3} },-\frac{1}{\sqrt{3} },-\frac{1}{\sqrt{3} })=2(-\frac{1}{\sqrt{3} })(-\frac{1}{\sqrt{3} })(-\frac{1}{\sqrt{3} })\\=-\frac{2}{3\sqrt{3} }\end{gathered}\)

Hence the maximum and minimum values of f(x,y,z) are \(\frac{2}{\sqrt{3} } and \frac{-2}{\sqrt{3} }\)

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Answer:

y = 15 - 3.6x.

Step-by-step explanation:

The initial amount of fuel before cruising begins = 15,000 gallons.

The equation is  y = 15 - 3.6x where y is in thousands of gallons and x = number of hours.

Answer: y would be -5

Step-by-step explanation: