Use the given Maclaurin series to evaluate the limit

The experimental probability the placebo pill induced better concentration on the student exams is 0.64

The question has to do with probability.

Probability is the likelihood of an event occurring.

The probability of an event A is given by

P(A) = number of occurrences of event A/total number of occurrences of all events.

Given that in the study on the placebo effect on 100 students, 64 were found to perform better on tests after taking a fake pill to improve concentration.

The event A = students performing better.

Since 64 students performed better, the number of occurrences of event A = 64.

Since there were 100 students, the total number of occurrences = 100.

So, P(A) = P(students perform better)

= number of occurrences of event A/total number of occurrences of all events.

= 64/100

= 0.64

So, the experimental probability the placebo pill induced better concentration on the student exams is 0.64

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Answer: 8

Step-by-step explanation:

PEMDAS

Answer:

Even

Step-by-step explanation:

Answer:

Rajani needs 7.8 (39/5) cups of yogurt to make 13 smoothies.

Step-by-step explanation:

3/5 = 0.6

The amount of cups of yogurt needed to make 13 smoothies = 13 x 0.6

This equals to 7.8 cups or 39/5 cups of yogurt to make 13 smoothies.

Hope this helps!

The correct answer is 7.2 inch.

The nearest tenth of a 7inch.

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Using proportions, it is found that Mrs. Wood should expect 1,898 books out of the 36,500 to have major damage.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

For this problem, the proportion of books with major damage is:

43/(716 + 68 + 43) = 0.051995.

Hence, out of 36,500 books, the expected amount of books with major damage is:

0.051995 x 36,500 = 1898.

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The solution to this problem is (s2+1)Y(s)−2s−1=2s2+4 .

We let  L[y(t)]=Y(s) . With that, tabular Laplace-transform laws entail

L[y′]=sY(s)−y(0)=sY(s)−2

L[y′′]=s2Y(s)−sy(0)−y′(0)=s2Y(s)−2s−1

∴L[y′′+y]=(s2+1)Y(s)−2s−1 .

Since the Laplace transform of  sin(kt)  is  ks2+k2 , we have

(s2+1)Y(s)−2s−1=2s2+4 .

This equation readily solves to  Y(s)=2s3+s2+8s+6(s2+1)(s2+4) . We compute its partial fraction decomposition as  Y(s)=2s+53s2+1+−23s2+4 .

Our final step is to use tabular Laplace-transform laws ( sin(kt)↦ks2+k2 , and  cos(kt)↦ss2+k2 ) to get  y(t)=2cost+53sint−13sin(2t) . One can check that this indeed satisfies the initial value problem.

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The interpretation of the slope is that (b) the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute

Linear equations are equations that have constant average rates of change, slope or gradient

From the table of values, we have the following points

(x, y) = (5, 5.5) and (10, 5)

The slope of the table of values is calculated as:

m = (y2 - y1)/(x2 - x1)

Substitute the known values in the above equation

m = (5 - 5.5)/(10 -5)

Evaluate the difference

m = -0.5/5

Evaluate the quotient

m = -0.1

This means that the slope is -0.1

From the table of values, we have

x represents the elapsed time and y represents the volume of helium

So, the interpretation of the slope is that (b) the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute

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The value of trigonometry terms sin(2x) is 120/169 and cos(2x) is 119/169 and tan(2x) is 120/119.

According to the statement

We have given that the sin(x) = 5/13 , x in quadrant iii

And we have to Find the value of cos x using the following:

So, For this purpose, we know that the trigonometry terms are:

sin2(x) + cos2(x) = 1;  

or cos2(x) = 1-sin2(x)

And

cos2(x) = 1-(-5/13)2 =

cos2(x) = 144/169;  

We know that the

In quadrant III both the sin and cos are negative so

cos(x) = -12/13 (after taking square roots).

And

Then tan(x) = sin(x)/cos(x) = (-5/13)/(-12/13) = 5/12.

Now you can use the angle addition formulas to find sin(2x), cos(2x), and tan(2x).

Now

sin(x + x) = sinx * cosx + cosx * sinx

              = (-5/13)*(-12/13) + (-12/13)(-5/13) = 120/169

And

cos(x + x) = cosX * cos(x) - sinx*sinx

               = (-12/13)(-12/13) - (-5/13)(-5/13)

               =  119/169

So,

You could use the tan double angle formula, but it is easiest to use  

tan(2x) = sin(2x)/cos(2x)  = (120/169) / (119/169)

          = 120/119.

So, The value of trigonometry terms sin(2x) is 120/169 and cos(2x) is 119/169 and tan(2x) is 120/119.

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The expression √180 * 2√30 is equivalent to the expression 60√6

An equation is an expression that shows the relationship between two numbers and variables.

The square root is a factor of a number that, when multiplied by itself, gives the original number.

Given the expression √180 * 2√30

Collecting like terms give:

= 2√(180 * 30)

Simplifying:

= 60√6

The expression √180 * 2√30 is equivalent to the expression 60√6

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Answer:

23.6

Step-by-step explanation:

→ Identify length not given

Opposite

→ Find a formula without opposite

Cos = Adjacent ÷ Hypotenuse

→ Rearrange

Adjacent = Cos × Hypotenuse

→ Substitute

cos 38 × 30 = 23.6

Answer:

[tex]x = 23.6[/tex]

Step-by-step explanation:

To find the missing side of a right-angled triangle, first look at the given angle, and notice its relationships with the given and required sides.

In this case:

• The side adjacent to the given 38° angle is [tex]x[/tex] (required).

• The hypotenuse is 30 units.

The trigonometric ratio that relates the adjacent side and hypotenuse of a triangle is cosine (cos), where:

[tex]\boxed{cos \space\ \theta = \frac{adjacent}{hypotenuse}}[/tex].

Substituting into the formula:

[tex]cos (38^{\circ}) = \frac{x}{30}[/tex]

⇒ [tex]x = cos(38^{\circ}) \times 30[/tex]

⇒ [tex]x = 23.6[/tex]

Answer:

Step-by-step explanation:

Equation

f(x) = (8x + 1) / (2x + 9)

Notice the brackets. They are necessary to show what comes before the division sign, and what comes after.

Behavior

The best way to state the behavior is to get something like a graphing program to show you what the curve looks like -- where it's critical points are for example. I use Desmos for  this kind of question, Just do a search for Desmos and bookmark it. You will use it quite often.

So you want to know the behavior.

Right Curve

Crosses the x axis at (-0.125, 0)

Crosses the y axis at (0,0,111)

The right curve has a domain of -∞ < x < ∞

The  right curve has a range of -∞ < x < ∞

The range is going to have to go out quite a ways before you see any dramatic decrease in the way it is drawn.

Left Curve.

The right hand curve never crosses either the x or y axis.  Nor does it just touch the x or y axis.

The domain is -∞ <x < 0

The range is 0<x<∞

Answer:

Step-by-step explanation:

base=b=7.2yd

height =h=7yd

area of parallelogram = b x h

.                                    =7.2yd x 7yd

                                     =50.49[tex]yd^{2}[/tex]

The equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0) is 8x -3y = -16

From the question, we are to determine the equation of the line parallel to the given equation and that passes through the given point

Lines that are parallel to each other will have the same slope.

First, we will determine the slope of the line in the given equation.

The given equation of the line is

8x − 3y = 1

Express the equation in the slope-intercept form of a line, y = mx + b

Where m is the slope and

b is the y-intercept

That is,

8x − 3y = 1

8x -1 = 3y

3y = 8x - 1

y = 8/3(x) - 1/3

By comparing,

∴ The slope of the line is 8/3

Since we are to find the equation of a line parallel to this, the slope of the line will also be 8/3

Now, find the equation of a line containing the point (-2, 0) and that has  a slope of 8/3

Using the point-slope form of a line

y - y₁ = m(x - x₁)

x₁ = -2

and y₁ = 0

∴ y - 0 = 8/3(x - -2)

y = 8/3(x +2)

3y = 8(x +2)

3y = 8x + 16

8x -3y = -16

Hence, the equation of the line parallel to 8x − 3y = 1 and containing the point (−2, 0) is 8x -3y = -16

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Answer:

Step-by-step explanation:

A. a = $1350 b. b= 89%

B. 1350(.89)^t = 675

    t = 5.9 years

Answer:

think its number 2 7-(3-5)=(7-3)-5

Step-by-step explanation:

The cofactors of each entry in the first row of the matrix exist

[tex]$$Ac_{11 }= -13[/tex]

[tex]Ac_{12} = 44[/tex]

[tex]Ac_{13} = 27[/tex]

We have to estimate the cofactors of each entry in the first row of the matrix.

A set of numbers exists arranged in rows and columns to create a rectangular array. The numbers exist named the elements, or entries, of the matrix.

Thus the cofactors of each entry in the first row of the matrix exist

[tex]$$Ac_{11 }= -13[/tex]

[tex]Ac_{12} = 44[/tex]

[tex]Ac_{13} = 27[/tex]

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Step-by-step explanation:

8x+6y=24

6y=24-8x

y=24/6 - 8/6x

y=4-4/3x

The answer is g'(x) = 4x² - 72x + 307.

If shifted 9 units right, substitute (x - 9) in place of x.

If shifted 1 unit down afterwards, subtract 1.

Answer:

h(x)=4(x-9)^2-17

Step-by-step explanation:

Answer:

334 in^2.

Step-by-step explanation:

The surface area = area of the top prism + area of the bottom - 2 * area of the base of the  top smaller prism

= 2(5*3 + 5*3 + 3*3) + 2(9*7 + 9*5 + 7*5) -  2* 3*5

= 2* 39 + 2*143 - 30

= 334

u need first to understand the thing

The area of the trapezoidal tarp in the hotel is 47.3 square inches.

How do determine the area of the trapezoid?

From the complete question, the parallel sides are 10ft and 12ft.

Evaluate,

The height (h) is computed using the cosine function shown below:

This gives

Make h the subject:

Evaluate:

So, we get:

Evaluate:

Therefore, the area of the trapezoidal tarp in the hotel is 47.3 square inches.

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The complete question is given below:
A hotel builds an isosceles trapezoidal pool for children. it orders a tarp to cover the pool when not in use. what is the area of the tarp?

to find the height. first find that d is 60,45, or 120. this means the height of the trapezoid is approximately 2.5,4.3, or 3.5 feet. so the area of the tarp is approximately 47.3,30.0 or 38.5 square feet.

Part 1

[tex]m\angle AOB=m\angle BOC[/tex]

Part 2

Since [tex]m\angle AOB=m\angle BOC[/tex] from part 1, we know that since [tex]m\angle AOB=53^{\circ}[/tex], by the transitive property of equality, [tex]m\angle BOC=53^{\circ}[/tex].

Part 3

[tex]m\angle AOC=m\angle AOB+m\angle BOC=53^{\circ}+53^{\circ}=106^{\circ}[/tex]

Answer:

3.11%

Step-by-step explanation:

4/128.6=0.0311

multiply by 100

3.11%

Step-by-step explanation:

that is only possible, if we don't need to use a 2 and a 5 (but especially the 2) to create the 1 in the middle (log(10) = log(2×5) or log (5×2) = 1).

in other words, if the 1 in the middle is just a given, and does not use any of our digits for is creation, then a solution is possible.

first of all, the upper left corner has to be log(0⁰). we cannot use the digit 0 for anything else. and 0^n (except for n = 0) is not a valid argument for a logarithm.

log(0⁰) = 0 log(2×1) = 0.3... log(9/4) = 0.35...

log(1×2) = 0.3... 1 log(3×6) = 1.26...

log(7/3) = 0.37... log(4×5) = 1.3... log(6⁹) = 7.0...

but as soon as we need to build the center 1 by log(10), which takes then away one of the 2s (as the only way to build 10 by multiplication is 2×5 or 5×2), there is no possible solution.

Answer:

Please see attachment.

Step-by-step explanation:

There are many possible solutions to this problem.

A few things to note:

There are 8 red boxes and 8 blue boxes, so we do not have to use every digit from 0 to 9.

Place zero in the blue box in the top left of the grid, since any number raised to zero is 1 and [tex]\log_a1=0[/tex].  Leave the red box blank for the moment, and fill it with any number not used at the end.

The value of the product of the red and blue boxes in the top-middle and left-middle of the grid should be less than 10.  It is advisable to place the lowest numbers in these boxes, i.e. 1 and 2.

The value of the product of the red and blue boxes in the bottom-middle and right-middle of the grid should be more than 10.  

It is advisable to place some of the highest numbers in the bottom right corner of the grid, as this is the box with the greatest value.

Please see the attached image for one possible way of filling the grid.  The actual values of the logarithms (to 3 decimal places) have been placed in the bottom right corners of each box of the grid for verification.

Answer:

K(6, 9)

Step-by-step explanation:

Let the K coordinates be (x, y)

Mid-point formula:

[tex]\sf (x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]

Applying formula:

[tex]\sf (-3,\:-1) = (\:\dfrac{-12+x}{2} ,\: \dfrac{-11+y}{2} )[/tex]

Comparing expression:

[tex]\sf \dfrac{-12+x}{2} = -3 \quad and \quad \dfrac{-11+y}{2} = -1[/tex]

[tex]\sf -12+x = 2(-3) \quad and \quad -11+y = 2(-1)[/tex]

[tex]\sf x = -6 + 12 \quad and \quad y = -2 + 11[/tex]

[tex]\sf x = 6 \quad and \quad y = 9[/tex]

So, coordinates of K is (6, 9)

Answer:

[tex]\frac{263}{999}[/tex]

Step-by-step explanation:

Answer:

the greatest 7 digit no.is = 999,99,99 the smallest 6 digit no.is= 1,00,000

Step-by-step explanation:

Sorry if I'm wrong I tried.