(1 point) write the taylor series for f(x)=x3 about x=−1 as ∑n=0[infinity]cn(x 1)n.

Answer:

213.69 units

Step-by-step explanation:

We have to first find the height of the cone.

We can use Pythagoras rule because the slant height, height and radius of a cone all form a right angled triangle:

\(h^2 = a^2 + b^2\)

where h = hypotenuse

a and b = the other two sides of the triangle

The radius is 4 units and the slant height is 13 units:

\(13^2 = a^2 + 4^2\\\\169 = a^2 + 16\\\\a^2 = 169 - 16 = 153\\\\a = \sqrt{153}\\\\a = 12.37units\)

The height of the cone is 12.37 units.

The surface area of a cone is given as:

SA = \(\pi r (r + \sqrt{h^2 + r^2} )\)

\(SA = \pi * 4(4 + \sqrt{12.37^2 + 4^2} )\\\\SA = 12.57(4 + \sqrt{13^2} )\\SA = 12.57 (4 + 13)\\\\SA = 12.57(17)\\\\SA = 213.69 units\)

The surface area of the cone is 213.69 units.

The actual dimension of the distance is approximately 0.0046667 cm.

To compute the actual dimension of a distance given a drawing measurement and a scale, you can use the following formula:

Actual Dimension = Drawing Measurement × Scale Factor

In this case, the given drawing measurement is 28 cm, and the scale is 1:60 m.

To calculate the scale factor, we need to convert the scale to the same unit as the drawing measurement. Since the drawing measurement is in centimeters (cm), we need to convert the scale from meters (m) to centimeters (cm).

1 meter = 100 centimeters

So, the scale factor is:

Scale Factor = 1:60 m = 1 cm : 60 cm = 1 : 6000 cm

Now we can calculate the actual dimension:

Actual Dimension = Drawing Measurement × Scale Factor

Actual Dimension = 28 cm × 1/6000

Actual Dimension = 28/6000 cm

Simplifying the fraction, we get:

Actual Dimension ≈ 0.0046667 cm

Therefore, the actual dimension of the distance is approximately 0.0046667 cm.

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Using the hypergeometric distribution, it is found that there is a 0.1515 = 15.15% probability that you pick at least 3 green balls.

The balls are chosen without replacement, hence the hypergeometric distribution is used.

The formula is:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The probability that you pick at least 3 green balls is:

\(P(X \geq 3) = P(X = 3) + P(X = 4)\)

Hence:

\(P(X = 3) = h(3,12,4,5) = \frac{C_{5,3}C_{7,1}}{C_{12,4}} = 0.1414\)

\(P(X = 4) = h(4,12,4,5) = \frac{C_{5,4}C_{7,0}}{C_{12,4}} = 0.0101\)

Then:

\(P(X \geq 3) = P(X = 3) + P(X = 4) = 0.1414 + 0.0101 = 0.1515\)

0.1515 = 15.15% probability that you pick at least 3 green balls.

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The linear function f with the given values is f(x) = (1/2)x.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

From the table we get,

f(-4) = -2

f(-2) = -1

f(0) = 0

The linear function f can be written as,

f(x) = mx + c

m = (f(-2) - f(-4)) / (-2 + 4)

m = (-1 + 2) / 2

m = 1 / 2

Now,

f(-4) = -2 can be used as (-4, -2).

-2 = (1/2) x (-4) + c

-2 = -2 + c

c = -2 + 2

c = 0

Now,

f(x) = (1/2)x + 0

f(x) = (1/2)x

Thus,

The linear function f with the given values is f(x) = (1/2)x.

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The graph of the equation "y = 1/5x - 2" is shown: (Refer to the graph attached below.)

So, graph of equation: y = 1/5x - 2

Therefore, the graph of the equation "y = 1/5x - 2" is shown.

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Answer:

x = -3

Step-by-step explanation:

3(x-4)-6=9x

Distribute

3x -12 -6 = 9x

Combine like terms

3x -18 = 9x

Subtract 3x from each side

3x -18-3x =9x-3x

-18 = 6x

Divide by 6

-18/6 = 6x/6

-3 = x

Answer:

X=-3

Step-by-step explanation:

Let's begin with the line that goes from minus infinity to zero

the equation of this line is

because of the filled circle we know that this interval touch the zero

in inequality, this will be

then for the line that is between 0 and 2, we have a filled circle in the number two therefore we can touch this number

the interval will be

in inequality notation

the interval

in inequality notation

Therefore the piecewise function i

the correct option is the second one

Answer:

0.0089

Step-by-step explanation:

Because when we want to change decimal as percents we need to replace the period on the left side 2 times. But when we want to change percent as a decimal, then we need to move the period 2 times on the right.

ex:

.72 decimal= 0.0072

Answer:

89 as a percentage is 0.0089%

Answer:

8 bags

Step-by-step explanation:

It is given that, a make-your-own ice pop kit says to pour 4 fluid ounces of juice into each bag.

We need to find the number of ice pop bags we can fill with 1 quart of juice.

We know that,

1 quart = 32 ounces

We have  32 ounces of juice and each bag contains 4 fluid ounces.

Therefore, 8 ice pop bags we can  fill with 1 quart of juice.

Answer:

no they are too far apart

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

The first multiplier is the number of terms being added.

The second multiplier is one more than the first multiplier, that is

2 + 4 + 6 + 8 + 10 ← has 5 terms being added and 6 is one more than 5, thus

2 + 4 + 6 + 8 + 10 = 5 × 6

Answer:

The first multiplier is the number of terms being added.

The second multiplier is one more than the first multiplier, that is

2 + 4 + 6 + 8 + 10 ← has 5 terms being added and 6 is one more than 5, thus

2 + 4 + 6 + 8 + 10 = 5 × 6

Answer:

Step-by-step explanation:

4-2(3+7)=4-2.3+2.7

4-2(10)=4+0.4

4-20=4.4

-16=4.4 which clearly is false

The margin of error is 2.326 for the supplied values of  c, σ, and n, which are 0.98, 0.78, and 150 respectively.

Margin is the term used to describe the equity that a trader has in their account. Using funds borrowed from a broker to buy stocks is referred to as "marging" or "buying on margin." Instead of a typical brokerage account, you must have a margin account to execute this. Beginning with your gross profit, which is the distinction between revenue and COGS, you may compute profit margin. Find the percentage of revenue that represents gross profit next. Calculate it by dividing your gross profit by your revenue. You can calculate your margin % by multiplying the sum by 100.

Given that,

Population standard deviation =  

 = 0.78

Sample size = n =150

α = 1 - 98% = 1 - 0.98 = 0.02

α= 2 = 0.02/ 2 = 0.01

Z*α = 2 = 0.01 = 2.326     (  Using z table    )  

Margin of error = E =  Z

The margin of error is 2.326 for the supplied values of  c, σ, and n, which are 0.98, 0.78, and 150 respectively.

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The predicted value of y is 53 for the given equation of the trend line.

Given equation of trend line is Yx = 3 + 10x.

We are supposed to determine the predicted value of y if x is 5.

To find the value of y, we have to substitute the value of x in the given equation:

Yx = 3 + 10x

When x = 5,

Then Yx = 3 + 10(5)

           = 3 + 50 = 53

So, the predicted value of y is 53. Therefore, 53 is the correct answer.

Trend lines are drawn at an angle and are used to determine a trend and help making trading decision.

A trend line should be connected by at least three highs or lows to make it valid.

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The stem and leaf for the data values is

51       | 6  

55       | 7

64       | 8

70       | 2

72       | 9

73       | 2

75       | 0 4

78       | 4

79       | 8

80       | 4  4  9

From the question, we have the following parameters that can be used in our computation:

Data values:

75.4 80.9 75 73.2 78.4 70.2 51.6 79.8 80.4 72.9 80.4 64.8 55.7

Sort in order of tens

So, we have

51.6  

55.7

64.8

70.2

72.9

73.2

75 75.4

78.4

79.8

80.4 80.4 80.9

Next, we draw the stem and leaf as follows:

a | b

Where

a = stem

b = left

number = a.b

Using the above as a guide, we have the following:

51       | 6  

55       | 7

64       | 8

70       | 2

72       | 9

73       | 2

75       | 0 4

78       | 4

79       | 8

80       | 4  4  9

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The absolute measurement specifies the magnitude of the difference

which may be positive or negative.

The completed table is presented as follows;

\(\begin{tabular}{|l|c|c|c|}&\textbf{Apple}&\textbf{Grapefruit}&\textbf{Watermelon}\\\textbf{Keiko's measurement}&15 cm&24 cm& \underline{81 cm}\\\textbf{Actual measurement}&\underline{10 cm}&30 cm&90 cm\\\textbf{Absolute difference}&5 cm&\underline{6 cm}&9 cm\\\textbf{Percent error}&\underline{50\%}&\underline{20\%}&\underline{10\%}\end{array}\right]\)

Reasons:

The formulas for the inputs in the table are;

Absolute difference = Keiko's measurement - Actual measurement

The difference between Keiko's measurement and the actual measurement can be positive or negative while the absolute difference is always positive

\(\displaystyle Percent \ error = \mathbf{\frac{Keiko's \ measurement - Actual \ measurement}{Actual \ measurement} \times 100}\)

Therefore;

\(\displaystyle Percent \ error = \frac{ \mathbf{Absolute \ difference}}{Actual \ measurement} \times 100\)

Which gives for Apple;

The actual measurement for Apple = 15 cm - 5 cm = 10 cm

\(\displaystyle Percent \ error \ for \ Apple = \frac{5 \, cm}{10 \, cm} \times 100 = \mathbf{50\%}\)

Grapefruit column of the table;

Absolute difference for Grapefruit = |24 cm - 30 cm| = |-6 cm| = 6 cm

The absolute difference for Grapefruit = 6 cm

\(\displaystyle Percent \ error \ for \ Grapefruit = \mathbf{\frac{6 \, cm}{30 \, cm} \times 100} = 20\%\)

Percent error for Grapefruit = 20%

Watermelon column of the table;

Keiko's measurement = Absolute difference + Actual measurement

Using the given options, we have, 90 - 9 = 81

Therefore, the difference = -9, while the absolute difference = 9

Keiko's measurement for Watermelon = 90 cm - 9 cm = 81 cm

\(\displaystyle Percent \ error \ for \ Grapefruit= \frac{9 \, cm}{90 \, cm} \times 100 = 10\%\)

The completed table is as follows;

\(\begin{tabular}{|l|c|c|c|}&\textbf{Apple}&\textbf{Grapefruit}&\textbf{Watermelon}\\\textbf{Keiko's measurement}&15 cm&24 cm& \underline{81 cm}\\\textbf{Actual measurement}&\underline{10 cm}&30 cm&90 cm\\\textbf{Absolute difference}&5 cm&\underline{6 cm}&9 cm\\\textbf{Percent error}&\underline{50\%}&\underline{20\%}&\underline{10\%}\end{array}\right]\)

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To determine which rectangle with one corner on the x-axis, one corner on the y-axis, one corner at the origin, and the other corner on the line y = 2 + (1/3)x has the maximum area.

We need to consider the dimensions of the rectangles and calculate their areas.

Let's consider a rectangle with one corner at the origin (0, 0). Since the other corner lies on the line y = 2 + (1/3)x, the coordinates of that corner can be represented as (x, 2 + (1/3)x). The length of the rectangle would be x, and the width would be (2 + (1/3)x).

The area A of the rectangle is calculated by multiplying the length and width, so we have A = x(2 + (1/3)x).

To find the maximum area, we can take the derivative of A with respect to x, set it equal to zero, and solve for x. Differentiating and solving, we find x = 3. Therefore, the dimensions of the rectangle with the maximum area are x = 3 and width = (2 + (1/3)x) = (2 + (1/3)(3)) = 3.

Hence, the rectangle with one corner on the x-axis, one corner on the y-axis, one corner at the origin, and the other corner on the line y = 2 + (1/3)x, which has the maximum area, has dimensions of length = 3 units and width = 3 units.

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Answer:  Choice A.

an = 10 + 8(n - 1)

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

Explanation:

a1 = 10 is the first term

The common difference is d = 8 since we add 8 to each previous price to get the next price.

We have the arithmetic sequence with nth term of

an = a1 + d*(n-1)

an = 10 + 8(n - 1)

If you wanted, you could simplify that to get

an = 10 + 8n - 8

an = 8n + 2

Answer:

Assuming its "Modeling a Water Wheel" from EDGE its

Distance: a= 1/2 b=1 c=3/2

Heights: d=1  e=0  f=-1

Step-by-step explanation:

The solution is, a = 6, b = 7, c = 8, d = 7 and e = 6.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

Let's remember that the complete revolution of the wheel is 360 degrees, and the distance traveled by a complete revolution is the length of the circumference: 2*pi*radius.

The inicial height of the point is 6 ft, and the radius of the wheel is 1 ft.

When the distance traveled is 0, the wheel turned 0 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.

So the height will be a = 6 + 0 = 6 ft

When the distance traveled is pi/2, the wheel turned 90 degrees, and the point will be half the complete height of the wheel, which is 2 feet.

So the height will be b = 6 + 1 = 7 ft

When the distance traveled is pi, the wheel turned 180 degrees, and the point will be at the top of the wheel, which is 2 feet higher than the lower point of the wheel.

So the height will be c = 6 + 2= 8 ft

When the distance traveled is 3pi/2, the wheel turned 270 degrees, and the point will be half the complete height of the wheel, which is 2 feet.

So the height will be d = 6 + 1 = 7 ft

When the distance traveled is 2pi, the wheel turned 360 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.

So the height will be e = 6 + 0 = 6 ft

So the answers are:

a = 6, b = 7, c = 8, d = 7 and e = 6

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On a graph, the absolute value of a number is always non-negative.

The absolute value of a number is defined as the distance of that number from zero on the number line. Since the distance can never be negative, the absolute value of a number is always non-negative.

This is reflected in the graph of an absolute value function. The graph of an absolute value function, |x| is a V-shape that opens upward, with the vertex of the V being the point where the absolute value function equals zero. The two arms of the V extend out from this point, going in opposite directions along the number line. The coordinates of the vertex (0,0) and the graph is always non-negative.

It's important to note that although the absolute value is always non-negative on a graph, the input value (x) can be both positive and negative. The output of the absolute value function (|x|) will always be positive.

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The variable d in the given equation represents the number of minutes that Lilianna spends walking to the park.

Calories that Lilianna uses by sitting = 3/4

Calories that Lilianna uses by walking = calories used sitting + 1 : 1 + 3/4

Calories that Lilianna uses when she walks to the park = calories used per minute when walking x number of minutes spent walking.

Calories that Lilianna uses when she walks to the park = d(1 + 3/4)

12 1/4 = d(1 + 3/4)

d - 12 1/4 ÷ 1 3/4

d = 49 / 4 x 4/7

d = 7 minutes

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Q.2: A review of the t-test on the significance of individual independent variable suggests that, based on the p-values. None of the independent variables could be retained. This is because if the p-value is high, it means the significance is low.

Q3: Choose the right option below. Based on the full regression model involving all of the independent variables. VIF for Size = 5.3352, VIF for Fireplace = 10.1873, VIF for bedrooms = 2.7885.

Q.4: Based on VIF values, there is concern for collinearity in this dataset. True

Q5: Based on the normal probability plot, the normality assumption seems to be met. True

Q7: Based on conducting residual analysis the model seems. Adequate.

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Lines l and m are parallel. That makes angle 1 and the angle, which measures 75°, corresponding angles. Corresponding angles are congruent. Therefore angle 1 measures 75°.

---

Corresponding angles are angles that are on the same side of the transversal and they are also in the same position (but in different line).

Answer:

Step-by-step explanation:

p=  a/3  -  1/3

Answer:

£29.37

Step-by-step explanation:

Type in the question- like type it. Not a screenshot, type in part of the question into the Brainly search bar and you'll find it.

Answer:

No

Step-by-step explanation:

she should have just factored x² - 6x - 7 = 0

(x + 1)(x - 7) = 0

x = -1, x = 7

Nominal, ordinal, interval, and ratio are measurement scales used in statistics to categorize and rank data.

Nominal, ordinal, interval, and ratio are four sorts of information estimation scales utilized in measurements.

Nominal scales are utilized to mark or classify information into particular gatherings, where each gathering is fundamentally unrelated and altogether comprehensive. Instances of ostensible information incorporate orientation, race, and occupation.

Ordinal scales include positioning information in a particular request, however the distinctions between values are not significant. Instances of ordinal information incorporate positioning motion pictures in view of their prominence or understudy execution on a test.

interval scales include positioning information in a particular request, however the distinctions between values are significant, and there is no obvious zero point. Instances of stretch information incorporate temperature, intelligence level scores, and time.

ratio scales are like span scales, however they have a genuine zero point, implying that values can be duplicated and partitioned. Instances of proportion information incorporate weight, level, and pay.

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The complete question is:

what is the nominal, ordinal, interval and ratio?

Answer:

117/(x-2)

Step-by-step explanation:

Symbolab

They would need to have at least 3 computers.

Here, we have,

According to the given data we have the following:

Arrival rate = 15 persons per hour

Servicing rate = 60 / 10 = 6 persons per hour with one computer

Servicing rate with x number of computers = 6x per hour

Servicing rate at 90% utilisation = 6x (0.90) = 5.40x per hour

Therefore to service 13 arrivals per hour, we will need x computers

= 15/ 5.40 = 2.78

With 2 computers, the service capacity will be 12 per hour and the utilisation will be

15/12 = 125%,

which exceeds the organiser’s standard of 90% utilization.

With 3 computers, the service capacity increases to 18 persons per hour. If only 13 persons arrive, the utilisation rate will be

15 / 18 = 83.33%,

below the required maximum of 90% utilisation.

Therefore, the 2.78 can be rounded off to next whole number 3 computers.

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