Cole and his sister took part in a canned food drive. Cole brought in 21 cans of food. His sister brought in 7 fewer cans than he did. Together, how many cans did they bring in?

Answers

Answer 1

If Cole brought 21 cans and his sister brought 7 cans less, then the total number of cans brought by them is 35 cans.

The number of cans which Cole brought = 21 cans of food.

His sister brought in 7 fewer cans than he did, which means she brought in:

⇒ 21 - 7 = 14 cans of food,

Let the total number of food-cans be = "f",

So, the equation to find the number of cans is written as :

⇒ x = 21 + 14,

On adding the number of cans,

We get,

⇒x =  21 + 14 = 35,

Therefore, together they brought in 35 cans of food.

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Related Questions

Sally owns a restaurant in Wooville. The city is trying to get a minor league team to move there in 2021, either to location A (near her restaurant) or location B. The team might stay in location C in another city. The probability of these events, and her estimated annual profit in 2021 are shown in the table below.

Answers

The standard deviation of the restaurant profits in 2021 is given by $71181.

Restaurant profit for outcome 'move to A' = $ 260000

Restaurant profit for outcome 'move to B' = $ 120000

Restaurant profit for outcome 'stay in C' = $ 100000

The mean of restaurant profits = $(260000 + 120000 + 100000)/3 =$ 160000.

Standard deviation of the restaurant profits in 2021 is given by

= $ √({(260000 - 160000)² + (120000 - 160000)² + (100000 - 160000)²}/3)

= $ √(((100000)² + (40000)² + (60000)²)/3)

= $ √(15200000000/3)

= $ √5066666667

= $ 71181 (rounded to the nearest dollar)

Hence standard deviation of the restaurant profits in 2021 is given by $71181.

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The question is incomplete. The complete question will be -

Which diagram depicts as a positive angle in standard position?

Answers

Answer:

A.

Step-by-step explanation:

A positive angle has the initial side at the positive x-axis and the terminal side rotated counterclockwise from it.

That is shown in diagram A.

Figure 1 and Figure 2 below are congruent. Which point corresponds to point C'?

Answers

The point in Figure 2 that corresponds to point L in Figure 1 is the midpoint of line segment NP.

When two figures are congruent, it means that they have the same shape and size. This implies that corresponding points in the two figures have the same position and distance from each other.

In Figure 1, the points I, J, L, K, N, P, and Q are labeled. To find the point in Figure 2 that corresponds to point L, we need to look for a point that has the same relative position and distance as point L in Figure 1.

From Figure 1, we can see that point L is the midpoint of the line segment JK. Therefore, to find the corresponding point in Figure 2, we need to look for a point that is the midpoint of the line segment that corresponds to JK. In Figure 2, the line segment that corresponds to JK is NP, and the midpoint of NP corresponds to the point that is equivalent to point L. Therefore, the point that corresponds to point L in Figure 2 is the midpoint of line segment NP.

It is important to note that identifying corresponding points in congruent figures is a fundamental concept in geometry and is often used to solve problems involving congruence and similarity.

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Plese answer fast 30 points!
The graph represents a relation where x represents the independent variable and y represents the dependent variable.

a coordinate plane with points at negative 5 comma 1, negative 3 comma 0, 0 comma negative 3, 2 comma 3, 5 comma negative 1, and 5 comma 1

What is the domain of the relation?

{−5, −3, 0, 2, 5}
{−5, −3, −1, 0, 1, 2, 3, 5}
{−3, 0}
{−3, −1, 0, 1, 3}

Answers

The domain of the relation, given the points the coordinate plane has, is A.{−5, −3, 0, 2, 5}

How to find the domain of the relation?

The range of representable x-values in a function or relation when plotted on a coordinate plane are regarded as the domain. This values serve as inputs that can generate correspondig outputs within functions and relations. Displayed along the x-axis, domains strictly adhere to their input-based designation.

The x values from the graph are, - 5, - 3, 0, 2, 5 .

This means that the domain is {−5, −3, 0, 2, 5}.

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What is the mean of the data set?
{20, 1, 14, 14, 9, 8}
Enter your answer in the box.

Answers

The mean of this number set it 11

A runner sets up her training schedule. Each week she will increase the number of miles she runs. The number of miles she runs this week will be 2 more than the number she ran last week. Let x = miles she ran last week Let y = miles she runs this week Which equation represents the situation? O A. y = 2x OB. y= 2/ OC. y=x-2 O D. y = x + 2​

Answers

y = x + 2 represents the correct equation for the situation.

Option D is the correct answer.

We have,

The problem states that the number of miles the runner runs this week (y) will be 2 more than the number of miles she ran last week (x).

We can express this relationship using the equation:

y = x + 2

This equation means that if we know the number of miles the runner ran last week (x), we can find the number of miles she runs this week (y) by adding 2.

Thus,

y = x + 2 represents the correct equation for the situation.

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ABCD is a parallelogram. P is a point on AB such that LPAD = 110° and PC = BC. Calculate (a) LABC, LDCP
please do it with explanation.​

Answers

The value of the angles in the parallelogram are:

∠ABC = 70°

∠DCP =70°

How to calculate the angles in the parallelogram?

Recall that two adjacent angles in a parallelogram add up to 180 degrees. We can say:

∠BAD + ∠ABC = 180°  (Where ∠BAD = 110°)

∠ABC = 180 - 110 = 70°

Since PC = BC, ∠BPC = 70°

Also, ∠BCP = 180 - 70 - 70 = 40° (Sum of angles in a triangle)

∠ACB = ∠BAD (opposite angles of parallelogram are equal)

Where ∠BAD = 110°

Thus, ∠ACB = 110°

∠ACB = ∠DCP + ∠BCP

110 = ∠DCP + 40

∠DCP = 110 - 40

∠DCP =70°

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could i have the different proofs for this thank you

Answers

The proof for the above is given as  follows:

∠A ≅ ∠C -  Given

BD ⊥ ∠ABC - Given
AC ⊥ BD - Angle Bisector Theorem

What does the Angle Bisector Theorem say?

According to the angle bisector theorem, a triangle's opposing side is split into two segments that are proportionate to its other two sides. A ray that splits a given angle into two equal angles is known as an angle bisector.

Thus, it is correct to state that AC ⊥ BD according to the angle bisector theorem.

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Find the partial sum for the sequence.

{2, 3, 5, 8, 13, ...}; S8
S8=

Answers

The partial sum of the sequence {2, 3, 5, 8, 13, ...} for the first 8 terms is 761/2.

The sequence given is a Fibonacci sequence, where each term is the sum of the previous two terms. To find the partial sum for the first 8 terms, we can use the formula for the sum of a finite geometric series:

Sₙ = a(1 - rⁿ)/(1 - r),

where Sₙ is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 2, r = 3/2 (since each term is 1.5 times the previous term), and n = 8. Plugging these values into the formula, we get:

S₈ = 2(1 - (3/2)⁸)/(1 - (3/2))

Simplifying the expression, we get:

S₈ = 761/2

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Find the probability that a point chosen at random would lie in the shaded area of the figure. Round to the nearest tenth of a percent.

with the steps and explanation

Answers

Answer:

Okay, let's solve this step-by-step:

   The figure shows a rectangle partitioned into 6 smaller rectangles

   4 of these rectangles are shaded

   To find the probability a randomly chosen point lies in a shaded area, we calculate:

Probability = (Number of shaded squares) / (Total number of squares)

   There are 6 smaller rectangles

   4 of these are shaded

   So Number of shaded squares = 4

   And Total number of squares = 6

   Plugging this in:

   Probability = (4) / (6)

   = 2/3

   Converting to a percent:

   2/3 = 66.7%

   Rounded to the nearest tenth: 67%

So the final answer is:

The probability that a point chosen at random would lie in the shaded area of the figure is 67% (rounded to the nearest tenth of a percent).

Let me know if this helps explain the steps and solution. I can provide more details if needed.

Good luck!

Step-by-step explanation:

A student is graduating from college in 12 months but will need a loan in the amount of $11,650 for the last two semesters. The student may receive either an unsubsidized Stafford Loan
or a PLUS Loan. The terms of each loan are:
Unsubsidized Stafford Loan: annual interest rate of 5.95%, compounded monthly, and a payment grace period of six months from time of graduation
PLUS loan: annual interest rate of 6.55%, compounded monthly, with a balance of $12,436.41 at graduation
Which loan will have a lower balance, and by how much, at the time of repayment?
O The PLUS loan will have a lower balance by $298.35 at the time of repayment.
O The Stafford loan will have a lower balance by $298.35 at the time of repayment.
O The PLUS loan will have a lower balance by $527.14 at the time of repayment.
O The Stafford loan will have a lower balance by $527.14 at the time of repayment

Answers

Based on the information, the Stafford loan will have a lower balance by $527.14 at the time of repayment

How to calculate the loan

Using the formula for compound interest, the total cost of the loan can be calculated as follows:

Total cost of Stafford loan = $11,650 x (1 + 0.0595/12)^(12*0.5) = $12,652.14

Total cost of PLUS loan = $12,436.41 x (1 + 0.0655/12)^12 = $13,179.28

Therefore, the Stafford loan will have a lower balance at the time of repayment by $527.14 ($13,179.28 - $12,652.14).

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using the line of best fit​

Answers

The monthly cell phone bill when shared data equals zero is given as follows:

$26.

How to define a linear function?

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

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PLEASE HELP ITS DUE TODAY
For the quadratic equations shown here, which statement is true?

Question 2 options:

The graphs open downward.


The graphs open upward.


The graphs are listed from narrowest to widest.


The graphs are symmetric about the x-axis.

Answers

Answer:

The graphs open downward.

pe
Q2: A total of 160 students were surveyed from the countries of Australia, Canada, and the United Kingdom. One of
the questions asked students to report which hand they considered to be their most dominant.
Results are shown in the table.
Right-Hand Dominant Left-Hand Dominant Total
79
Australia
Canada
United Kingdom 25
Total
a.
68
46
139
dominant with approximately b
b.
Australia
Canada
tinu o lo
United Kingdom
11
160
Select an option from each drop-down menu to complete the sentence.
The country a
de salle
6
4
21
52
68%
86%
120
88%
29
had the greatest percentage of its students report being right-hand
nt ont

Answers

The country that had the greatest percentage of its students report being right-hand dominant with approximately 87% is UK

How to calculate the percentage

For Australia, 79 out of 120 students reported being right-hand dominant. So, the percentage of right-hand dominant students in Australia is:

(79/120) x 100 = 65.8%

For Canada, 68 out of 80 students reported being right-hand dominant. So, the percentage of right-hand dominant students in Canada is:

(68/80) x 100 = 85%

For the United Kingdom, 139 out of 160 students reported being right-hand dominant. So, the percentage of right-hand dominant students in the UK is

(139/160) x 100 = 86.9%

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A mountain lodge charges a weekly cabin rental fee of $450 for a single guest, plus $125
for each additional guest.
Which of these equations models the relationship between the number of guests, x, and
the total charge, y?
A. y = 450 + 125x
B. y = 450+ 125(x - 1)
C. y = 450+ (125 - 1)x
D. y = (450-x) + 125

Answers

The equation that models the relationship between the number of guests, x, and the total charge, y is A. y = 450 + 125x. The base charge for a single guest is $450, and for each additional guest, the charge increases by $125. So, we add 125 times the number of additional guests to the base charge of $450.

Which method can be used to find the range of a set of data?Find the difference between the maximum and minimum values.Find the difference between the upper and lower quartiles.Find the median of the upper half of an ordered data set.Find the sum of the maximum and minimum values.

Answers

The method can be used to find the range of a set of data is Find the difference between the maximum and minimum values. Option A

What is the range of a given set of data?

The range of a given set of data can simply be defined as  the difference that exists between the lowest and highest values of the data.

This is done irrespective of the arrangement of data like in ascending or descending order.

The range of values can be misleading sometimes when there are extremely high or low values.

For a range of function, it is the mean value of all the outputs of that function.

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For f(x) = x2 -4 and g(x) = 2x + 3, what is the domain of f - g?
A) (-90, ∞0)
B) (-2, 2)
C) (2, ∞)
D) [0, %)

Answers

Answer:

To determine the domain of f - g, we need to first find the expression for f - g.

f - g = (x^2 - 4) - (2x + 3)

f - g = x^2 - 2x - 7

The domain of f - g is the set of all real numbers for which the expression x^2 - 2x - 7 is defined.

We know that a quadratic expression of the form ax^2 + bx + c is defined for all real numbers x, so long as the expression under the square root in the quadratic formula (b^2 - 4ac) is non-negative.

In this case, a = 1, b = -2, and c = -7, so the expression under the square root is:

b^2 - 4ac = (-2)^2 - 4(1)(-7) = 4 + 28 = 32

Since 32 is positive, we know that the expression x^2 - 2x - 7 is defined for all real numbers x, and therefore the domain of f - g is all real numbers.

So the answer is not among the choices given.

Using a scientific calculator or graphing calculator find the inverse tangent of the ratio. Round to the nearest degree.
StartFraction 3 Over 1 EndFraction
a.
71°
b.
19°
c.
72°
d.
18°

Answers

Answer:

The inverse tangent of 3/1 can be found using a scientific calculator or graphing calculator by taking the arctan(3/1), which gives the angle in radians. To convert to degrees, we can multiply by 180/π. Rounding to the nearest degree gives:

arctan(3/1) = 71.57° ≈ 72°

Therefore, the answer is option C: 72°.

Ivy Tech Tuition was $88.34 per credit hour in 2006. Use the CPI values to determine what the school would be charging in 2013 if they only increased tuition based on inflation.

Answers

Answer: they would be charging $102.66 per credit hour in 2013.

Step-by-step explanation:

To determine what Ivy Tech would be charging in 2013 if they only increased tuition based on inflation, we need to use the CPI values to adjust for inflation between 2006 and 2013.

First, we need to calculate the inflation rate between the two years:

Inflation rate = CPI in 2013 / CPI in 2006

Inflation rate = 234.531 / 201.6 = 1.162

This means that the cost of living increased by 16.2% between 2006 and 2013.

Next, we can use this inflation rate to calculate the adjusted tuition cost for 2013:

Tuition in 2013 = Tuition in 2006 x (CPI in 2013 / CPI in 2006)

Tuition in 2013 = $88.34 x (234.531 / 201.6)

Tuition in 2013 = $102.66 (rounded to the nearest cent)

Therefore, if Ivy Tech only increased tuition based on inflation, they would be charging $102.66 per credit hour in 2013.

IN CASE YOU ARE LOOKING FOR THE ANSWER

In 2010, the population of Houston, Texas, was 2,099,451 and the population density was 3501 people per square mile.

What was Houston's land area in 2010?

Enter your answer as a decimal in the box. Round your answer to the nearest tenth.

Answers

Answer: 599.7 square miles

Step-by-step explanation: Divide 2,099,451 by 3501 and then round to the nearest tenth.

what is the surface area of a sphere with a radius of 12 centimeters

A) 302cm^2

B) 452cm^2

C) 576cm^2

D) 1810cm^2

Answers

The surface area of the sphere is 1810 cm²

What is a sphere?

A sphere is a three-dimensional object that is round in shape. Examples of object with spherical shape is a ball, an egg e.t.c.

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of sphere is expressed as;

A = 4πr². where r is the radius.

A = 4 × 3.14 × 12²

A = 1809.7 cm²

approximately to the nearest whole number

A = 1810 cm²

Therefore the surface area of the sphere to the nearest whole number is 1810 cm².

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What is the surface area of the figure for #11?


*with work on how to solve please!

Answers

The surface areas of the figures are:

10.  1,376 ft² or F 1,344 ft²11.  B. 1,058.4 in².

How to determine surface area?

10.To find the surface area of this rectangular prism, find the area of each face and then add them together.

Face 1: The front and back faces both have dimensions of 12 ft by 14 ft, so the area of each is:

12 ft × 14 ft = 168 ft²

Two of these faces, so the total area is:

2 × 168 ft² = 336 ft²

Face 2: The top and bottom faces both have dimensions of 20 ft by 14 ft, so the area of each is:

20 ft × 14 ft = 280 ft²

Two of these faces, so the total area is:

2 × 280 ft² = 560 ft²

Face 3: The left and right faces both have dimensions of 12 ft by 20 ft, so the area of each is:

12 ft × 20 ft = 240 ft²

Two of these faces, so the total area is:

2 × 240 ft² = 480 ft²

Now add up the areas of all the faces:

336 ft² + 560 ft² + 480 ft² = 1,376 ft²

11. To find the surface area of the figure, add the areas of all six faces.

Find the area of the rectangular faces:

The front and back faces both have dimensions of 14 in by 14 in, so each has an area of 14 in x 14 in = 196 in².

The top and bottom faces both have dimensions of 13 in by 8.9 in, so each has an area of 13 in x 8.9 in = 115.7 in².

Find the area of the triangular faces. Use the Pythagorean theorem to find the length of the third side of each triangle:

The two side faces are congruent triangles with legs of 14 in and 13 in.

Using the Pythagorean theorem, find the length of the hypotenuse to be √(14² + 13²) ≈ 19.14 in. The area of each triangle is then 1/2 base x height = 1/2 x 19.14 in x 8.9 in ≈ 85.3 in².

Using the Pythagorean theorem, find the length of the hypotenuse to be √(8.9² + 13²) ≈ 15.8 in. The area of each triangle is then 1/2 base x height = 1/2 x 15.8 in x 14 in ≈ 110.6 in².

Finally, add up the areas of all six faces:

Front and back faces: 2 x 196 in² = 392 in²

Top and bottom faces: 2 x 115.7 in² = 231.4 in²

Side faces: 2 x 85.3 in² = 170.6 in²

End faces: 2 x 110.6 in² = 221.2 in²

The total surface area is the sum of these areas:

392 in² + 231.4 in² + 170.6 in² + 221.2 in² ≈ 1,015.2 in²

Therefore, the answer is B. 1,058.4 in².

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Drop the ball from a height equal to one of your group member's height (high is 5.3)
Determine the amount of time the ball takes to touch the ground (with a timer)
Time to touch the ground: 1.08 seconds
Initial velocity of the ball: ) ft/sec

Plug the initial velocity and the time to touch the ground into:
-16t^2 + v X t+h=0

Solve your equation for h. Based on the height of the person you dropped the ball from, how accurate is your answer for h?

Answers

The time taken for the ball to touch the ground is 0.61 s.

What is the time of motion of the ball?

The time taken for the ball to touch the ground is calculated by applying the  following method.

-16t² + vt + h = 0

where;

v is the initial velocity of the ballh is the height of fall of the ballt is the time of motion

when the height of the ball = 5.3 ft, with initial velocity = 1.08 ft/s, the time of motion of the ball is calculated as follows;

-16t² + vt + h = 0

-16t² + 1.08t + 5.3 = 0

16t² - 1.08t - 5.3 = 0

solve the quadratic equation, using formula method;

a = 16, b = -1.08, c = -5.3

t = 0.61 second.

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end of the year math project can't fail it SOS

Answers

The steps for the construction are given below:

It should be noted that to begin, take a ruler and draw a straight line.Next, employ the use of a compass to draw a circle with its center at one end of said line.Maintain your compass width and place it on the opposite end of the line, drawing another circle that collides with the initial circular figure.

How to explain the construction

A new line can be created connecting the points where these two circles intersect using just a simple ruler.

Now that you have succeeded in this task, feel free to experiment and manipulate the astonishing construction you've completed using the same innovative tools.

While this is only an elementary blueprint, there are numerous advanced constructions that can be produced by taking advantage of both GeoGebra and traditional paper/pencil/ruler/compass techniques.

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Find the length of the segment.

Answers

Answer:

CD = 4 , AD = 6

Step-by-step explanation:

AC is an angle bisector of ∠ BAD and divides the opposite side from the angle into segments that are proportional to the other two sides, that is

[tex]\frac{BC}{CD}[/tex] = [tex]\frac{AB}{AD}[/tex] ( substitute values )

[tex]\frac{6}{y-1}[/tex] = [tex]\frac{9}{2y-4}[/tex] ( cross- multiply )

6(2y - 4) = 9(y - 1) ← distribute parenthesis

12y - 24 = 9y - 9 ( subtract 9y from both sides )

3y - 24 = - 9 ( add 24 to both sides )

3y = 15 ( divide both sides by 3 )

y = 5

Then

CD = y - 1 = 5 - 1 = 4

AD = 2y - 4 = 2(5) - 4 = 10 - 4 = 6

Given the dimensions of a rectangle are (x-1)&(x+7) meters, find the value of x if the area of the rectangle is 128 square feet

Answers

Answer:

x = 12

Step-by-step explanation:

We are given that the dimensions of a rectangle are (x-1) and (x+7) meters, and we know that the area of the rectangle is 128 square meters.

We can set up an equation to solve for x as follows:

Area of rectangle = Length × Width

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

Expanding the right side, we get:

128 = x^2 + 6x - 7

Bringing all the terms to one side, we get:

x^2 + 6x - 135 = 0

Now we can use the quadratic formula to solve for x:

x = (-6 ± √(6^2 - 4(1)(-135))) / (2(1))

x = (-6 ± √936) / 2

x = (-6 ± 30) / 2

x = -3 ± 15

x = -18 or x = 12

Since x represents a length, it must be positive. Therefore, the value of x is 12.

Find the polar coordinates of a point with Cartesian coordinates (x,y)=(2√3,2).Select the correct answer below:


(4,π/6)
(2,2π/3)
(4,2π/3)
(2,7π/6)
(4,7π/6)
(2,π/6)

Answers

Answer:

(4,π/6)

Step-by-step explanation:

The correct polar coordinates of the point (2√3, 2) are (r, θ) = (4, π/6).

Explanation:

Using the formulas for converting Cartesian coordinates to polar coordinates:

r = √(x^2 + y^2)

θ = atan2(y, x)

Plugging in the given values:

r = √((2√3)^2 + 2^2)

= √(12 + 4)

= √16

= 4

θ = atan2(2, 2√3)

≈ 0.5236 radians

However, in the polar coordinate system, angles are typically expressed in radians between 0 and 2π. The angle π/6 is equivalent to 0.5236 radians, so the correct polar coordinates of the point (2√3, 2) are (r, θ) = (4, π/6).

ap calculus problem
no need full detail solution

Answers

The Taylor series for f(x) = e^2x at x = 1 is option D. Σ2ⁿ e²ˣ/n! (x - 1)ⁿ

How did we get the value?

The Taylor series for a function f(x) centered at x = a is given by:

f(x) = f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...

f'(a), f''(a), f'''(a), ... depict the first, second, third, and higher derivatives of f(x) evaluated at x = a.

In this case:

f(x) = e^(2x)

The first derivative is:

f'(x) = 2e^(2x)

The second derivative is:

f''(x) = 4e^(2x)

The third derivative is:

f'''(x) = 8e^(2x) etc.

Finding the Taylor series for f(x) = e^(2x) at x = 1, evaluate each derivative at x = 1:

f(1) = e^(2)

f'(1) = 2e^(2)

f''(1) = 4e^(2)

f'''(1) = 8e^(2) etc.

Plug these values into the Taylor series formula:

f(x) = f(1) + f'(1)(x-1)/1! + f''(1)(x-1)^2/2! + f'''(1)(x-1)^3/3! + ...

f(x) = e^(2) + 2e^(2)(x-1)/1! + 4e^(2)(x-1)^2/2! + 8e^(2)(x-1)^3/3! + ...

Simplify:

f(x) = e^(2) + 2e^(2)(x-1) + 2e^(2)(x-1)^2 + 4e^(2)(x-1)^3/3 + ...

Therefore, the Taylor series for f(x) = e^(2x) at x = 1 is: Σ2ⁿ e²ˣ/n! (x - 1)ⁿ which is option D.

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hi can someone help with this question

Answers

Based on the information, we can infer that the investment was made 11.53 years ago.

How to calculate how many years ago was the investment made?

To calculate how many years ago was the investment mafe we have to can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal (initial amount invested)

r = the interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

Let's start by finding the initial principal (P) by working backwards from the final amount (A):

A = P(1 + r/n)^(nt)

31372.0 = P(1 + 0.022/1)^(14)(1 + 0.022+0.007/1)^(1(t-4))

Simplifying, we get:

31372.0 = P(1.093248)(1.029)^(t-4)

P = 27500 euros (initial investment)

Now we can solve for t:

31372.0 = 27500(1.093248)(1.029)^(t-4)

1.1412 = (1.029)^(t-4)

log(1.1412) = log(1.029)^(t-4)

t - 4 = log(1.1412)/log(1.029)

t = log(1.1412)/log(1.029) + 4

t = 11.53

Therefore, the investment was made about 11.53 years ago.

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120 students
and 8 teachers go on a school trip.
The recommended ratio of adults to students is 1:15.
Is the ratio of adults to students correct?

Answers

Answer:

Yes.

Step-by-step explanation:

8:120 = 4:60 = 2:30 = 1:15

You divide by two each time to simplify.

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