Use the Alternating Series Estimation Theorem to estimate the range of values of x for which the given approximation is accurate to within the stated error. Check your answer graphically. (Round your answers to three decimal places.)
cos x ≈ 1 - x²/2 + x⁴/24
(|error| < 0.0005)
< x

23

Step-by-step explanation:

\(f(3) = {(3)}^{2} + 3(3) - 7 = 9 + 9 - 7 \\ = 18 - 7 = 11\)

\(g(3) = 5(3) - 3 = 15 - 3 = 12\)

\(f(3) + g(3) = 11 + 12 = 23\)

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The statement you provided mentions two separate events involving different companies lower rates

1. Hertz runs a sale: Hertz, a car rental company, is having a sale. This implies that they are offering in  discounted prices or promotional deals on their rental services.

2. Avis buys new cars and Budget lowers rates: Avis, another car rental company, is purchasing that  new cars to add to their fleet. On the other hand, Budget, yet another car rental   the company, is reducing their rental rates.

These events indicate of independent actions taken by the respective companies and are not directly connected to each other.

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"But" is a common phrase that can be a language barrier because it negates everything said previously

This is further explained below.

Generally,  When persons from different cultural backgrounds or who speak different languages (or even dialects) have trouble communicating with one another, they are said to be facing a "language barrier."

In conclusion, But is a typical statement that may be a barrier to communication due to the fact that it contradicts everything that was stated before.

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Answer:

let x represent the time it took Caroline to complete the puzzle .

let 3x represent the time it took Felix to complete the puzzle.

let 0.25x represent the time it took Graham to complete the puzzle

the the ratio of their time would be

x:3x:0.25x

The ratio of their time is 4 :12 : 1.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

let the time taken by Caroline be x.

So, the time taken by Graham is x/4.

and, the time taken by Felix is 3x.

So, the ratio of time

Caroline time: Felix time: Graham time

= x: 3x : x/4

= 1 : 3 : 1/4

= 4 : 12 : 1.

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Answer:

h = -4

Step-by-step explanation:

7h-5(3h-8) = 72

Distribute

7h - 15h +40 = 72

Combine like terms

-8h +40 = 72

Subtract 40 from each side

-8h+40-40 = 72-40

-8h = 32

Divide each side by -8

-8h/-8 = -32/-8

h = -4

Steps:

Step 1: Simplify both sides of the equation.

7h−5(3h−8)=72

7h+(−5)(3h)+(−5)(−8)=72(Distribute)

7h+−15h+40=72

(7h+−15h)+(40)=72(Combine Like Terms)

−8h+40=72 −8h+40=72

Step 2: Subtract 40 from both sides.

−8h+40−40=72−40

−8h=32

Step 3: Divide both sides by -8

Answer:  h=−4

The answer for this question is h=-4

Please mark me brainliest

Hope this helps.

Answer 11 Hours

Step-by-step explanation:

11x7=77+6=84

Needed 86

It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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Answer:

Let's actually find the line of best fit...

m=(nΣyx-ΣyΣx)/(nΣx^2-ΣxΣx)

m=(11*836-130*55)/(11*385-3025)

m=2046/1210  

m=93/55

b=(Σy-93Σx/55)/n

b=(55Σy-93Σx)/(55n)

b=(7150-5115)/(55*11)

b=185/55, so the line of best fit is:

y=(93x+185)/55

A)  The approximate y-intercept (the value of y when x=0) is 185/55≈3.36.

Which means that those who do not practice at all will win about 3.36 times

B) y(13)=(93x+185)/55

y(13)≈25.34

So after 13 months of practice one would expect to win about 25.34 times.

An eigenvalue is a scalar value that is associated with a linear system of equations, such as a matrix. It is used to determine how much a particular vector in the system is scaled by the matrix.

The equation for finding an eigenvalue is:
Ax = λx
where A is the matrix, x is the vector, and λ (lambda) is the eigenvalue.

In the case of the matrix m-si, we can set up the equation:
(m-si)x = λx

To find the eigenvalue, we need to solve for λ. We can do this by rearranging the equation:
(m-si)x - λx = 0
(m-si - λ)x = 0

Since we are looking for non-zero solutions for x, we can set the determinant of the matrix equal to zero:
det(m-si - λ) = 0

This will give us a polynomial equation that we can solve for λ to find the eigenvalue(s) of the matrix m-si.

Without the actual values of m and si, it is not possible to solve for the eigenvalue(s) of the matrix. However, the above process is how you would go about finding the eigenvalue(s) of any matrix.

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Answer: I got answers A, B and E

Step-by-step explanation:

The correct three statements are supported by Joseph's data are as follows;

Joseph should plan for around 560 students at each dance based on the data.

The dances will be attended by around 700 of the students that attend the school.

Out of the 800 students, 288 do not like to attend dances after the football games.

A data set is a collection of numbers or values that relate to a particular subject.

Joseph attends a school that has 800 students. He is in charge of school dances this year.

He surveyed a random sample of 100 students and got the following feedback.

1. Here 7/10 of the students would attend any of the dances held at the school.

\(=\dfrac{ 7}{10}\times 800\\\\= 7 \times 80\\\\= 560\)

Joseph should plan for around 560 students at each dance based on the data.

2. 18% of the students are not allowed to attend dances at school.

\(= (1-0.18)\times 800\\\\= 0.82 \times 800\\\\=656\)

The dances will be attended by around 700 of the students that attend the school.

3. 64% of the students think that the dances should be held after football games.

\(=(1-0.64 )\times 800\\\\= 0.36 \times 800\\\\=288\)

Out of the 800 students, 288 do not like to attend dances after the football games.

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Integers lying in between in interval  (1, 8) are 3, 4, 5, 6, 7, which  satisfy the given inequality.

4x - 5 > 4

4x > 9

x > 2.25

Integers lying in between in open interval  (1, 8) are 3, 4, 5, 6, 7

Thus, integers lying in between in interval  (1, 8) are 3, 4, 5, 6, 7, which  satisfy the given inequality.

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The correct question is-

State all integer values of x in the interval (1, 8) that satisfy the following inequality:

4x - 5 > 4

A relation ~ on R' is defined as a relation where (a,b) ~ (c,d) if and only if a3+b3=c3+d3. This relation is transitive but not symmetric.

Transitivity of the relation states that if (a, b) ~ (c,d) and (c, d) ~ (e, f) then (a, b) ~ (e, f). This means that if a3+b3=c3+d3 and c3+d3=e3+f3 then a3+b3=e3+f3, thus, the relation is transitive.

Symmetry of the relation means that if (a, b) ~ (c, d) then (c, d) ~ (a, b). This, however, does not hold in this relation since it is possible for a3+b3=c3+d3 and yet c3+d3≠a3+b3. For example, (1,2) ~ (8,4), this is true since 13+23=83+43, however, this does not mean that (8,4) ~ (1,2) since 83+43≠13+23. Therefore, this relation is not symmetric.

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Answer:

7

Step-by-step explanation:

7+2=9

7 puzzles

7 puzzles

Answer:

When x= 4, then f(x)= 13.

When x= g(x), then f(x)=g

When x= -3, then f(x)= -1

When x= -15(x), then f(x)= -15

The probability that exactly 3 out of the first 11 customers buy a magazine is 2.23%

The proportion of customers that buy a magazine = 8.4%

If 3 out of the first 11 customers buy a magazine, then this proportion is given as; 3/11 or 27.27%

Therefore, the probability that 3 out of the first 11 customers will buy a magazine is calculated as follows;

probability = 8.4% × 27.27%

probability = (8.4/100) × (27.27/100)

probability = 0.084 × 0.2727

probability = 0.0223

Converting it into percentage as follows;

probability = 0.0223 × 100

probability = 2.23%

Therefore, the probability that 3 out of the first 11 customers buy a magazine is calculated to be 2.23%.

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Answer:

\(\sqrt{5} \ or -\sqrt{5}\)

Step-by-step explanation:

simplify both sides

\(x^{2} +35=40\)

subtract 35 from both sides

\(x^{2} =5\)

x = 10 ounces,y = 23 ounces,and z = 42 ounces are the number of ounces of each kind of food should be used in a meal consisting of the three foods that allows exactly 660 calories, 25 grams of protein, and 425 milligrams of vitamin C.

Given Information:Three foods have the following nutritional content per ounce.

Goal:We need to find out how many ounces of each kind of food should be used in a meal consisting of the three foods that allows exactly 660 calories, 25 grams of protein, and 425 milligrams of vitamin C.

Step 1:Represent unknown quantities by variables.Let x, y, and z be the number of ounces of the first, second, and third food respectively.

Step 2:Translate from the verbal conditions of the problem to a system of three equations in three variables.As per the given information, the nutritional content per ounce for each of the three foods is given by the following table. Now, as per the problem, a meal consisting of the three foods allows exactly 660 calories, 25 grams of protein, and 425 milligrams of vitamin C.

Therefore, the system of three equations in three variables is given as follows;

x + 2y + 4z = 660     …(1)

6x + 8y + 2z = 25       …(2)

200x + 250y + 50z = 425  …(3)

Step 3:Solve the system of equations using any of the methods such as elimination, substitution, matrix, etc.

Let us solve the above system of equations by elimination method by eliminating z first.

Multiplying equation (1) by 2 and subtracting equation (2), we get,

2x - 2z = 610        …(4)

Multiplying equation (3) by 2 and subtracting equation (2), we get,

194x + 198y - 2z = 175   …(5)

Now, we have two equations (4) and (5) in terms of two variables x and z.

Let's eliminate z by multiplying equation (4) by 97 and adding it to equation (5) which gives,

194x + 198y - 2z = 175       …(5)

97(2x - 2z = 610)              …(4)------------------------------------------------------------------------------

490x + 196y = 6115

Dividing both sides by 2, we get,

245x + 98y = 3057  …(6)

Now, let us solve equation (1) for z.z = 330 - x/2 - 2y     …(7)

Substituting equation (7) into equation (5), we get,

194x + 198y - 2(330 - x/2 - 2y) = 175

Simplifying and solving for x, we get,x = 10 ounces.Substituting this value of x into equation (7), we get,

z = 65 - y      …(8)

Substituting the values of x and z from equations (7) and (8) into equation (1), we get,

5y = 115

Solving for y, we get,y = 23 ounces.

Therefore, x = 10 ounces,y = 23 ounces,and z = 42 ounces are the number of ounces of each kind of food should be used in a meal consisting of the three foods that allows exactly 660 calories, 25 grams of protein, and 425 milligrams of vitamin C.

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Answer:

C

Step-by-step explanation:

Prime numbers are only divisible by themselves and 1  ....all even numbers are divisible by '2' ,  so all primes are odd numbers

Answer: 68

Step-by-step explanation: 32 + 2=34 34*2 + 68 2 because a person naturaly has 2 feets  

A collector offers to buy state quarters for 2000% of their face value. The face value of each quarter is 25 cents. At that rate 20 dollars Bryden will get for his four state quarters.

In the given question, a collector offers to buy state quarters for 2000% of their face value.

The face value of each quarter is 25 cents.

We have to find at that rate how many dollars Bryden will get for his four state quarters.

As given that,

Collector buy state quarters = 2000% of their face value

We can write 2000% as 20×100%.

It means that state quarters is 20 times of their face value.

As we know that, 4 quarter is equal to the one dollar. So,

Bryden get for his four state quarters = 20×1 dollars

Bryden get for his four state quarters = 20 dollars

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The points that belong to the image of the equation of a line are (4, - 8) and U' = (1, 4).

In this question we find the definition of the equation of a line, whose image must be found by a kind of rigid transformation known as dilation:

U'(x, y) = O(x, y) + k · [U(x, y) - O(x, y)]

Where:

If we know that O(x, y) = (5, - 8), k = 1 / 4 and y = - 4 · x - 4, then the image of the point:

U'(x, y) = (5, - 8) + (1 / 4) · [(x, - 4 · x - 4) - (5, - 8)]

U'(x, y) = (5, - 8) + (1 / 4) · (x - 5, - 4 · x + 4)

U'(x, y) = (5, - 8) + (x / 4 - 5 / 4, - x + 1)

U'(x, y) = (x / 4 + 15 / 4, - x - 7)

Now we evaluate the expression at each x-value:

x = 1

U' = (1 / 4 + 15 / 4, - 1 - 7)

U' = (4, - 8) (YES)

x = - 11

U' = (- 11 / 4 + 15 / 4, - (- 11) - 7)

U' = (1, 4) (YES)

x = - 23

U' = (- 23 / 4 + 15 / 4, - (- 23) - 7)

U' = (- 2, 16) (NO)

x = 17

U' = (17 / 4 + 15 / 4, - 17 - 7)

U' = (8, - 24) (NO)

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Given that the actual recharging time required is uniformly distributed between 70 and 110 minutes, we can assume that the probability density function of the recharging time is a uniform distribution given by:

f(x) = 1/(110-70) = 1/40 for 70 <= x <= 110

f(x) = 0 otherwise

To find the probability that the recharge time will be less than 91 minutes, we need to calculate the cumulative distribution function (CDF) of the uniform distribution up to 91 minutes:

F(x) = integral from 70 to x of f(t) dt

F(x) = integral from 70 to x of (1/40) dt

F(x) = (x-70)/40

Therefore, the probability that the recharge time will be less than 91 minutes is:

P(X < 91) = F(91)

P(X < 91) = (91-70)/40

P(X < 91) = 0.525

So, the probability that the recharge time will be less than 91 minutes is 0.525 (rounded to three decimal places).

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Answer:

40 feet (after 1.5 seconds).

Step-by-step explanation:

The height h of the ball after t seconds is modeled by the function:

\(h(t)=-16t^2+48t+4\)

And we want to determine the ball's maximum height.

Since the given function is a quadratic, the maximum height occurs at the vertex point.

For quadratics, the vertex point is given by the formulas:

\(\displaystyle \Big(-\frac{b}{2a},f\Big(-\frac{b}{2a}\Big)\Big)\)

In this case, a = -16, b = 48, and c = 4.

Therefore, the t-coordinate at which the vertex occurs is:

\(\displaystyle t=-\frac{48}{2(-16)}=\frac{48}{32}=\frac{3}{2}\)

So, the maximum height occurs after 1.5 seconds.

Then the maximum height will be:

\(\begin{aligned}\displaystyle h\Big(\frac{3}{2}\Big)&=-16\Big(\frac{3}{2}\Big)^2+48\Big(\frac{3}{2}\Big)+4\\\\ &=-16\Big(\frac{9}{4}\Big)+24(3)+4\\\\&=-4(9)+72+4\\\\&=40\text{ feet}\end{aligned}\)

So, the maximum of the ball is 40 feet (after 1.5 seconds).

The slope field for the differential equation dy/dx = x² y² can be generated by plotting short line segments at each point (x, y) in the x-y plane. The direction of each line segment is determined by the value of x and y at that point, with steeper slopes indicating a larger rate of change.

To generate a slope field for the differential equation dy/dx = x² y², we need to plot short line segments at each point (x, y) in the x-y plane. The direction of each line segment is determined by the value of x and y at that point, with steeper slopes indicating a larger rate of change.

First, we can identify the stationary points of the differential equation by setting dy/dx = 0. This gives us the two lines y=0 and x=0, which intersect at the origin. We can see from the equation that any solution passing through the origin will have a slope of zero at that point, so the slope field will have horizontal lines for y=0 and vertical lines for x=0.

Next, we can look for other interesting features of the slope field. One such feature is the line y=1/x, which is a solution to the differential equation. To see this, we can substitute y=1/x into the equation and verify that both sides are equal. Along this line, the slope of the solution will be zero, since both x and y are changing at the same rate. Therefore, the slope field will have horizontal line segments along the curve y=1/x.

Overall, the slope field for dy/dx = x² y² will have horizontal lines for y=0, vertical lines for x=0, and horizontal line segments for y=1/x. In between these features, the slope of the line segments will increase as we move away from the origin, indicating that the rate of change of the solution is increasing.

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Answer: B and D

Step-by-step explanation:

Answer:

x=8

Step-by-step explanation:

7x-5=3(x+9)

distribute

7x-5=3x+27

-3x      -3x

4x-5=27

+5     +5

4x=32

÷4  ÷4

x=8

I HOPE THIS HELPS:)

The stripe's area in square feet is 240 square units.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. Draw a square on a sheet of paper using a pencil. It is a two-dimensional figure. The area of the form on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares.

Here,

The cylinder can be "unwrapped" into a rectangle, and we see that the stripe is a parallelogram with base 3 and height 80.

area=3*80

=240 square units.

the area of the stripe in square feet is 240 square units.

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