1) linearize the function f(x) = (1 −4x) sin 3x about x0 = π/4.

By cross multiplication, the state of Oregon has 4 golf courses per 100,000 people.

According to statement of this question, the state of Oregon has 190 golf couses for a population of 4,301,089, the amount of golf courses for a population of 100,000 by cross multiplication:

x = 190 × (100,000 / 4,301,089)

x = 4,417

x = 4 ↓

By means of cross multiplication, there are 4 golf courses per 100,000 people in the state of Oregon.

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Answer:

vertical line

Step-by-step explanation:

I did that on my test

Answer:

The parallel line will have a slope of 2/7

Step-by-step explanation:

y=2/7x+20

This line is in the form

y = mx+b  where m is the slope and b is the y intercept

The slope is 2/7

Parallel lines have the same slope

The parallel line will have a slope of 2/7

The cooking time for Erica's 7-pound roast is 196 minutes.

To determine the cooking time for Erica's 7-pound roast, we can set up a proportion based on the relationship between the weight of the roast and the cooking time.

Let's assume that the cooking time is directly proportional to the weight of the roast. Therefore, the proportion can be set up as follows:

(Weight of 3-pound roast)/(Cooking time for 3-pound roast) = (Weight of 7-pound roast)/(Cooking time for 7-pound roast)

Using the values given in the problem, we can substitute the known values into the proportion:

(3 pounds)/(84 minutes) = (7 pounds)/(x minutes)

To solve for x, we can cross-multiply and then solve for x:

3 * x = 7 * 84

3x = 588

x = 588/3

x = 196

It's important to note that cooking times can vary depending on factors such as the type of oven and desired level of doneness. It is always a good idea to use a meat thermometer to ensure that the roast reaches the desired internal temperature, which is typically around 145°F for medium-rare to 160°F for medium.

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Answer:

x = 5, y = 6

Step-by-step explanation:

x + 5y = 35, поэтому 3x + 15y = 105 (уравнение 1)

Кроме того, 3x + 2y = 27 (уравнение 2)

Мы должны найти y, вычитая второе уравнение из первого

Получаем, 13 y = 78, значит y = 6

А теперь подставьте y в любое уравнение, чтобы найти x = 5

We used the concept of generating functions and the binomial theorem, there are 33,649 collections of six positive, odd integers that have a sum of 18.

To find the number of collections, we used the concept of generating functions and the binomial theorem. We represented the possible values for each integer as terms in a generating function and found the coefficient of the desired term. However, since we were only interested in the number of collections and not the specific values, we simplified the calculation using the stars and bars method. By arranging stars and bars to represent the sum of 18 divided into six parts, we calculated the number of ways to arrange the dividers among the spaces. This resulted in a total of 33,649 collections of six positive, odd integers with a sum of 18.

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The given equation is

We have to solve the product, then we move all terms to the left side of the equality.

Answer:

15%

Step-by-step explanation:

RS. 6450 = 15%

6450 percent *15 =

(6450:100)*15 =

(6450*15):100 =

96750:100 = 967.5

Answer:

monthly income=rs14000

annual income =rs14000×12=rs 168000

since it is greater than rs125000

he needed to pay tax=x% let

tax amount =6450

x% of rs (168000-125000)=6450

x/100×43000=6450

x=6450/430=15

therefore required tax %=15%

Answer:

117

Step-by-step explanation:

b1+b2÷2×h is the formula.

Just fill in the formula with the numbers you have.

12+14=26

26÷2=13

13×9=117

Answer:

Barry's kart is faster as he goes 21 Mph while Alan only goes 19.89 Mph.

Step-by-step explanation:

First to get this answer we need to convert feet per minute to miles per hour. So we multiple 1750 feet per minute by 60 to get a hour. This gets up 105000 total feet in a hour. Now we need to divide this by 5280, which is how long a mile is, to get 19.89 miles which is how many miles he travels in a hour making him travel 19.89 mph which is less than 21 making Barry faster.

The number of decimal places should be one more than the least accurate measurement, and the number of significant figures can be determined by counting the digits in the number, excluding the decimal point.

Rounding a number is important when providing an answer to a calculation or question. The number of decimal places and significant figures the answer should be rounded to depends on the accuracy of the answer that is required.

To calculate the number of decimal places and significant figures the answer should be rounded to, the general rule is to round to one more decimal place than the least accurate measurement. For example, if the least accurate measurement used in the calculation is rounded to two decimal places, the answer should be rounded to three decimal places.

The significant figures of the rounded answer can be determined by counting the number of digits in the number, excluding the decimal point. For example, the number 6,782 would have four significant figures, as there are four digits in the number.

In conclusion, the number of decimal places and significant figures the answer should be rounded to depends on the accuracy of the answer that is required. The number of decimal places should be one more than the least accurate measurement, and the number of significant figures can be determined by counting the digits in the number, excluding the decimal point.

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Answer:

BP

Step-by-step explanation:

the letters are congruent in order, so the last 2 letters of both sides are congruent

Answer:

$11,321,630

Step-by-step explanation:

We solve using Exponential growth formula

A(t) = Ao (1 + r)^t

Ao = Initial worth = $94,000

r = Growth rate = 7.3% = 0.073

t = Time in years = 2020 - 1952

= 68 years

A(t) = Current worth in 2020 = After 68 years

A(t) = 94000 × ( 1 + 0.073)^68

A(t) = 94000 × 120.44286946

A(t) = 11,321,629.729

Therefore, the estimated worth of the Van Gogh painting in 2020 approximately = $11,321,630

The probability of exactly 1 of the chosen magazines being an issue of Newsweek is approximately 0.2107 or 21.07%. The probability of choosing the December 1st issue of Time is approximately 0.0526 or 5.26%.

To solve this problem, we can use the concept of combinations and the total number of possible outcomes.

(1) Probability that exactly 1 is an issue of Newsweek:

Total number of ways to choose 4 magazines out of the given 8 Newsweek issues, 7 Popular Science issues, and 4 Time issues is C(19, 4) = 19! / (4! * (19-4)!) = 3876.

To choose exactly 1 Newsweek issue, we have 8 options. The remaining 3 magazines can be chosen from the remaining 18 magazines (excluding the one Newsweek issue chosen earlier) in C(18, 3) = 18! / (3! * (18-3)!) = 816 ways.

Therefore, the probability of choosing exactly 1 Newsweek issue is 816 / 3876 ≈ 0.2107 or 21.07%.

(2) Probability of choosing the December 1st issue of Time:

The probability of selecting the December 1st issue of Time is 1 out of the 4 Time issues.

Therefore, the probability of choosing the December 1st issue of Time is 1 / 19 ≈ 0.0526 or 5.26%.

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Answer:

number of glasses he bought = 60

Step-by-step explanation:

Let the variable x represent the number of glasses he bought

Total cost of x glasses at Rs. 12 each = 12x

5 glasses broke so remaining number of glasses = x- 5

He sold this quantity of glasses for Rs. 16 each

Total sale price of (x - 5) glasses = 16(x - 5)

Total profit = Total sales - Total cost = 160

=> 16(x - 5) - 12x = 16

Expand brackets for 16(x - 5): 16x - 16 x 5 = 16x - 80

Therefore we get

16x - 80- 12x = 160

4x - 80 = 160

Add 80 on both sides:

4x -80 + 80  = 160 + 80

4x = 240

x = 240/4 = 60

Answer:

The awnser is 4.472135955

Answer: x = 1, y = 4, z = -2

Step-by-step explanation:

First, solve the third equation by the method of substitution for variable y.

2x + y + 3z = 0 -> y = -2x - 3z

Then, plug in y = -2x - 3z into the first equation of the system.

8x - 6y + 2z = -20

8x - 6 * (-2x - 3z) + 2z = -20

8x + 12x + 18z + 2z = -20

20x + 20z = -20

Repeat for the second equation.

-3x + 6y - 15z = 51

-3x + 6 * (-2x - 3z) -15z = 51

-3x - 12x - 18z - 15z = 51

-15x - 33z = 51

I have chosen to solve the equation  20x + 20z = -20 for z.

20z = -20x - 20

Divide both sides by 20.

z = -x - 1

Plug in z = -x - 1 into the equation -15x - 33z = 51 from an earlier step to find x.

-15x - 33 * (-x - 1) = 51

-15x + 33x + 33 = 51

18x = 51 - 33

x = 1

Now we have that:

x = 1

y = -2x - 3z

z = -x - 1

Plug in your value of x into the equation z = -x -1 to find z.

z = -1 - 1

z = -2

Plug in both your values of x and z into the equation y = -2x - 3z to find y.

y = -2 * 1 - 3 * (-2)

y = -2 + 6

y = 4

Answer:

18√2

Step-by-step explanation:

2√3 x 3√6

2 x 3 x (√6 x √3)

=> 6√18

=> 6√(3x3x2)

=> 6 x 3√2

=> 18√2

As per the standard deviation, the average number of hours per week spent studying for students at her college is less than 17 hours per week.

The term standard deviation is defined as the statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.

Here we have given that one faculty member in statistics believed the average number of hours/week spent studying stat 200 was 4, but most other faculty members think it is less than 4. the faculty want to see if the average is less than 4. (the sample average was 3.7 hours/week with a sample standard deviation of 1.8 hours/week) and we need to find analysis should they use.

While we reading the question, we know that

Sample average = 3.7

Standard deviation = 1.8

Then the null and alternative hypothesis is written as,

p-value = P(z ≤ 29.07) = 1.0000

Rejection Rule is Reject H0 if p-value < a

p-value 1.0000 > a = 0.05

Therefore,  the conclusion said that here we do Not Reject H0

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The tangential component of the acceleration vector is 36j.
The normal component of the acceleration vector is 18i / √(1 + 4t^2).

Tangential component: The tangential component of the acceleration vector is given by the derivative of the velocity vector. The velocity vector is the derivative of the position vector. In this case, the position vector is r(t) = 6(3t - t^3)i + 18t^2j. Taking the derivative of the position vector, we get the velocity vector v(t) = 18i + 36tj. Taking the derivative of the velocity vector, we find that the tangential component of the acceleration vector is a(t) = 0i + 36j. Therefore, the tangential component of the acceleration vector is 36j.

Normal component: The normal component of the acceleration vector can be found by taking the derivative of the velocity vector with respect to arc length. The magnitude of the velocity vector is the rate of change of arc length, so we can find the arc length s(t) by integrating the magnitude of the velocity vector. In this case, the magnitude of the velocity vector is |v(t)| = √(18^2 + (36t)^2) = 18√(1 + 4t^2). Integrating this expression, we find that the arc length is s(t) = 18t√(1 + 4t^2) + C, where C is a constant of integration. Taking the derivative of the arc length with respect to time, we find that ds(t)/dt = 18√(1 + 4t^2) + 36t^2/√(1 + 4t^2). The derivative of the velocity vector with respect to arc length is then given by dv(t)/ds(t) = (18i + 36tj) / (18√(1 + 4t^2) + 36t^2/√(1 + 4t^2)). Simplifying this expression, we find that the normal component of the acceleration vector is a_n(t) = 18i / √(1 + 4t^2). Therefore, the normal component of the acceleration vector is 18i / √(1 + 4t^2).

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Answer:

-2

Step-by-step explanation:

here is a pic explanation

The range of a set of values is the difference between the maximum and minimum values in the set, the range is 3 - (-2) = 5.

The expression "X - Y" subtracts the value of Y from each value in the set X. If Y is assigned the value 2, then for each x in X, we have:

X - Y = x - 2

the calculation of X - Y for each value in the set X = (0, 1, 2, 3, 4, 5) with

Y = 2

So, if X = (0,1,2,3,4,5), then:

(0) - 2 = -2

(1) - 2 = -1

(2) - 2 = 0

(3) - 2 = 1

(4) - 2 = 2

(5) - 2 = 3

So, the resulting set is (-2, -1, 0, 1, 2, 3).

The resulting set is (-2, -1, 0, 1, 2, 3) and the range is 5.

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Answer:

The cost per person varies inversely with the number of people, so y = k/x for some fixed number k.

"It costs $90 each for five people", meaning that x = 5 and y = 90 pair up. Plug these values in and solve for k.

y = k/x

90 = k/5

90*5 = k

450 = k

k = 450

Therefore the equation updates to y = 450/x

Now we want to know how many passengers there are (x) when the cost per person is y = 56.25

Let's find out:

y = 450/x

56.25 = 450/x ... replace y with 56.25

56.25x = 450

x = 450/56.25

x = 8

If you have 8 people, then it costs $56.25 per person.

side note: the total cost is $450 which is the value of k we found earlier. Divide 450 over 8 and you should get 56.25 exactly. Optionally you can turn y = k/x into x*y = k form. So the equation y = 450/x is the same as x*y = 450.

Step-by-step explanation:

Answer:

C. order

Step-by-step explanation:

The associative property of addition allows you to change the of numbers without affecting the sum.

Answer: Grouping

Step-by-step explanation:

Changing the grouping of addends does not change the sum. For example, ( 2 + 3 ) + 4 = 2 + ( 3 + 4 ) (2 + 3) + 4 = 2 + (3 + 4) (2+3)+4=2+(3+4)left parenthesis, 2, plus, 3, right parenthesis, plus, 4, equals, 2, plus, left parenthesis, 3, plus, 4, right parenthesis.

Step-by-step explanation:

<CED + < AEC =180°

x + (2x +72) = 180

3x = 108

x = 36 deg

so <BEC = 90° - x = 90° - 36° = 54° ANS

Answer:

We know that point A is at -11, and B is 5 less than it, so we only have to substract 5 to -11, and see what we get by doing this operation:

-11 - 5 = -16

So now, we know that point A is located at -11 and we also know point B is located at -16

a) The probability that the diameter of a randomly selected tree will be at least 10 in. is: 0.1587

P (X ≥ 10) = 1 - P (X < 10)

Using the standard normal distribution table or a calculator with normalcdf function, we find:

P(X ≥ 10) = 0.1587

The probability that the diameter of a randomly selected tree will exceed 10 in. is the same as P(X > 10), which is:

P(X > 10) = 1 - P (X ≤ 10) = 1 - 0.8413 = 0.1587

b) Since the distribution is normal, the probability that the diameter of a randomly selected tree will exceed 20 in. is very low, and can be approximated as:0

P (X > 20) ≈ 0

c) The probability that the diameter of a randomly selected tree will be between 5 and 10 in. is: 0.7935

P(5 < X < 10) = P (X < 10) - P(X < 5)

Using the standard normal distribution table or a calculator with normalcdf function, we find:

P(5 < X < 10) = 0.8413 - 0.0478 = 0.7935

d) We need to find the value c such that the interval (8.8 - c, 8.8 + c) includes 98% of all diameter values. Using the standard normal distribution table or a calculator with invNorm function, we find:

P(-c < Z < c) = 0.98

where Z is the standard normal variable. Therefore, we have:

c = invNorm(0.99) * σ

c = 2.33 * 2.8 ≈ 6.5

So, the interval (8.8 - c, 8.8 + c) ≈ (2.3, 15.3) includes 98% of all diameter values.

e) The probability that at least one of the four trees has a diameter exceeding 10 in. can be calculated using the complement rule and the fact that the trees are independently selected:

P (at least one tree has diameter > 10) = 1 - P (no tree has diameter > 10)

P (no tree has diameter > 10) = P(X ≤ 10)^4

Using the standard normal distribution table or a calculator with normalcdf function, we find: 0.506

P (no tree has diameter > 10) = 0.8413^4 ≈ 0.494

Therefore, we have:

P (at least one tree has diameter > 10) = 1 - 0.494 ≈ 0.506

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Answer: I believe 20.

Take one pair of lines. They will intersect at a point (no lines parallel). The other four lines will intersect at different points (no more than two lines through one point) giving four triangles. There are 6C2 = 15 different pairs of lines so 15*4 = 60 triangles. However, each triangle will come from three different points so we need 60/3 = 20 distinct triangles.

EDIT: Now that I’m more awake, it occurs to me there is a much easier answer. Since no two lines are parallel and no three lines are coincident, every combination of three lines must form a triangle. There are 6C3 = 20 triangles.

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

combinations

C(n,r)= n! / (r! * (n−r)!)

n = 6 : total number of lines

r = 3 : because its 3 lines to make a triangle

6 lines

6C3 = 20 triangles

quora glenn clemens

mathplanet

C = top speed of cheetah

P = top speed of peregrine falcon

"The top speed of a peregrine falcon is 20 miles per hour less than three times the top speed of a cheetah"

So in short,

P = 3C - 20

Now if x was the top speed of the cheetah, then we replace C with x to get

P = 3x - 20