Solve for m in the following equation:
x= 3k(n + m)

Using Taylor series, the approximation P3(1.2) = 0.77083. Error R3(1.2) < 0.000235. Thus, P3(1.2) - |R3(1.2)| = 0.770599, within 0.001 of f(1.2).

In part C, we found the third-order Taylor polynomial for f about x=1 to be P3(x) = 1 - 1/2(x-1) + 1/8\((x-1)^2\)- 1/48\((x-1)^3\).

To show that this approximation is within 0.001 of the exact value of f(1.2), we need to estimate the error using the remainder term. The remainder term for the third-order Taylor polynomial is given by R3(x) = f(x) - P3(x) = (1/4!)\((x-1)^4\)f⁴(c), where c is some number between 1 and x.

Using the given formula for fⁿ(1), we can compute f⁴(c) = (-1)³(3!)/2⁴ = -3/16. Thus, we have R3(1.2) = (1/4!)\((0.2)^4\)(-3/16) = -0.000234375.

Since R3(1.2) is negative, we know that P3(1.2) > f(1.2), so our approximation is too high. Therefore, to ensure that our approximation is within 0.001 of the exact value of f(1.2), we need to subtract the error bound from our approximation. That is, we need to use P3(1.2) - |R3(1.2)| as our estimate. Substituting values, we get P3(1.2) - |R3(1.2)| = 0.770833333 - 0.000234375 = 0.770598958.

Since |f(1.2) - P3(1.2)| < |R3(1.2)|, we can conclude that our approximation is within 0.001 of the exact value of f(1.2).

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Step-by-step explanation: The solution to this system of equations will be where the two lines on the graph intersect with each other.

Notice that both of them intersect to the left of the y-axis which means our x - coordinate must be negative.

They also intersect above the x-axis so our y-coordinate must be positive.

So the only option with a negative x-coordinate

and a positive y-coordinate is (-1/4, 3/4).

Answer:

-6

Explanation:

(-3) · 2

= -6

[Think of it as -3, twice]

(-3) + (-3)

= -6

Answer:

-3×2 = -6   (you add the negative to the 6 because negative times positive is negative)

Answer: 7 inches

Step-by-step explanation:

From the question, we are informed that the ratio of the side length of a square to the square's perimeter is always 1 to 4.

We are further told that Peter drew a square with a perimeter of 28 inches. The side length of the square Peter drew will be gotten by dividing 28 inches by 4. This will be:

= 28/4

= 7 inches

Therefore, the side length or the square is 7 inches.

Answer:

$31.20

Step-by-step explanation:

40% of 78 is 31.2

Answer:

m = 8h

Step-by-step explanation:

The money she earns in one hour is $8.

8 dollars x hours worked = her total money for a day.

Hope this helps! :-)

The volume of the remaining piece of ice cube is 6911.5 cubic cm

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

The figure

Where, we have

Radius, r = 20/2  = 10 cm

Height, h = 33 cm

The volume of the remaining piece is calculated is

V = 2/3πr²h

Substitute the known values in the above equation, so, we have the following representation

V = 2/3 * 22/7 * 10² * 33

Evaluate

V = 6911.5

Hence, the volume of the remaining piece is 6911.5 cubic cm

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Our conclusion is that there is strong evidence to suggest that the average weight of Yummy Mix bags is less than 5 pounds and further investigation should be conducted to identify and address any potential issues in production or packaging.

Based on the given information, we can conclude that the sample of labeled 5 pound bags of Yummy Mix is statistically significantly different from the assumed population mean of 5 pounds.

The average weight of 3.5 pounds is less than 5 pounds, which indicates that there may be an issue with the production process or packaging.

To determine the level of statistical significance, we can perform a one-sample t-test. The null hypothesis is that the population mean weight is equal to 5 pounds, and the alternative hypothesis is that it is less than 5 pounds.

Using a significance level of 0.05, we can calculate the t-statistic and compare it to the critical value from a t-distribution with n-1 degrees of freedom.

If the calculated t-statistic is less than the critical value, we reject the null hypothesis and conclude that the sample mean is statistically significantly different from the population mean.

In this case, since we are given that the probability of observing a sample mean of 3.5 pounds or less is less than 5%, we can assume that the calculated t-statistic is less than the critical value and reject the null hypothesis.

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If the economy starts to weaken and the FOMC determines that employment is falling short of maximum employment, an appropriate policy implementation would be to lower the interest on reserve balances rate, ON RRP offering rate, and discount rate.

This would make it cheaper for banks to borrow money and encourage them to lend more, which could stimulate economic activity and create more job opportunities. Option c, Lower the interest on reserve balances rate, ON RRP offering rate, and discount rate, is the best answer. The other options are not as effective in this scenario - raising rates would likely make it more expensive for businesses and consumers to borrow money, which could further slow down the economy, while using open market operations to decrease reserves could lead to a shortage of liquidity in the banking system.

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The length of the shorter leg is 2.2 feet and the length of the longer leg is 4.2 feet

From the question, we have the following dimensions

Hypotenuse = 5 feet

One leg = 2 feet longer than the other

This means that

x = 2 + y

h = 7

Where x and y are the legs of the triangle

By the Pythagoras theorem, we have the following equation

h^2 = x^2 + y^2

Substitute the known values in the above equation

So, we have the following equation

(2+ y)^2 + y^2 = 5^2

Evaluate

4 + 4y + y^2 + y^2 = 25

So, we have

2y^2 + 4y - 19 = 0

Using a graphing tool, we have

y = 2.2

Substitute y = 2.2 in x = y + 2

x = 2.2 + 2

Evaluate

x = 4.2

Hence, the triangle have its legs to have lengths of 2.2 feet and 4.2 feet

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(a)  (r, θ) = (√58, arctan(7/3)).

(b) (r, θ) = (8√2, π/4).

(c) (r, θ) = (√85, -arctan(7/6)).

(d) (r, θ) = (√85, arctan(-2/9)).

(e) (r, θ) = (√89, -arctan(8/5)).

(f) (r, θ) = (4, -π/2).

To find the polar coordinates (r, θ) from the given Cartesian coordinates (x, y), we use the following conversions:

r = √(x^2 + y^2)

θ = arctan(y/x)

(a) For (x, y) = (3, 7):

r = √(3^2 + 7^2) = √58

θ = arctan(7/3)

Therefore, (r, θ) = (√58, arctan(7/3)).

(b) For (x, y) = (8, 8):

r = √(8^2 + 8^2) = √128 = 8√2

θ = arctan(8/8) = arctan(1) = π/4

Therefore, (r, θ) = (8√2, π/4).

(c) For (x, y) = (-6, 7):

r = √((-6)^2 + 7^2) = √(36 + 49) = √85

θ = arctan(7/-6) = -arctan(7/6)

Therefore, (r, θ) = (√85, -arctan(7/6)).

(d) For (x, y) = (9, -2):

r = √(9^2 + (-2)^2) = √85

θ = arctan((-2)/9)

Therefore, (r, θ) = (√85, arctan(-2/9)).

(e) For (x, y) = (-5, 8):

r = √((-5)^2 + 8^2) = √89

θ = arctan(8/-5) = -arctan(8/5)

Therefore, (r, θ) = (√89, -arctan(8/5)).

(f) For (x, y) = (0, -4):

r = √(0^2 + (-4)^2) = √16 = 4

θ = arctan((-4)/0) = -π/2

Therefore, (r, θ) = (4, -π/2).

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JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.

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Answer:

6:2

Step-by-step explanation:

Answer:6:2 I hope this is helpful

Step-by-step explanation:

6 apples to 2 mangos is 6:2

Answer:

6

Step-by-step explanation:

Answer: Two parallel lines have the same slope. Therefore, we can use the slope of the given line y = -4x + 5 to find the slope of the line that is parallel to it.

The slope of y = -4x + 5 is -4. Therefore, the slope of any line parallel to it will also be -4.

Now we have the slope of the line and a point that it passes through. We can use point-slope form to write the equation of the line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point on the line.

Plugging in the values we know, we get:

y - (-1) = -4(x - (-2))

y + 1 = -4(x + 2)

y + 1 = -4x - 8

y = -4x - 9

Therefore, the equation of the line that is parallel to y = -4x + 5 and passes through the point (-2,-1) is y = -4x - 9.

Step-by-step explanation:

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

Explanation:

Choice a) can be ruled out because angles A and D are supplementary. Supplementary angles add to 180 degrees by definition. They form a straight line or straight angle.

Choice b) and choice d) are eliminated for similar reasoning as choice a).

Choice c) is the only thing left. It turns out that angles B and D are not supplementary, but rather they are vertical angles. They are opposite one another in this X shape. Vertical angles are always congruent.

Note: Angles B and D are supplementary if and only if the angles are 90 degrees each.

Answer:

(t) = 326millions. The logistic model for the US population would be:

P(t) = 800 / (1 + e^(-k(t-2000)))

Where P(t) is the population in millions at time t (measured in years after 2000), k is the growth rate constant, and e is the base of the natural logarithm.

Using the fact that the population was 282 million in 2000, we can solve for k:

282 = 800 / (1 + e^(-k(0-2000)))
282(1 + e^(-k(2000))) = 800
1 + e^(-k(2000)) = 2.83687943
e^(-k(2000)) = 1.83687943
-k(2000) = ln(1.83687943)
k = -ln(1.83687943) / 2000
k ≈ 0.0071

Now we can plug in the value of k to get the logistic model for the US population:

P(t) = 800 / (1 + e^(-0.0071(t-2000)))

So, for example, the population in 2020 (t = 20) would be:

P(20) = 800 / (1 + e^(-0.0071(20-2000))) ≈ 326 million

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Answer:

Step-by-step explanation:

in the form y = mx + b m is the slope and y is the y intercept. Rewrite each problem to solve.

11) y = 7x - 5

-5 is the y intercept

12) y = -x + 9

9 is the y intercept

13) 4y - 8 = 2x

4y = 2x + 8

y = (2x + 8)/4

y = 1/2x + 2

2 is the y intercept

14) 11x - 8y = - 48

-8y = -11x - 48

y = (-11x - 48)/-8

y = 11/8x + 6

6 is the y intercept

15) x - 3y = 8

-3y = 8 - x

y = (8 - x)/-3

y = -3/8 + 1/3x

y = 1/3x - 3/8

-3/8 is the y intercept

Answer:

ten point zero twenty two

Step-by-step explanation:

How do you write 37.025 in word form?

How to Write Out Number 37.025 in Words: thirty-seven and twenty-five thousandths in (US) American English, Number Converted (Spelled Out) to Words.

The first constraint is a linear equation that relates the variables x1, x2, and x3, and the second constraint is an inequality constraint involving x1 and x2The given problem is a linear programming problem in its primal form.

The objective is to maximize the expression z = 7x1 - 5x2 - 2x3, subject to two constraints.. The goal is to find the values of x1, x2, and x3 that maximize the objective function while satisfying the given constraints.

In the primal problem, the objective is to maximize the expression z, which is a linear combination of the decision variables x1, x2, and x3. The coefficients 7, -5, and -2 represent the weights assigned to each variable in the objective function. The constraints represent the relationships and limitations imposed on the variables. The first constraint is an equality constraint, which means that the left-hand side of the equation must equal the right-hand side. The second constraint is an inequality constraint, indicating that the value of the expression 2x1 + x2 must be less than or equal to a certain value.

To solve this linear programming problem, various optimization techniques such as the simplex method or interior point methods can be applied. These methods iteratively adjust the values of the decision variables to find the optimal solution that maximizes the objective function while satisfying the given constraints. By solving the primal problem, the values of x1, x2, and x3 can be determined, leading to the maximum value of the objective function z.

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After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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Sebastian ran 11 kilometers before school on weekdays. To find out how many kilometers he ran before school on weekdays, we need to subtract the distances he ran on weekend from the total distance he ran in a week.

We know that Sebastian ran a total of 22.7 kilometers in 1 week. This includes the distances he ran on Saturday, Sunday, and the weekdays before school.

On Saturday, he ran 8 kilometers, and on Sunday, he ran 3.7 kilometers. These two distances combined account for 8 + 3.7 = 11.7 kilometers of his total distance.

To determine the distance he ran before school on weekdays, we need to subtract the distance covered on Saturday and Sunday from the total distance. This can be calculated as follows:

Total distance before school on weekdays = Total distance - Distance on Saturday - Distance on Sunday

= 22.7 kilometers - 8 kilometers - 3.7 kilometers

= 11 kilometers

Therefore, Sebastian ran 11 kilometers before school on weekdays.

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Answer:

Answer is B

Step-by-step explanation:

Answer:

Step-by-step explanation:

An equilateral triangle is a triangle that has all of its sides equal.

Perimeter of an equilaterial triangle = 3s where;

s is one side of the triangle.

Given the perimeter of ABC = 96mm

Substituting into the formula above to get s;

96 = 3s

s = 96/3

s = 32mm

Hence the length of one side of the triangle is 32mm

If a perpendicular bisector is drawn from angle A to side Line segment B C at point M, then MC will be half of BC and ΔAMC will be a right angled triangle.

Since all the sides of the triangle are equal, hence BC = 32mm. Since MC is the half of BC, then MC = 1/2 of 32mm

MC = 1/2 * 32mm

MC = 16mm

Hence the length of Line segment MC is 16mm

The correct option is A. 16 mm.

Given, the perimeter of equilateral triangle is 96 mm.

We know that perimeter is the sum of all sides and all sides of equilateral triangle are equal .

So, one side of equilateral triangle will be,

\(Side=\dfrac{96}{3} \\\\side=32\).

Since the perpendicular bisector is drawn from angle A to side B C at point M.

Hence it bisect the BC in two equal parts.

so,the length of MC will be,

\(MC=\dfrac{32}{2} \\\\\MC=16\)

Hence the length of MC is 16 mm.

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The probability of selecting the letter S from the word "MISSISSIPPI" is 4/11, the probability of selecting the letter I is 4/11, the probability of selecting the letters M or P is 3/11, and the probability of not selecting the letter P is 9/11.

To determine the probabilities of selecting specific letters from the word "MISSISSIPPI," we need to consider the frequency of each letter in the word.

The word "MISSISSIPPI" contains:

- 4 S's

- 4 I's

- 1 M

- 2 P's

1. The probability of selecting the letter S:

The probability of selecting S is the number of occurrences of S divided by the total number of letters in the word.

Probability of selecting S = (Number of S's) / (Total number of letters)

Probability of selecting S = 4 / 11

2. The probability of selecting the letter I:

The probability of selecting I is the number of occurrences of I divided by the total number of letters in the word.

Probability of selecting I = (Number of I's) / (Total number of letters)

Probability of selecting I = 4 / 11

3. The probability of selecting the letters M or P:

The probability of selecting M or P is the sum of the probabilities of selecting M and selecting P.

Probability of selecting M or P = (Number of M's + Number of P's) / (Total number of letters)

Probability of selecting M or P = (1 + 2) / 11

4. The probability of not selecting the letter P:

The probability of not selecting P is 1 minus the probability of selecting P.

Probability of not selecting P = 1 - (Probability of selecting P)

Probability of not selecting P = 1 - (Number of P's / Total number of letters)

Probability of not selecting P = 1 - (2 / 11)

Therefore, the probabilities are:

- Probability of selecting S: 4/11

- Probability of selecting I: 4/11

- Probability of selecting M or P: 3/11

- Probability of not selecting P: 9/11

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Answer:

The blank is 3

Step-by-step explanation:

1 - Give the blank a variable

x = our blank

2 - Write it out

\(\frac{5}{7} + \frac{x}{6} = \frac{51}{42}\)

3 - Get the denominators equal

\(\frac{5}{7}(\frac{6}{6}) +\frac{x}{6}(\frac{7}{7}) = \frac{51}{42} \\\frac{30}{42}+\frac{7x}{42} = \frac{51}{42}\)

4 - Simplify

\(\frac{30+7x}{42} = \frac{51}{42} \\ \frac{30+7x}{42} = \frac{51}{42}\)

5 - Solve for the numerators

30+7x = 51

-30         -30

      7x = 21

        x = 3

Answer: it’s 3

Step-by-step explanation: Sorry if im wrong lol

      From: me?