1 Consider the following series: Σ n=1 n56 We will test this series for convergence or divergence. (i) What test(s) is(are) applicable to test this series? Click for List (ii) Determine whether this series converges or diverges. O Converges O Diverges

Step-by-step explanation:

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When President Dwight Eisenhower ordered the Arkansas National Guard into service to enforce court orders to desegregate schools, it was an example of a) executive orders.

Executive orders are directives issued by the President of the United States that have the force of law. They are used to manage and govern the operations of the federal government. In this case, President Eisenhower used his executive authority to deploy the Arkansas National Guard to enforce the desegregation of schools as mandated by the courts.

The Supreme Court's landmark decision in Brown v. Board of Education in 1954 declared that segregation in public schools was unconstitutional. However, resistance to desegregation persisted in some areas of the country, including Arkansas. To ensure compliance with the court's ruling, President Eisenhower exercised his executive power and deployed the National Guard to Little Rock, Arkansas, to protect and enforce the rights of African American students seeking to attend previously all-white schools.

Therefore, President Eisenhower's action of ordering the Arkansas National Guard to enforce court orders to desegregate schools falls under the category of a) executive orders, as he used his executive authority to implement a policy decision.

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Answer:

No choices, but 3(2x) is simplified to 6x

Step-by-step explanation:

3(2x) = 3 × 2x = 6x

Answer: The expression that is equivalent to (2x)3 is 6

Step-by-step explanation: The answer is 6 because x is equal to 3 so 3*2=6

After four hours, the height of the candles will be the same.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A red candle has an 8-inch height and burns at a 7/10-inch per hour rate. A 6-inch tall blue candle burns at a rate of 1/5 inch per hour.

Let x be the number of hours and y be the height.

y = -0.70x + 8           ...1

y = -0.20x + 6             ...2

From equations 1 and 2, then we have

- 0.20x + 6 = - 0.70x + 8

(0.70 - 0.20)x = 8 - 6

0.50x = 2

x = 4 hours

After four hours, the height of the candles will be the same.

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Answer: You shouldn't hate trig.

Step-by-step explanation:

SinΘ= opposite/hypotenuse

SinΘ=y/x

Sin(16) = 9/x

x = 9/Sin(16)

x= 32.7 cm

Answer:

\( \) \( \) \( \) \( \)

Answer:

1900 km

Step-by-step explanation:

train = 1050km

bus = 200 less than train or 1050-200 = 850

1050+850=1900

Answer:

625, just got it right

Step-by-step explanation:

The point estimate here is 0.

Calculating the Mean of Each Set

The sample set of production rates exhibited by workers before workshop, S1 = {20, 25, 27, 23, , 22, 20, 17}

The sample set of production rates exhibited by workers after workshop, S2 = {22, 23, 27, 20, 25, 19, 18}

The mean of set S1 = (20+25+27+23+22+20+17)/7

= 154/7

= 22

The mean of set S2 = (22+23+37+20+25+19+18)/7

= 154/7

=22

Calculating the Point Estimate

The formula for point estimate is given as,

Point Estimate  = The mean of set S1 - The mean of set S2

Point Estimate = 22-22

Point Estimate = 0

Therefore, the point estimate for the difference between the means of the two populations or sets is 0

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Given :

The four sides of a garden measure 8 1/3 feet, 17 1/4 feet, 17 1/2 feet, and

11 3/4 feet.

To Find :

The length (in ft) of the fence needed to enclose the garden.

Solution :

First simplifying the given mixed numbers :

8 1/3 = 25/3 feet

17 1/4 = 69/4 feet

17 1/2 = 35/2 feet

11 3/4 = 47/4 feet

Now, length of fence needed to enclose the garden is :

\(L = \dfrac{25}{3}+ \dfrac{69}{4}+ \dfrac{35}{2}+ \dfrac{47}{4}\\\\L = \dfrac{(25\times 4)+ ( 69\times 3) + ( 35\times 6) + (47 \times 3 )}{12}\\\\L = \dfrac{658}{12}\ feet\)

Hence, this is the required solution.

Answer:

-8

Step-by-step explanation:

Following Order of Operations rules, we evaluate anything within parentheses first:

8-[12-(-4)] = 8 - 16 = -8

Answer:

well you need to attech the graph

Step-by-step explanation:

The correct option which would decrease the margin of error is Option B.

The margin of error is inversely proportional to the square root of the sample size. This means that increasing the sample size will decrease the margin of error.

Constructing a 90% confidence interval will increase the margin of error, and constructing a 95% confidence interval will increase the margin of error even more. This is because a higher confidence level requires a wider confidence interval.

Therefore, the correct option is using a sample size of 200.

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The approximate solutions to the equation cos x = -0.60 for the domain 0° ≤ x ≤ 360° are 53° and 307°.

First, we need to identify the angles for which the cosine function is equal to -0.60. We can use a calculator or reference table to find that the cosine of 53° is approximately -0.60. However, we need to check if 53° is within the given domain of 0° ≤ x ≤ 360°. Since 53° is within this range, it is a possible solution to the equation.

Next, we need to check if there are any other angles within the domain that satisfy the equation.

To do this, we can use the periodicity of the cosine function, which means that the cosine of an angle is equal to the cosine of that angle plus a multiple of 360°. In other words, if cos x = -0.60 for some angle x within the domain, then cos (x + 360n) = -0.60 for any integer n.

We can use this property to find any other possible solutions to the equation by adding or subtracting multiples of 360° from our initial solution of 53°.

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From the given gallons of solution to make 50% solution approximately 4.7 gallons of 35% solution need to be mixed.

As given in the question,

Quantity of 60% solution in making 50% solution is = 7 gallons

Let us consider y gallons be the quantity of 35% solution to make 50% solution.

Quantity used to make 50% solution is (7 + y)

Required equation is:

(y × 35%) + (7× 60%) = (7+y) 50%

⇒(35y/100) + (420/100) = (350 + 50y)/100

⇒35y + 420 = 350 + 50y

⇒50y - 35y = 420 -350

⇒15y = 70

⇒y = 4.666..

⇒y = 4.7 gallons ( approximately)

Therefore, from the given gallons of solution to make 50% solution approximately 4.7 gallons of 35% solution need to be mixed.

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Answer:  $19,864.60

Step-by-step explanation:

The future value formula could have been used to find the price in the 6th year. As we now know the price, the formula can now be used to find the original price.

Price at 6th year = Original price * ( 1 + rate) ^ number of years

12,045 = Og * ( 1 - 8%) ⁶

12,045 = Og * 0.606355001344

Og = 12,045 / 0.606355001344

Og = $19,864.60

Rate is subtracted because price was reducing.

The equation of the tangent line to f-1(x) at the point (3, -1) is y = 1/(-2) x - 1/2.

This is because the slope of the tangent line to f(x) at (-1,3) is -2, and since f(x) and f-1(x) are inverse functions, the slopes of their tangent lines are reciprocals.

Therefore, the slope of the tangent line to f-1(x) at (3,-1) is -1/2. To find the y-intercept, we can use the fact that the point (3,-1) is on the tangent line. Plugging in x=3 and y=-1 into the equation y = -1/2 x + b, we get b = 1/2. Therefore, the equation of the tangent line to f-1(x) at (3,-1) is y = 1/(-2) x - 1/2.

In summary, to find the equation of the tangent line to f-1(x) at a point (a,b), we first find the point (c,d) on the graph of f(x) that corresponds to (a,b) under the inverse function.

Then, we find the slope of the tangent line to f(x) at (c,d), take the reciprocal, and plug it into the point-slope formula to find the equation of the tangent line to f-1(x) at (a,b).

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Step-by-step explanation:

> find the angle of center circle:

cos~¹ 5/(5+12) = cos~¹ 5/17 = 72°

so the sector area of the shaded

region =

(360-72)/360 × 3.14 × 5²

= 288/360 × 78.5

= 62.8

> the height of triangle (red Line) =

4×tan 72° = 4× 3.078 = 12.31

the height of pyramid (green

Line) = √12.31²-8.5² =√74.16

= 8.61

so the volume of pyramid =

⅓×(17×8)×8.61 = 390.32

a) The probability of exactly 2 flaws in 1 millimeter of wire is approximately 0.2645.

b)  There is no positive constant c that satisfies all the properties of a cumulative distribution function.

(a) The probability of exactly 2 flaws in 1 millimeter of wire is given by the Poisson probability mass function:

P(X = 2) = (e^(-λ) * λ^x) / x!

where λ = 2.3 and x = 2.

Substituting these values, we get:

P(X = 2) = (e^(-2.3) * 2.3^2) / 2! = 0.2645 (rounded to four decimal places)

Therefore, the probability of exactly 2 flaws in 1 millimeter of wire is approximately 0.2645.

(b) The probability of at most 2 flaws in 5 millimeters of wire is given by the cumulative distribution function of a Poisson distribution with mean λ = 5*2.3 = 11.5:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= (e^(-11.5) * 11.5^0) / 0! + (e^(-11.5) * 11.5^1) / 1! + (e^(-11.5) * 11.5^2) / 2!

= 0.0086 + 0.0495 + 0.1420

= 0.2001 (rounded to four decimal places)

Therefore, the probability of at most 2 flaws in 5 millimeters of wire is approximately 0.2001.

(c) The cumulative distribution function F(x) is given by:

F(x) = c(8x^2 – 3x), 0 <= x <= 2

Since F(x) is a cumulative distribution function, it satisfies the following properties:

F(x) is non-negative for all x

F(x) is non-decreasing as x increases

Lim x->-∞ F(x) = 0 and Lim x->+∞ F(x) = 1

Using these properties, we can solve for the constant c:

Lim x->-∞ F(x) = 0 => c(8*(-∞)^2 – 3*(-∞)) = 0 => c = 0

Lim x->+∞ F(x) = 1 => c(8*(+∞)^2 – 3*(+∞)) = 1 => c = 0 (since 8*(+∞)^2 is much larger than 3*(+∞))

Therefore, there is no positive constant c that satisfies all the properties of a cumulative distribution function.

Hence, the given function cannot be a cumulative distribution function.

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Hey there! I'm happy to help!

First, let's find the area of the top of the bar.

30×70=2100

This is the same as the bottom of the bar, so we have another 2100 mm, giving us 4200 in total.

Now we want to find the two long sides. This is 70×4.5, which is 315. Since there are two of these sides, we have another 315, giving us 630 in total there.

Now we have the short sides.

30×4.5=135

135×2=270

Now, we add up all of these measurements.

4200+630+270=5100

Therefore, Will's Wrapping Company will need 5100 mm² of paper to make their wrapper.

Have a wonderful day! :D

Answer:

Step-by-step explanation:

(10 - 1)/(0 - 3) = -9/3 = -3

y - 1 = -3(x -3)

y - 1 = -3x + 9

y = -3x + 10

Answer:

c. y = 1/2x - 2

Step-by-step explanation:

they have the same gradient so are parallel

Answer: you got to Find the focus of a parabola given its equation. If you have the equation of a parabola in vertex form , then the vertex is at and the focus is . Notice that here we are working with a parabola with a vertical axis of symmetry, so the -coordinate of the focus is the same as the -coordinate of the vertex.

Step-by-step explanation:

Answer:

  circumcenter

Step-by-step explanation:

You want to know the name of the point equidistant from the vertices of a triangle.

The circle that passes through the vertices of a triangle is called a "circumcircle". It circumscribes the triangle. Its center is equidistant from all points on the circle, so is equidistant from the triangle's vertices.

The point equidistant from the vertices of a triangle is the circumcenter.

__

Additional comment

The circumcenter is at the intersection of the perpendicular bisectors of the sides of the triangle.

Answer:

The answer is 590.

Answer:

The nearest tenth would be 590 since you round 86 to the nearest tenth. 86 is closer to 90 instead of 80, once again your answer is 590.

Step-by-step explanation:

The probability of choosing a vowel from the word PROBABILITY, expressed as a decimal, is approximately 0.364.

To find the probability of choosing a vowel from the word PROBABILITY, you'll need to follow these steps:

1. Identify the total number of letters in the word: There are 11 letters in the word PROBABILITY.
2. Identify the number of vowels in the word: There are 4 vowels (O, A, I, and I).
3. Calculate the probability by dividing the number of vowels by the total number of letters: Probability = (number of vowels) / (total number of letters) = 4/11.

A decimal indication that the probability of selecting a vowel from the word PROBABILITY is roughly 0.364.

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In 5 mi there are 316800 in . Which is the same to say that 5 miles is 316800 inches.

Answer:

316,800

Step-by-step explanation:

I hope this helps!

Answer:

angles

1x

3x

5x

1x +3x +5x = 180 (ASP)

9x = 180

x= 180÷9

x= 20

1x= 20

3x= 60

5x=100

angles are 20°, 60°, 100°

Step-by-step explanation:

hope it helps u

Answer:

The width is 5 meters

Step-by-step explanation:

The rectangular field is 24 meaning adding just one width and length of the rectangle would be 12.

x = width

2x - 3 + x = 12

3x - 3 = 12

3x - 3 + 3 = 12 + 3

3x = 15

x = 5