Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to approximate the sum of the series with an error of less than 0.001. [infinity] (−1)n + 1 n2 n = 1

Answer: Choice C) 4

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Work Shown:

Set the denominator equal to zero and solve for x

4x-16 = 0

4x-16+16 = 0+16 ... add 16 to both sides

4x = 16

4x/4 = 16/4 ... divide both sides by 4

x = 4

--------

If x = 4, then the denominator is 0

4x-16 = 4(4)-16 = 16-16 = 0

So this x value is what we exclude from the domain to avoid a division by zero error.

Answer:

The probability that a randomly selected day in April will be rainy or windy is 0.62 or 62%.

Step-by-step explanation:

We are given that the probability of rain on any day in the month of April is 34%. The probability that it will be windy on any day in the month of April is 38%, and the probability of both is 10%.

And we have to find the probability that a randomly selected day in April will be rainy or windy.

Let the probability of rain on any day in the month of April = P(A) = 0.34

The probability of windy on any day in the month of April = P(W) = 0.38

The probability of both windy and rainy on any day in the month of April = P(R [tex]\bigcap[/tex] W) = 0.10

Now, the probability that a randomly selected day in April will be rainy or windy is given by = P(R [tex]\bigcup[/tex] W)

        P(R [tex]\bigcup[/tex] W) = P(R) + P(W) - P(R [tex]\bigcap[/tex] W)

                        = 0.34 + 0.38 - 0.10

                        = 0.62 or 62%

So, the probability that a randomly selected day in April will be rainy or windy is 62%.

Answer:

A. 2(16 + 12)

Step-by-step explanation:

If we look at choice A, it says 2 times 16 + 12.

When we solve this, 2 × 16 = 32 + 2 × 12 = 24, we get 32 + 24 because we used the distributed property on answer A.

The correct statement will be;

⇒ 8 (4 + 3)

Option C is true.

What is Distributive property?

By the rule of distributive property, multiplying the sum of two or more addends by a number gives the same result as when each addend is multiplied individually by the number and the products are added together.

Given that;

The expression is,

⇒ 32 + 24

Now,

The greatest common factor of 32 and 24 = 8

So, We can take 8 as common factor, we get;

⇒ 32 + 24

⇒ 8 x 4 + 8 x 3

⇒ 8 (4 + 3)

Thus, The correct statement will be;

⇒ 8 (4 + 3)

Option C is true.

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Answer:

c = 8

Step-by-step explanation:

3/6=4/c

Cross products

3c = 6*4

3c = 24

Divide each side by 3

3c/3 =24/3

c = 8

Greetings from Brasil...

We have to remember 2 details:

→ When X = 0, the function intersects the Y axis

→ When Y = 0, the function intersects the X axis

So

1: X = 0

Y = X + 5

Y = 0 + 5

Y = 5

X = 0 and Y = 5 ⇔ (0; 5)

2: Y = 0

Y = X + 5

0 = X + 5

X = - 5

Y = 0 and X = - 5 ⇔ (- 5; 0)

Then the point at which the graph intersects the X and Y axis will be

(0; 5) and (- 5; 0)

Answer:

p: x = 4  

q: y = -2

If p happens then q will also happen

Step-by-step explanation:

Given two propositions, we want to rearrange them in a conditional statement.

The correct answer is:

p → q

First, a conditional statement is something of the form:

If [Hypothesis] then [Conclusion]

So, if the first part is true, then the second part must be true.

Now, here we have two propositions:

p: "x  = 4"

q: "y = -2"

We want to write:

"if x = 4, then y = -2"

this is just written as: "p implies q" or:

p → q

Where "→" means "then", and the initial "if" is tacit.

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Answer:

55mph . None of the options are correct

Step-by-step explanation:

If the speed varies inversely as the time it takes to drive, then v ∝ 1/t. where;

v is the speed

t is the time taken

Hence;

v = k/t with k being the constant of proportionality.

Since it takes Kris 5 hours when driving at 55 mph, we will substitute v = 55mph and t = 5 hours. into the equation above to get the value of k as shown:

55 = k/5

Cross multiply

k = 55*5

k = 275

Hence, to calculate the speed it will Martin to  drive for 5 hours, we will substitute k = 275 and t = 5 into the original equation v = k/t  as shownl

v = 275/5

v = 55 mph

Hence, we can conclude that Martin will also need to drive at a speed of 55mph if he wants to take 5hours.

6.458 = 6 + 0.4 + 0.05 + 0.008

Each blank slot is filled with a digit from the original number. The zeros are placeholders to make sure we have the right alignment.

Answer:

Step-by-step explanation:

6.458

---------------------

6.000

0.400

0.050

0.008

6.458 = 6.000 + 0.400 + 0.050 + 0.008

trailing zeros can be omitted

Answer: D

Step-by-step explanation:

Since we are given that the x value is -1, we can eliminate A and C because the -1 is in the y coordinate.

To find the proper y value, we plug x into the equation.

y=-2x+5                                                 [plug in x=-1]

y=-2(-1)+5                                              [multiply -2 and -1]

y=2+5                                                    [add 2 and 5]

y=7

Now that we have the y value, we know the coordinate (-1,7) which makes D the correct answer.

Answer:

4,130

Step-by-step explanation:

4780-650=4130 ft

Answer:

x = 145

Step-by-step explanation:

If we look at the right triangle with sides of 24 and 30, we can find the missing leg using the Pythagorean Theorem. If we look carefully, we notice that 18:24:30 is basically the 3:4:5 Pythagorean Triple multiplied by 6, so the missing side is 18. If we look at the right triangle with sides of x and 24, we can find the missing side by calculating 161 - 18 = 143. Using the Pythagorean Theorem, we know that 143² + 24² = x² so x = 145.

Answer:

1 solution; (1,4)

Step-by-step explanation:

Whenever two lines intersect, their solution is the point that the two share in common. Here, it's (1,4), so that is the answer.

Answer:

c

Step-by-step explanation:

Answer:

Hey there!

There are 13 clubs in a deck of cards.

There are 4 tens.

However, the tens overlap with the clubs, so there are 16 cards to choose.

16/52=4/13

Let me know if this helps :)

The events are mutually inclusive. Option B is correct because the required probability is [tex]\dfrac{4}{13}[/tex].

Important information:

A deck of cards has total 52 cards, which includes 4 suits and each suit has 13 cards. If S be the sample space, then n(S) = 52.

Let A be the event that the card is a club card and B be the event that it is a ten card.

The number of club cards is 13. So, n(A) = 13.

There are 4 cards of 10. So, n(B) = 4.

One ten card is of club. So, [tex]n(A\cap B)=1[/tex].

Since [tex]n(A\cap B)=1\neq 0[/tex], therefore the events are mutually inclusive.

The number of club or a ten card is:

[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]

[tex]n(A\cup B)=13+4-1[/tex]

[tex]n(A\cup B)=16[/tex]

Now,

[tex]P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}[/tex]

[tex]P(A\cup B)=\dfrac{16}{52}[/tex]

[tex]P(A\cup B)=\dfrac{4}{13}[/tex]

Therefore, the probability of choosing a card from a deck of cards that is a club or a ten is [tex]\dfrac{4}{13}[/tex]. Hence, option B is correct.

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Answer:

Hey there!

For the first one:

Chips: x

Pretzels: 3x

Nachos: 3x-2

Total snacks: x+3x+3x-2=7x-2

For the second one:

In the equation, 150+5d, 150 represents the starting amount of money, in this case, 150 dollars. 5d means that for every day, five dollars get put into his account.

For the third one:

In this equation, 1.50 represents to initial fee, and 2.25m represents the cost per mile. Dividing by 2 gives us what each person in the cab pays.

Let me know if this helps :)

Answer:

I am almost positive it is 9.729

Step-by-step explanation:

my teacher used to say 4 or less let it rest, 5 or more raise the score. In this situation it is 2 so leave it be and that’s your answer. Also, 9.7 is tenths, 9.72 is hundredth, which means 9.729 is thousanths.

Answer: 9.729

Step-by-step explanation:

my teacher used to say 4 or less let it rest, 5 or more raise the score. In this situation it is 2 so leave it be and that’s your answer. Also, 9.7 is tenths, 9.72 is hundredth, which means 9.729 is thousanths.

Answer:

The slope is the inclination of a surface or a line with respect to the horizontal. It can be measured at an angle in degrees, radians or grades or even in percentage, that is to say according to the height to length ratio multiplied by 100.

Step-by-step explanation:

Answer:

x = 36°

Step-by-step explanation:

The sum of the exterior angles of a pentagon is always 360°. Since the pentagon is regular, meaning that all of its sides and interior angles are congruent, we know that all of the exterior angles are also congruent. Since a pentagon has 5 sides, we know that there are 5 congruent exterior angles, therefore:

5 * 2x = 360

10x = 360

x = 36°

The value of x in the Pentagon is 36.

Option D is the correct answer.

A pentagon is a polygon that has five sides and five angles.

The sides and angles of a pentagon are not all equal unless it is a regular pentagon.

A regular pentagon has five equal sides and five equal angles.

We have,

The sum of the exterior angles of any polygon is 360 degrees.

Since a regular pentagon has 5 sides, the sum of its exterior angles is 360 degrees.

Each exterior angle of a regular pentagon has a measure of:

= 360 degrees / 5

= 72 degrees

We are given that one exterior angle of the pentagon has a measure of (2x) degrees.

2x = 72

Solving for x.

x = 36

Therefore,

The value of x is 36, and the measure of the given exterior angle.

= (2x)

= 72 degrees.

Thus,

The value of x is 36.

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l = 16 feet

w = 3 feet

A = l×w

l = 10+2w

48 = (10 + 2w)w

48 = 10w + 2w² | : 2

24 = 5w + w²

w² + 5w - 24 = 0

w² + 8w - 3w - 24 = 0

w(w + 8) - 3(w + 8) = 0

(w - 3)(w + 8) = 0

w - 3 = 0 => w = 3 feet

w + 8 = 0 => w = - 8 ∉ N

l = 10 + 2w

l = 10 + 6

l = 16 feet

A = l×w = 16ft×3ft = 48ft²

Answer:

Select option D.

Step-by-step explanation:

Notice the input is n and the output is n+4. This simply means you add 4 to the input value. So,

-3 + 4 = 1

1 + 4 = 5

6 + 4 = 10

Cheers.

Answer:

x = -3

Step-by-step explanation:

16x − 4 + 5x = -67

Combine like terms

21x -4 = -67

Add 4 to each side

21x-4+4 = -67+4

21x = -63

Divide each side by 21

21x/21 = -63/21

x = -3

Answer:

[tex]\huge \boxed{x = -3}[/tex]

Step-by-step explanation:

[tex]16x - 4 + 5x = -67[/tex]

Combine like terms.

[tex]21x - 4 = -67[/tex]

Add 4 to both sides.

[tex]21x = -63[/tex]

Divide both sides by 21.

[tex]x = -3[/tex]

Answer:

The answer is nonexistent

Step-by-step explanation:

Answer: [tex]\chi^2[/tex] test statistic.

Step-by-step explanation:

The chi-square ([tex]\chi^2[/tex]  ) test is a non-parametric statistical test(also known as Goodness of fit test) which is used to determine if a distribution of observed frequencies differs from the expected frequencies.

Chi-square statistic uses either nominal (categorical) or ordinal level data.

Hence, When determining how well an observed set of frequencies fits an expected set of frequencies, the test statistic is [tex]\chi^2[/tex] test statistic.

Answer:

Option B.

Step-by-step explanation:

The given equation is

[tex]17h+6=40[/tex]

We need to find the property of equality to move the constant term to the right side of the equation.

In the given equation 6 is the constant term on the left side.

Using subtraction property of equality, subtract 6 from both sides.

[tex]17h+6-6=40-6[/tex]

[tex]17h=34[/tex]

So, the appropriate property of equality to move the constant term to the right side of the equation is Subtraction Property of Equality.

Therefore, the correct option is B.

Answer:

Step-by-step explanation:

[tex]\frac{67+72+63+77+59+75}{6} \\\\\frac{413}{6} \\\\68.833333 or 68.8[/tex]

Answer:

Step-by-step explanation:

Given the amount invested for a particular period of time at an interest rate, the equation that can model the Interest achieved on investment is expressed using the simple interest formula as shown;

Simple Interest = PRT/100 where;

P is the principal (amount invested)

R is the rate (in %)

T is the time (in years)

From the equation I = PRT/100, we need to express tht time T as a function of the rest of the variable as shown;

I = PRT/100

cross multiply

100I = PRT

Divide both sides by PR

100I/PR = PRT/PR

100I/PR = T

Hence the the time it takes to earn a certain amount of interest on a principal amount in an investment with simple interest is expressed as

T = 100I/PR

Answer:

8 feet = L

Step-by-step explanation:

The period T(in seconds) of a pendulum is given by T=2 pi root L over 32

T= 2π√(L/32)

where the L stands for Length(in feet) of the pendulum.

If π= 3.14, and the period is 3.14 seconds

Length will be

T= 2π√(L/32)

3.14= 2*(3.14)√(L/32)

(3.14/3.14)/2= √(L/32)

(1/2)²= L/32

1/4 = L/32

32/4= L

8 feet = L

Answer:

3

Step-by-step explanation:

The number line is showing x>3.

If the circle were closed it would be x≥3.

Answer:

3.

Step-by-step explanation:

Answer:

140.8 football fields.

Step-by-step explanation:

8 miles = 8 * 1760 yard.

So the number of football fields that he ran

= (8 * 1760) / 100

= 8 * 17.6

= 140.8.