Is the 50th partial sum s50 of the alternating seriesan overestimate or an underestimate ofthe total sum? Explain.

Answer:

Step-by-step explanation:

a. The numerical expression representing the changes in Yu Yan's account is x = 25 + 32.75.

b. After evaluating expression (a), we see that $57.75 is the total amount changed from her account.

What is a numerical expression?

In mathematics, a numerical expression is a combination of sets of numbers and integer combined using addition, subtraction, multiplication, or division. When used with mathematical operators like addition, subtraction, multiplication, or division, it is said that a numerical expression is a combination of different integer numbers. The following are a few typical examples of numerical expressions: 5 + 10150 - 2520 × 2 + 5 40 ÷ 10 × 2 - 8 + 1 75 + 6 - 8.

To learn more about numerical expression, use the link given
https://brainly.com/question/28808560
#SPJ1

Answer:

4 years

Step-by-step explanation:

The table values using function rule y = -10x - 2 is (8,-2,-12,-52)

Given function

y = -10x - 2

From the table

x = -1 , 0 , 1 , 5

substitute x values in function

if x = -1

y = -10x - 2

= -10(-1) - 2

= 10 - 2

y = 8  

if x = 0

y = -10(0) -2

y = -2

if x = 1

y = -10(1) - 2

y  = -12

if x = 5

y = -10(5) -2

y = -52

y values (8,-2,-12,-52)

Table:

x      y

-1     8

0    -2

1     -12

5    -52

Learn more about the values and function rule here:

https://brainly.com/question/20527725

#SPJ1

The correct option is  B) increase.

To decrease sample error, a pollster must increase the number of respondents. The larger the sample size, the more representative it is likely to be of the target population, leading to a lower margin of error.

When conducting surveys or polls, it is essential to obtain responses from a diverse and random group of individuals. By increasing the number of respondents, the pollster can capture a broader range of perspectives, which helps to reduce sampling bias and increase the accuracy of the results.

For example, let's say a pollster wants to understand the political preferences of voters in a particular city. If they only survey 50 people, the sample may not accurately reflect the larger population, and the margin of error could be high. However, if they survey 500 or even 1000 people, the results are more likely to provide a reliable estimate of the overall population's preferences.

Therefore, to decrease sample error, pollsters should increase the number of respondents in their surveys or polls. This approach helps to ensure a more accurate representation of the population's views and minimize the potential for misleading or biased results.

Learn more about pollsters here:

brainly.com/question/2729655

#SPJ11

The statement that is true among the given options is: "The population mean and a sample mean for a sample selected from the population will usually be different values." This statement accurately describes the relationship between the population mean and a sample mean.

In statistics, the population mean refers to the average value of a variable in the entire population, while a sample mean represents the average value of the variable calculated from a subset of the population (a sample). It is important to note that unless the sample is the entire population itself, the sample mean will typically differ from the population mean.

The reason for this discrepancy is due to sampling variability. When we select a sample from a population, we are observing a smaller subset of the whole, which introduces some level of randomness or uncertainty. Different samples from the same population may yield slightly different values for the sample mean.

However, as the sample size increases, the sample mean tends to converge towards the population mean.

In summary, the population mean and sample mean are generally not identical, and their values are likely to differ due to sampling variability. The sample mean provides an estimate of the population mean, and the accuracy of this estimate improves with larger sample sizes.

For more such questions on sample mean

https://brainly.com/question/31101410

#SPJ8

Answer:

2x-7=13 (x=10)       3x+4=25 (x=7)

Step-by-step explanation:

1. 2x-7=13

Add 7 to both sides, then simplify. Then, divide both sides by two. Simplify furthermore to get the answer.

2x-7+7=2x    13+7=20.....2x=20     2x/2=x   20/2=10.....x=10

You can use the same process for the other equation.

Answer:

The coordinates of the Midpoint of AB will be: (1/2, 5)

Step-by-step explanation:

Given the points

Finding the midpoint between (-2, 6) and (3, 4)

\(\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\)

\(\left(x_1,\:y_1\right)=\left(-2,\:6\right),\:\left(x_2,\:y_2\right)=\left(3,\:4\right)\)

\(M.P=\left(\frac{3-2}{2},\:\frac{4+6}{2}\right)\)

        \(=\left(\frac{1}{2},\:5\right)\)

Therefore, the coordinates of the Midpoint of AB will be: (1/2, 5)

Answer:

-2

Step-by-step explanation:

-3+2=-1

-1+4=3

3-5=-2

Answer:

x=1

Step-by-step explanation:

3x-y=3

y=3-3x

9x-3y=9

9x-3(3-3x)=9

9x - 9 + 9x=9

9x + 9x=9 + 9

18x=18

x=18÷18

x=1

Answer:

not enough information

Step-by-step explanation:

There are no options

Answer:

5/6 of $1,200 is $1,000

The answer is $1000

ps: dont add the ($) only numerical answer

Answer:

c

Step-by-step explanation:

Substitute the coordinates of the points into the left side of the equation and if equal to the right side then the point lies on the line.

(4, 2 ) → 15(4) + 60(2) = 60 + 120 = 180 ← point on line

(12, 1 ) → 15(12) + 60(1) = 180 + 60 = 240 ← point not on line

(0, 3 ) → 15(0) + 60(3) = 0 + 180 = 180 ← point on line

(8, 1 ) → 15(8) + 60(1) = 120 + 60 = 180 ← point on line

The point (12, 1 ) is not on the line → c

Answer:

x=11∘

Step-by-step explanation:

So to do this, you need to understand that the sum of angles in a triangle is 180∘. If we understand this, we can add up all of the angles in ΔGHI and make the sum 180∘ to get an algebraic equation:

10x+9+3x+13+x+4=180 - Combine like terms

14x+26=180 - subtract 26 on both sides

14x = 154 - divide by 14 on both sides

x=11∘

Please mark brainliest if this helped

Answer:

\((10x + 9) \degree + (3x + 13) \degree + (x + 4) \degree = 180 \degree \\ 10x + 3x + x + 9 + 13 + 4 = 180 \degree \\ 14x + 26 = 180 \\ 14x = 180 -26 \\ 14x = 154 \\ x = \frac{154}{14} \\ \boxed{x = 11} \)

To test subtitle 11 in x, your angles should add up to 180 degrees

  The ant's entire distance travelled along its semicircular journey is its total distance travelled overall. The ant is travelling around a circle with radius R, thus the distance it has travelled is equal to half of the circle's circumference, πR.

The change in the ant's position is represented by a vector quantity called the displacement of the ant. The ant in this scenario begins at one end of the semi-circular path and moves 2R away from the beginning point to reach the other end. The direction of the displacement vector is from the starting point to the ending point, and the displacement's magnitude is equal to the 2R distance between the two points.

    So, the option c is most suitable option.

Therefore, πR and 2R are the ant's displacement and the distance travelled, respectively.

To know more about circle at :

brainly.com/question/27447563

#SPJ4

The value of f[g(x)] is - 64x³ - 336x² - 588x - 340 and the value of g[f(x)] is -4x³ + 19

The functions are as follows; f(x) = -x³ +3 and g(x) = 4x+7

The value of f[g(x)] is obtained by replacing every x in f(x) with the value of g(x) as given below

f[g(x)] = f(4x + 7) = - (4x + 7)³ + 3

When we expand (4x + 7)³, it gives us 64x³ + 336x² + 588x + 343

Then

f[g(x)] = - 64x³ - 336x² - 588x - 340

Similarly, g[f(x)] is obtained by replacing every x in g(x) with the value of f(x) as shown below;

g[f(x)] = g(-x³ + 3) = 4(-x³ + 3) + 7g

[f(x)] = -4x³ + 19

Therefore,

f[g(x)] = - 64x³ - 336x² - 588x - 340

g[f(x)] = -4x³ + 19

Learn more about the function at

https://brainly.com/question/32520165

#SPJ11

The 95% confidence interval for the population variance of the second observer is 2.86 to 7.36.

To calculate the confidence interval for the population variance, we can use the Chi-Square distribution. The formula for the confidence interval is:

[ (n-1)*s^2 / χ^2_upper , (n-1)*s^2 / χ^2_lower ]

Where:
- n is the sample size
- s^2 is the sample variance
- χ^2_upper and χ^2_lower are the upper and lower critical values from the Chi-Square distribution

a) For the observer in Problem 7 with n = 8 and a pointing and reading standard deviation of ±1.2'', we can calculate the confidence interval for the population variance at a 95% confidence level.

The degrees of freedom for the Chi-Square distribution is (n-1) = (8-1) = 7. From the Chi-Square distribution table or a statistical software, the upper and lower critical values for a 95% confidence level and 7 degrees of freedom are approximately 14.07 and 2.17, respectively.

Substituting the values into the formula, we get:

[ (8-1)*(1.2^2) / 14.07 , (8-1)*(1.2^2) / 2.17 ]

Simplifying the expression, we have:

[ 0.09 , 0.47 ]

Therefore, the 95% confidence interval for the population variance is 0.09 to 0.47.

b) To compare the observer in Problem 7 with another observer who has a pointing and reading standard deviation of ±2.4'' after 16 times (n = 16) at a 90% and 95% confidence level, we need to calculate the confidence interval for the population variance for the second observer using the same formula as above.

For a 90% confidence level, with n = 16 and 15 degrees of freedom, the critical values from the Chi-Square distribution are approximately 9.06 (upper) and 5.63 (lower). Substituting these values into the formula, we get:

[ (16-1)*(2.4^2) / 9.06 , (16-1)*(2.4^2) / 5.63 ]

Simplifying the expression, we have:

[ 3.56 , 9.09 ]

Therefore, the 90% confidence interval for the population variance of the second observer is 3.56 to 9.09.

For a 95% confidence level, with n = 16 and 15 degrees of freedom, the critical values from the Chi-Square distribution are approximately 10.58 (upper) and 6.26 (lower). Substituting these values into the formula, we get:

[ (16-1)*(2.4^2) / 10.58 , (16-1)*(2.4^2) / 6.26 ]

Simplifying the expression, we have:

[ 2.86 , 7.36 ]

Therefore, the 95% confidence interval for the population variance of the second observer is 2.86 to 7.36.

Learn more about interval here: brainly.com/question/32278466
#SPJ11

Answer:

The speed at which Carol needs to drive to meet Irvin at Bananatown at exactly the same time is approximately 47.188 miles per hour

Step-by-step explanation:

The given information are;

The location of Bananatown from Appletown = 143 miles east and 45 miles north

The location of Coconutville from Appletown = 98 miles east and 32 miles south

Taking Appletown as the origin, we have;

The slope, gradient of highway 42 = 45/143

The equation of a line representing highway 42 is given as follows;

y - 0 = 45/143 × (x - 0)

y = 45/143·x

Therefore, at Coconutville, where x = 98, we have, y = 45/143 × 98 ≈ 30.84 miles north

Total distance north Carol has to drive to get to highway 42 = 32 + 30.84 = 62.84 miles

Total distance along highway 42 Carol will drive to get to Bananatown = √((143 - 98)² + (45 - 30.84)²) ≈ 47.175 miles

Total distance Carol drives to Bananatown = 47.175 miles + 62.84 miles ≈ 110.015 miles

The total distance Irvin needs to drive to arrive at Bananatown = √(143² + 45²) ≈ 149.91

The total distance Irvin needs to drive to arrive at Bananatown ≈ 149.91  miles

The time it takes Irvin to arrive at Bananatown = (149.91 miles)/(45 mph) ≈  3.33 hours

The time he arrives at Bananatown = 8 a.m. + 3.33 hours ≈ 11.33 a.m.

The time available for Carol to meet Irvin at Bananatown at exactly the same time = 11.33 a.m. - 9 a.m. = 2.33 hours

Therefore, the speed at which Carol needs to drive = (110.015 miles)/2.33 hour ≈ 47.188 miles per hour

The speed at which Carol needs to drive to meet Irvin at Bananatown at exactly the same time ≈ 47.188 miles per hour.

Answer:

Step-by-step explanation:

object       X-axis            Y-axis             y = x               y = -x

(0,6)          (0 , -6)            (0,6)                (6 ,0)             (-6 ,0)

(-3 , 5)       (-3, -5)            (3 , 5)              (5 , -3)           (-5 , 3)

(-4 , -6)      (-4 , 6)           (4 , -6)              (-6,-4)           (6 , 4)

(8,-3)         (8 , 3)             (-8,-3)              (-3, 8)           (3 , -8)

(0,3)           (0 ,-3)           (0 ,3)                ( 3, 0)          (-3 , 0)

(0, -9)          (0 , 9)           (0 ,9)              (-9 , 0)         ( 9 , 0)

(5,0)           (5, 0)              (-5,0)             (0 , 5)           (0 , -5)  

(-2,0)           (-2,0)            (2,0)               (0, -2)         (0,2)

(-7 , 8)        (-7 , -8)          (7 , -8)             (8, -7)           (-8,7)

(12 , -6)      (12, 6)           (-12,-6)              (-6,12)          (6 ,-12)

When a point is reflected over x-axis, x-coordinate remains same and y-coordinate  change to its opposite sign.

When a point is reflected over y-axis, y-coordinate remains same and x-coordinate  change to its opposite sign.

When a point is reflected over y = x axis, x-coordinate and y-coordinate change their places.

When a point is reflected over y = -x axis, x-coordinate and y-coordinate change their places and are negated

Answer:

18.4

Step-by-step explanation:

9.2 + 9.2 = 18.4

The probability of selecting a sample of 20 children and having exactly 3 children who are from multiple births is approximately 0.214

To calculate the probability of selecting a sample with exactly 3 children who are from multiple births, we need to use the binomial distribution formula

P(X = k) = C(n, k) × p^k × (1 - p)^(n - k)

where

X is the random variable representing the number of children from multiple births in the sample

k is the number of children from multiple births we are interested in (in this case, k = 3)

n is the sample size (in this case, n = 20)

p is the probability of selecting a child from a multiple birth (let's assume this is 0.03, or 3%, based on some statistics for multiple births in some regions).

C(n, k) is the number of ways to choose k children from a sample of n children, which is given by the binomial coefficient

C(n, k) = n! / (k! × (n - k)!)

Plugging in the values, we get:

P(X = 3) = C(20, 3) × 0.03^3 × (1 - 0.03)^(20 - 3)

= (20! / (3! × 17!)) × 0.03^3 × 0.97^17

≈ 0.214

Learn more about probability here

brainly.com/question/11234923

#SPJ4

The solution to the given system of equations is x = 1 and y = -3.

To solve the system, we can use the method of elimination or substitution. Let's use the elimination method here.

We have the following system of equations:

-2x + y = -5 (Equation 1)

4x + y = -2 (Equation 2)

To eliminate the y variable, we can add Equation 1 and Equation 2 together:

(-2x + y) + (4x + y) = (-5) + (-2)

2x = -7

Dividing both sides of the equation by 2, we get:

x = -7/2 = 1

Substituting the value of x into Equation 1, we can solve for y:

-2(1) + y = -5

-2 + y = -5

y = -5 + 2

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

Learn more about elimination method here:

https://brainly.com/question/13877817

#SPJ11

Answer:

2.5

Step-by-step explanation

Pi R squared

radius is half diameter, so .9

Square the .9

Multiple that to 3.142

Additional reference geometry such as user-created reference planes can be created to reference other planes besides the default top, left and right planes. The given statement is false

Additional reference geometry is a useful tool in CAD software that allows users to create reference planes, axes, and points to assist in the creation of complex models. While the default top, left and right planes are often used as a starting point for reference geometry, users are not limited to these planes. In fact, users can create reference geometry that references any existing plane, axis, or point within the model. This allows for greater flexibility and precision when creating complex models.

In conclusion, it is false that additional reference geometry must reference the default top, left, and right planes. Users can create reference geometry that references any existing plane, axis, or point within the model for greater flexibility and precision.

To know more about geometry visit:

brainly.com/question/31408211

#SPJ11

Answer: \(x= 187.5p\)

Step-by-step explanation:

Given : An equation relating packets to bytes of information : \(b = 1,500p\) where p represents the number of packets and b represents the number of bytes of information.

1 byte = 8 bits

Let x= Number of bits such that 1 b = 8x

Put b = 8x in given equation , we get

\(8x=1500p\)

Divide both sides by 8 , we get

\(x= 187.5p\)

Hence, the equation represent the relationship between the number of packets and the number of bits : \(x= 187.5p\)

Answer:

x=12000p

Step-by-step explanation:

It is Right

I Fink

Answer:

1 rectangle

Step-by-step explanation

Area= lxb

So 7.7 x 11 = 84.7

3 trapezoid

Area =(a+b/2)

Base a=13

Base b = 6

Height = 5

By 2

Answer= 47.5

4 Right angled triangle

Ab/2

Axb

Multiply each legs of the right angle triangle

So 3 1by4 x 4

By 2

Answer: See explanation

Step-by-step explanation:

1. That's a rectangle, the area of a rectangle is l (length) × w (width)

l = 11 cm

w = 7.7 cm

11 × 7.7 = 84.7

Area = 84.7 cm²

2. That is a triangle, the area of a triangle is 1/2 × b (base) × h (height)

b = 12 ft

h = 4ft

1/2 × 12 × 4 = 1/2 × 48 = 24

Area = 24 cm²

3. That is a trapezoid, the area of a trapezoid is \(\frac{a (base) + b(base)}{2} h(height)\)

a = 6 cm

b = 13 cm

h = 5cm

((6 + 13) ÷ 2) x 5

(19 ÷ 2) x 5 = 9.5 × 5 = 47.5

Area = 47.5 cm²

4. Same formula: 1/2 × b × h

b = 3 1/4 in

h = 4 in

1/2 × 3 1/4 × 4 = 1/2 × 13/4 × 4

1/2 × 13 = 6.5

Area = 6.5 in²

Hope I helped!

To find the probability of event A (first card drawn is a club), event B (second card drawn is a club), and event C (third card drawn is red), we can use the Multiplication Rule for independent events.

Given that the events are independent, the probability of all three events occurring is the product of their individual probabilities.

Let's calculate the probability step by step:

1. Probability of event A: P(A) = Number of clubs / Total number of cards

  There are 13 clubs in a deck of 52 cards, so P(A) = 13/52 = 1/4.

2. Probability of event B: P(B) = Number of clubs (after one club is drawn) / Total number of remaining cards

  After one club is drawn, there are 12 clubs left out of 51 remaining cards, so P(B) = 12/51 = 4/17.

3. Probability of event C: P(C) = Number of red cards / Total number of remaining cards

  There are 26 red cards (diamonds and hearts) out of 50 remaining cards, so P(C) = 26/50 = 13/25

Now, using the Multiplication Rule:

P(A and B and C) = P(A) * P(B) * P(C) = (1/4) * (4/17) * (13/25) = 0.03117647059.

Rounding this result to four decimal places, we get approximately 0.0312.

Therefore, the probability that the first two cards drawn are clubs and the last card is red is approximately 0.0312.

To learn more about probability, refer below:

https://brainly.com/question/11034287

#SPJ11