Does the infinite geometric series diverge or converge?
1/5 + 1/10 + 1/20 +1/40 + …

These are absolute value expressions evaluated under different conditions:

|x + 3| if x > 5:

Here x is greater than 5, so x + 3 will also be positive. In this case, |x + 3| = x + 3.

|x + 3| if x > 2:

Similar to the above, x is greater than 2, so x + 3 will be positive. Thus, |x + 3| = x + 3.

|x + 3| if x = 2:

In this case, x + 3 = 2 + 3 = 5, and the absolute value of 5 is just 5. Thus, |x + 3| = 5.

|x - 3| if x > 5:

If x is greater than 5, then x - 3 will be positive. Hence, |x - 3| = x - 3.

|120 + x| if x < -120:

Since x is less than -120, 120 + x will be negative. But the absolute value of a negative number is its positive counterpart, so |120 + x| = -(120 + x).

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The time taken for the pebble to hit the water is 1.41 seconds.

The time taken for the pebble to hit the water is calculated by using the equation of the motion as follows;

h = -16t² + 5

where;

when the height is 27 ft, the time of motion is calculated as;

-27 = -16t² + 5

16t² = 5  + 27

16t² = 32

t² = 32/16

t² = 2

t = √2

t = 1.41 seconds

Thus, the time of motion is determined by applying the equation of motion as shown above.

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Answer:

6

Step-by-step explanation:

bc

Answer:

the line is passing through 1 for y and -4 for x

Step-by-step explanation:

The function y = 1/4 + 1 contains all the information you need. The + 1 indicates the y intercept, so it is given. Since the slope of the line is 1/4, the graph would pass through (-4, 0) and (0, 1) as starting from a point would go up one unit and right 4 units.

Answer:

1. $990

2. Sn = Sn-1 + (r/100) * Sn-1

3. $27,037.44

Step-by-step explanation:

1. The interest earned each year can be calculated using the simple interest formula:

Simple Interest = (Principal * Rate * Time) / 100

Here, Principal = $22,000, Rate = 4.5%, and Time = 1 year

So, the interest earned each year would be:

= (22,000 * 4.5 * 1) / 100

= $990

Therefore, the interest earned each year would be $990.

2. The recurrence relation to model the value of investment from year to year is:

Sn = Sn-1 + (r/100) * Sn-1

where Sn represents the value of the investment after n years, Sn-1 represents the value after n-1 years, and r represents the annual interest rate.

Using this recurrence relation, we can calculate the value of the investment for different years:

- S1 = 22,000 + 990 = 22,990

- S2 = 22,990 + (4.5/100) * 22,990 = 24,026.55

- S3 = 24,026.55 + (4.5/100) * 24,026.55 = 25,103.46

And so on...

3. To determine the value of the investment after 5 years, we can simply substitute n = 5 in the recurrence relation:

S5 = S4 + (r/100) * S4

= S3 + (r/100) * S3 + (r/100) * S3

= S2 + (r/100) * S2 + (r/100) * S2 + (r/100) * S2

= S1 + (r/100) * S1 + (r/100) * S1 + (r/100) * S1 + (r/100) * S1

Substituting values from previous calculations:

S1 = 22,000 + 990 = 22,990

So,

S5 = 22,990 + (4.5/100) * 22,990 + (4.5/100) * 22,990 + (4.5/100) * 22,990 + (4.5/100) * 22,990

= $27,037.44

Therefore, the value of the investment after 5 years would be $27,037.44.

Joey’s monthly payment is solved to be

C. $79.70

20% down 600 to calculate the monthly payment on a 3 000 car we would pay 2 400.

the interest rate is 12% per annum which equates to 1% per month the term of the loan is three years which equates to 36 months we can use a formula to calculate the monthly payments

[tex]Monthly salary = (P * r * (1 + r)^n) / ((1 + r)^n - 1) .[/tex]

where

P is the principal (premium),

r is the monthly interest rate, and

n is the number of months.

Plug in the prices and we have:

[tex]Monthly salary = (2400 * 0.01 * (1 + 0.01)^{36} ) / ((1 + 0.01)^{36} - 1)[/tex]

= $79.65 per square foot

So Joey’s monthly payment would be $79.65.

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A form of 1 that you can use to rationalize the denominator of the expression 8/(∛4), the rationalizing factor is 9.

In mathematics, rationalization refers to the process of eliminating radical or irrational expressions from the denominator of a fraction. This is done by multiplying both the numerator and the denominator of the fraction by a suitable expression that will result in a rational denominator.

The resulting fraction has a rational denominator, which makes it easier to work with and manipulate algebraically. Rationalization is a useful technique in algebra, trigonometry, and calculus, and is often used to simplify expressions and solve equations.

To rationalize the denominator of the expression 8/(∛4), we need to multiply the numerator and the denominator by a rationalizing factor that will eliminate the radical in the denominator.

Since the root 4 is equal to 2, we can rewrite the expression as:

8/3²

The square of 3 is 9, so we can use 9 as the rationalizing factor.

Multiplying the numerator and denominator by 9, we get:

(8/3²) x (9/9) = 72/9

Simplifying, we get:

72/9 = 8

Therefore, the rationalizing factor is 9.

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Answer:

The range is 37

Step-by-step explanation:

highest - lowest = range

64-27= 37

Hope it helped! :)

Answer: To compute the t-test statistic for the paired sample data, we need to first calculate the sample mean difference and the sample standard deviation of the differences. Then we can use the formula:

t = (sample mean difference - hypothesized mean difference) / (standard error of the mean difference)

where the standard error of the mean difference is calculated as:

standard error = sample standard deviation / sqrt(sample size)

Let's first calculate the sample mean difference:

x 9 6 7 5 12

y 6 8 3 6 7

The differences between each pair of x and y values are:

(9-6), (6-8), (7-3), (5-6), (12-7) = 3, -2, 4, -1, 5

The sample mean difference is the average of these differences:

sample mean difference = (3 - 2 + 4 - 1 + 5) / 5 = 1.8

Next, we need to calculate the sample standard deviation of the differences. To do this, we first calculate the deviations of each difference from the sample mean difference:

(3 - 1.8), (-2 - 1.8), (4 - 1.8), (-1 - 1.8), (5 - 1.8) = 1.2, -3.8, 2.2, -2.8, 3.2

The sample standard deviation of the differences is the square root of the sum of the squared deviations divided by (n-1):

sample standard deviation = sqrt[(1.2^2 + (-3.8)^2 + 2.2^2 + (-2.8)^2 + 3.2^2) / 4] = 3.153

Finally, we can calculate the t-test statistic:

t = (sample mean difference - hypothesized mean difference) / (standard error of the mean difference)

where the hypothesized mean difference is 0, and the standard error of the mean difference is:

standard error = sample standard deviation / sqrt(sample size) = 3.153 / sqrt(5) = 1.410

Substituting the values, we get:

t = (1.8 - 0) / 1.410 = 1.277

Rounding the final answer to three decimal places, we get:

t = 1.277

Therefore, the correct option is B. t = 1.292.

Answer:

number 1111q

Step-by-step explanation:

the answer is 1

The result of multiplying 5u by the difference between 3v and 4w is the vector -240i + 70j + 10.

In linear algebra, we often use scalars and vectors to perform various operations. Scalars are just ordinary numbers that can be used to multiply or divide vectors. On the other hand, vectors are quantities that have both magnitude and direction.

In this problem, we are given three vectors, u, v, and w, and we are asked to find the result of multiplying 5u by the difference between 3v and 4w.

First, let's calculate 3v - 4w. Since v = 4i - 2j and w = -2j, we can substitute these values to get,

3v - 4w = 3(4i - 2j) - 4(-2j)

= 12i - 6j + 8j

= 12i + 2j

Next, we need to find the scalar product of 5u and 12i + 2j. To find the scalar product of two vectors, we need to multiply the corresponding components and add up the products.

Therefore: 5u(3v - 4w) = 5u(12i + 2j)

= 5(-4i + j)(12i + 2j)

= -20i(12i) + 5i(2j) + 60j(i) - 10j(j)

= -240i + 10j + 60j + 10

= -240i + 70j + 10

So, the result of multiplying 5u by the difference between 3v and 4w is the vector -240i + 70j + 10.

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Answer:

they are correct

Step-by-step explanation:

Therefore, the horizontal distance the golf ball travels before hitting the ground is approximately 254.55 meters.

In mathematics, an equation is a statement that shows the equality between two expressions, typically separated by an equal sign (=). An equation can contain one or more variables, which are symbols that represent unknown or varying values. The value of the variable(s) can be found by solving the equation.

Here,

The equation of the parabolic trajectory of the golf ball is given by:

f(x) = 0.84x - 0.0033x²

where x is the horizontal distance travelled by the ball and f(x) is the corresponding height at that distance. To find the highest point of the trajectory, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by:

x = -b / 2a

where a and b are the coefficients of the quadratic term and the linear term in the equation of the parabola, respectively. In this case, we have:

a = -0.0033 and b = 0.84

Substituting these values into the formula, we get:

x = -0.84 / 2(-0.0033)

= 127.27

So the horizontal distance at the highest point of the trajectory is approximately 127.27 meters. To find the height of the highest point, we substitute this value of x into the equation of the parabola:

f(127.27) = 0.84(127.27) - 0.0033(127.27)²

f(127.27) ≈ 21.67

So the highest point of the trajectory is approximately 21.67 meters above the ground.

To find the horizontal distance the golf ball travels before hitting the ground, we need to find the two values of x where the height of the ball is zero (i.e., where the ball hits the ground). We can set f(x) = 0 and solve for x:

0 = 0.84x - 0.0033x²

0.0033x² = 0.84x

x = 0 or x = 254.55

So the golf ball hits the ground twice, once at x = 0 (i.e., where it was hit from the tee) and once at x ≈ 254.55 meters.

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The angle of rotation about the origin, (0, 0) that maps WXYZ TO W’ X’ Y’Z are

180 degrees

540 degrees

900 degrees

The transformation rule for an angle of 180 degrees is simply a reflection or a flip. This means that any object or figure that undergoes this transformation will be flipped over a line or axis.

The rule is (x, y) will become (-x, -y)

Where 540 degrees = 360 + 180

where 900 degrees = 360 + 360 + 180

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The claim is: Testing if the time spent completing the obstacle course is improved by the energy drink

The null and the alternate hypotheses are added below

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

The table

Also, we have the following statistical question

Is there sufficient evidence at α = 0.05 to conclude that the students did better the second time?

This means that the null hypothesis are

H1: There is no significant difference in the time spent to complete the obstacle course before and after drinking the new energy drink.

The alternate hypothesis is the opposite of the null hypothesis

So, we have

H2: There is no significant difference in the time spent to complete the obstacle course before and after drinking the new energy drink.

Lastly, the claim is that

Testing if the time spent completing the obstacle course is improved by the energy drink

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3.) The quantity of students that are in the P.E class would be = 31 students.

4.) The number of students that ran 1 mile in under 9 minutes would be = 6 students.

For question 3.)

To calculate the quantity of students, all the values in the frequency column is added together. That is;

Total number of students= 6+2+8+6+9 = 31 students.

For question 4.)

To calculate the number of students that ran 1 mile in less than 9 minutes would be the time range of 8.00-8.59 minutes = 6 students.

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Step-by-step explanation:

X component  = 4.5 - 2.1  =   2.4

Y component  = 7.8 - 2.1  =    5.7

Find magnitude using Pythagorean theorem

  m^2 = 2.4^2 + 5.7^2

    magnitude  = 6.18    units

Remember for a right triangle   tangent Φ = opposite leg / adjacent leg

    angle = arctan ( 5.7 / 2.4 )   = 67.2 degrees

Answer:

2x+9y=18

Step-by-step explanation:

The resulting matrix formed by performing R2 -> 4R1 + R2 on M is given as follows:

[tex]M = \left[\begin{array}{ccc}-4&3&1\\-18&9&8\end{array}\right][/tex]

The matrix in the context of this problem is defined as follows:

[tex]M = \left[\begin{array}{ccc}-4&3&1\\-2&-3&r\end{array}\right][/tex]

The rows of the matrix are given as follows:

Hence the row 2 of the resulting matrix has the elements given as follows:

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Answer:

45w + 180 = 900

45w = 720

w = 16 weeks

The possible outcomes for each of the given events are:

A --> {1, 3, 5}

B --> {4, 5, 6}

For a regular number cube, the sample space (possible outcomes) is:

S = {1, 2, 3, 4, 5, 6}

Now we have two events.

A = rolling an odd number

Here the outcomes can be any of the odd numbers in the sample space, so the possible outcomes are:

A --> {1, 3, 5}

The second event is:

B = the number rolled is greater than 3. Again, the outcomes are thevalues in the sample space that are larger than 3, these are:

B --> {4, 5, 6}

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Answer:

4/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

D is the correct answer.

Answer:

D

Step-by-step explanation:

By reading the graph, place the art museum at location (5,5). Then check all the locations to see which statement is true.

A is not true because the art museum is located 4 units east and 1 unit north from the coliseum.

B is not true because the art museum is located 3 units east and 3 units north of the smith's tower.

C is not true because the art museum is located 1 unit east and 2 units north of the state capital.

This is why D is the correct answer.

The sum of the arithmetic sequence is 987

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence.

For example, the sequence, 2,4,6,8,10... is an arithmetic sequence.

The sum of an arithmetic sequence is given as;

Sn=n/2[2a+(n−1)d]. Where d is the common difference and a is the first term.

the last term is 87

therefore;

87= 7+(n-1) 4

87= 7+4n-4

91-7 = 4n

84 = 4n

n = 84/4

n = 21

therefore 87 is the 21st term

Sn=n/2[2a+(n−1)d]

= 21/2(2×7+(21-1)4

= 21/2 ( 14+80)

= 21×94/2

= 987

therefore the sum of the arithmetic sequence is 987

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The function g(x) is defined as follows:

D. g(x) = f(x) + 4.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The y-intercept for each function is given as follows:

Meaning that g(x) is a translation up four units of function f(x), hence it is defined as follows:

g(x) = f(x) + 4.

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Answer: D

Step-by-step explanation:

The function g(x) is defined as follows:

D. g(x) = f(x) + 4.

What is a translation?

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

Translation left a units: f(x + a).

Translation right a units: f(x - a).

Translation up a units: f(x) + a.

Translation down a units: f(x) - a.

The y-intercept for each function is given as follows:

f(x): y = -5.

g(x): y = -1.

Meaning that g(x) is a translation up four units of function f(x), hence it is defined as follows:

g(x) = f(x) + 4.

The percentage of percentage of the apples have diameters that are between 6.34cm and 8.5cm is given as follows:

99.7%.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

The measures of 6.34 cm and 8.50 cm are the bounds exactly within three standard deviations of the mean, hence the percentage is given as follows:

99.7%.

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If Frank spends $90 on his $1800 monthly income, then 95 percent of monthly check does not go toward food.

Let's say Frank spends $90 on food and has a monthly income of $1800. We can calculate the percentage of his monthly check that does not go towards food as follows:

Percentage = (Total Income - Food Expenses) / Total Income

Percentage = (1800 - 90) / 1800

Percentage = 0.95 = 95%

Therefore, 95% of Frank's monthly check does not go towards food.

Here are the steps in detail:

Subtract the food expenses from the total income to get the amount of money that is not spent on food.

Divide the amount of money that is not spent on food by the total income to get the percentage.

In this case, the amount of money that is not spent on food is $1800 - $90 = $1710. The percentage of the monthly check that is not spent on food is $1710 / $1800 = 0.95 = 95%.

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The margin of error is E = 0.67.

We can use the formula:

E = z* (σ / sqrt(n))

Where

In this case, we are given that C = 0.95, σ = 3.4, and n = 100. We can use a standard normal distribution table to find the z-score that corresponds to a 95% confidence level, which is approximately 1.96.

Substituting the values:

E = 1.96 * (3.4 / sqrt(100))

E = 1.96 * 0.34

E = 0.6664

Rounding to two decimal places, the margin of error is approximately 0.67.

Therefore, the margin of error is E = 0.67.

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