Find an equation for the nth term of the arithmetic sequence.
-17, -13, -9, -5, ...


an = -17 + 4(n + 2)

an = -17 x 4(n - 1)

an = -17 + 4(n - 1)

an = -17 + 4(n + 1)

Answer:

C) $826.82 to $873.18.

Step-by-step explanation:

Sample mean (M) = $850

Standard deviation (s) = $54

sample size (n) = 36

Z for 99% confidence interval (Z) = 2.576

The confidence interval is determined by the following relationship:

[tex]M \pm Z*\frac{s}{\sqrt{n}}[/tex]

Applying the given values, the lower (L) and upper (U) values are:

[tex]850 \pm 2.576*\frac{54}{\sqrt{36}}\\L=\$826.82\\U=\$873.18[/tex]

The answer is C) $826.82 to $873.18.

The range is 39

The interquartile range is 32

Explanation:

The given data is [tex]57,96,72,63,88[/tex]

Let us arrange the data in ascending order.

Thus, we have,

[tex]57,63,72,88,96[/tex]

We need to determine the range and interquartile range of the data.

Range:

The range of the data is the difference between the highest and the lowest value in the given data.

Highest value = 96

Lowest value = 57

Range = Highest value - Lowest value

           = 96 - 57

           = 39

Thus, the range of the data is 39

Interquartile range:

The interquartile range is the difference between the upper quartile and the lower quartile in the given data.

From, the given data, we have, 3 quartiles. They are [tex]Q_1 , Q_2[/tex] and [tex]Q_3[/tex]

[tex]Q_2=72[/tex]

[tex]Q_1=\frac{57+63}{2} =60[/tex]

[tex]Q_3=\frac{88+96}{2} =92[/tex]

Interquartile range = [tex]Q_3-Q_1[/tex]

                               =  [tex]92-60[/tex]

                               =  [tex]32[/tex]

The interquartile range is 32

List the data set from least to greatest:

57, 63, 72, 88, 96

Range: Highest value - Lowest value = answer

Range: 96 - 57 = 39

(IQR) Interquartile Range: Upper quartile - Lower quartile = answer

(IQR) Interquartile range: 88.5 - 57.5 = 31

Answer:

No, Mutually exclusive events and Independent events are not the same.

Step-by-step explanation:

Mutually exclusive events and Independent events are not the same.

Mutually exclusive events are those events that cannot occur together, i.e. they cannot take place at the same time.

For example, the events of tossing a Head and Tails are mutually exclusive. This is because when a coin is flipped it cannot land on both sides at once.

Independent events are those events that can occur at the same time without affecting each other, i.r. they are not dependent on the occurrence of other events in the sample space.

For example, on rolling two fair die the events of first die rolling 4 and the second die rolling 1 are independent.

Final answer:

Mutually exclusive events cannot occur simultaneously, which means P(A AND B) = 0. Independent events occur independently of each other, and their combined probability is P(A AND B) = P(A)P(B). They are different concepts; being mutually exclusive does not imply events are independent.

Explanation:

No, the statement that mutually exclusive events and independent events are the same is incorrect. Mutually exclusive events are two or more events that cannot happen at the same time. For example, when tossing a coin, the events of landing on heads and tails are mutually exclusive because the coin cannot land on both sides at once. This means that P(A AND B) = 0 for mutually exclusive events A and B.

Independent events, however, are those where the occurrence of one event does not affect the probability of the other event occurring. In other words, events A and B are independent if the probability of A occurring is the same, regardless of whether B has occurred, and vice-versa. This means that P(A AND B) = P(A)P(B) for independent events A and B.

Therefore, while mutually exclusive events must have a combined probability of zero (they cannot both occur), independent events are characterized by one event's occurrence not influencing the probability of the other event occurring. Essentially, mutually exclusive deals with the impossibility of events happening simultaneously, whereas independence is about the absence of any causal connection between them.

Answer:

Her employer should withhold from her check for social security is d) 26.01

Step-by-step explanation:

Given:

Kate Alexander worked 40 hours last week. Her pay rate is $8.50 per hour. Assuming 7.65% social security withholding.

Now, to find the amount her employer should withhold from her check for social security.

Total number of hours = 40.

Pay rate per hour = $8.50.

Now, the total amount of total number of hours she worked in accordance of her pay rate:

[tex]40\times 8.50\\\\=\$340.[/tex]

Social security withholding = 7.65%.

So, to get the amount of social security withholding:

[tex]7.65\%\ of\ \$340[/tex]

[tex]=\frac{7.65}{100} \times 340[/tex]

[tex]=\frac{2601}{100}[/tex]

[tex]=\$26.01.[/tex]

The amount of social security withholding is $26.01.

Therefore, her employer should withhold from her check for social security is d) 26.01

Answer:

30,000 phone numbers.

Step-by-step explanation:

If the first three numbers are already defined then it means that only the other 4 digits remain to be defined.

The solution would be the number of numbers between 0000 and 9999, because the order here matters, since each number is different.

Therefore between these two numbers there are a total of 10,000 numbers, that is to say that for each of the three initial numbers there are 10,000 numbers, therefore in the town there are a total of 30,000 numbers.

Final answer:

The small town has 30,000 available telephone numbers.

Explanation:

To calculate the number of available telephone numbers in the small town, we need to consider that local phone numbers have seven digits, with the first three being the telephone exchange numbers. The town uses three different telephone exchanges: 313, 359, and 387. Since the last four digits of a phone number can range from 0000 to 9999, that means there are 10,000 possible combinations for the last four digits.

Since there are three possible telephone exchanges, each with 10,000 combinations for the remaining four digits, we calculate the total number of available phone numbers by multiplying the number of exchanges by the number of combinations per exchange:

Number of exchanges x 10,000 (combinations per exchange) = Total number of phone numbers

3 x 10,000 = 30,000

Therefore, the small town has 30,000 available telephone numbers.

Answer:

Step-by-step explanation:

The coefficient of determination = [tex]r^{2} = 0.885^{2}[/tex] = 0.7832

It means about 78% variation in waist size of males can be explained by their weight and about 23% can not be explained.

Answer:

[tex]h_{max} = 30.012\,ft[/tex]

Step-by-step explanation:

The maximum height of the soccer can be determined with the help of the First Derivative and Second Derivative Tests, whose expression are introduced below:

[tex]\frac{dh}{dt} = -32\cdot t + 90[/tex]

[tex]-32\cdot t + 90 = 0[/tex]

[tex]t = 0.356\,s[/tex]

[tex]\frac{d^{2}h}{dt^{2}} = -32[/tex]

According to both tests, the critical value leads to maximum height. Then:

[tex]h_{max} = -16\cdot (0.356)^{2}+90\cdot (0.356)[/tex]

[tex]h_{max} = 30.012\,ft[/tex]

The volume of the cylinder is [tex]4000.36 \ cm^3[/tex]

Explanation:

Given that the radius of the cylinder is 7 cm

The height of the cylinder is 26 cm

We need to find the volume of the cylinder.

The volume of the cylinder can be determined using the formula,

[tex]Volume = \pi r^2 h[/tex]

Let us substitute the values [tex]\pi= 3.14[/tex] , [tex]r=7[/tex] and [tex]h=26[/tex] in the above formula.

Thus, we have,

[tex]Volume = (3.14)(7)^2(26)[/tex]

Simplifying the terms, we get,

[tex]Volume = (3.14)(49)(26)[/tex]

Multiplying the terms, we have,

[tex]Volume = 4000.36 \ cm^3[/tex]

Thus, the approximate volume of the cylinder is [tex]4000.36 \ cm^3[/tex]

Answer: x = - 2

y = 0

Step-by-step explanation:

The given system of linear equations is expressed as

x + 4y = - 2 - - - - - - - - - - - - - 1

- 5x + 5y = 10- - - - - - - - - - - - - 2

We would eliminate x by multiplying equation 1 by 5 and equation 2 by 1. It becomes

5x + 20y = - 10

- 5x + 5y = 10

Adding both equations, it becomes

25y = 0

Dividing both sides by 25, it becomes

y = 0/25 = 0

Substituting y = 0 into equation 1, it becomes

x + 4 × 0 = - 2

x = - 2

The system of equations have only one solution.

Answer:

$207.655

Step-by-step explanation:

Firstly, we calculate the value taken off the cost by the clearance sales tag.

That would be 30/100 * 349 =104.7

We subtract this from the original = 349-104.7 = 244.3

Now, he applied a 15% coupon. That would be 15/100 * 244.3 = 36.645

The cost of the chair before sales tax = 244.3-36.645 = 207.655

Answer:

C) None

Step-by-step explanation:

|k - 3| + 2 = 1

|k - 3| = -1

Which is not possible because a mod can never be negative

Final answer:

There are zero values of k that make the equation |k - 3| + 2 = 1 true because the absolute value of any number cannot be negative.

Explanation:

To determine for how many values of k the equation |k - 3| + 2 = 1 is true, we need to consider what the absolute value represents. The absolute value of a number is its distance from 0 on the number line, regardless of direction.

Thus, |k - 3| represents the distance of k from 3.

First, we simplify the equation by subtracting 2 from both sides:

|k - 3| = -1

Since the absolute value of a number is always non-negative, there can be no real number k that would make |k - 3| equal to -1.

Therefore, there are zero values of k that would satisfy the original equation.

Answer:

3:10

Step-by-step explanation:

Solution to the question is in the attached picture.

Answer:

3:10 trust

Step-by-step explanation:

Answer:

0.2696

Step-by-step explanation:

Number of People who responded Yes=175

Number of People who responded No=474

Total Number of Respondents=175+474=649

We want to determine the Probability that a person chosen at random believes that psychic can help solve murder cases.

Now,

[TeX]Probability=\frac{Number of Possible Outcome}{Total Number of Outcomes}[/TeX]

Number who believe psychic can help solve murder cases=175

Total Number=649

Therefore:

P(a person chosen at random person believes some psychics can help solve murder cases) = [TeX]\frac{175}{649}=0.2696[/TeX]

Final answer:

The probability that a randomly chosen person believes some psychics can help solve murder cases is 175 divided by the total number of respondents (649), resulting in approximately 26.96%.

Explanation:

The question asks for the probability that a chosen person believes some psychics can help solve murder cases, given that out of a group, 175 said 'Yes' and 474 said 'No'. To find this probability, divide the number of people who believe psychics can help (175) by the total number of people asked (175 + 474).

Steps to Calculate the Probability:

Calculate the total number of responses: 175 (Yes) + 474 (No) = 649.

Calculate the number of positive responses (people who believe psychics can help): 175.

Divide the number of positive responses by the total number of responses: Probability = 175 / 649.

Perform the division to get the probability.

Therefore, the probability that a person chosen at random believes some psychics can help solve murder cases is 175/649 or approximately 0.2696, which can be expressed as 26.96%.

Question:

A prism with a base area of 8 cm² and a height of 6 cm is dilated by a factor of 5/4 .

What is the volume of the dilated prism?

Enter your answer, as a decimal, in the box.

Answer:

The volume of the dilated prism is [tex]93.75 \ {cm}^{3}[/tex]

Explanation:

A prism with a base area of 8 cm² and a height of 6 cm

The volume of the prism can be determined by the formula, [tex]V=Bh[/tex]

Volume of the prism is given by

[tex]V=Bh[/tex]

[tex]V=(8)(6)[/tex]

[tex]V=46\ cm^3[/tex]

Thus, the volume of the prism is [tex]46 \ {cm}^{3}[/tex]

It is also given that the volume of the dilated prism is dilated by a factor of [tex]\frac{5}{4}[/tex]

Hence, the new volume is given by

[tex]Volume = 48(\frac{5}{4} )^3[/tex]

             [tex]=48(\frac{125}{64} )[/tex]

             [tex]=48(1.953125)[/tex]

             [tex]=93.75 \ {cm}^{3}[/tex]

Thus, the volume of the dilated prism is [tex]93.75 \ {cm}^{3}[/tex]

Final answer:

The volume of the dilated prism is 93.75 cm³ after applying the dilation factor of 5/4 to the original volume.

Explanation:

To find the volume of the dilated prism, we must apply the dilation factor to the original dimensions of the prism. Since a volume is a three-dimensional measure, the dilation affects all three dimensions (the base area and the height). The dilation factor is given as 5/4.

We must raise this factor to the third power when dealing with volumes, since we are dealing with three dimensions. Therefore, the original volume, V, of the prism is the base area multiplied by the height, which is:

V = 8 cm² × 6 cm = 48 cm³.

Applying the dilation factor, the volume V' of the dilated prism is:

V' = V × (5/4)³.

First, calculate:

(5/4)³3 = 125/64.

Then multiply the original volume by this factor:
V' = 48 cm³ × (125/64) = (48 × 125) / 64 = 6000 / 64 = 93.75 cm³.

Answer:

2/7

Step-by-step explanation:

To find the this first you need the total number of marbles minus one since the blue marble was taken.

4+5+6-1=14

after one blue marble being picked there are 4 blue left, so the fraction is

4/14 and after being simplified it is 2/7

Answer:

the true is the answer is g

Step-by-step explanation:

Answer:

6) x = 17 ft

7) 42 in

Step-by-step explanation:

6) length of the tangents are equal.

2x - 7 = 27

2x = 34

x = 17

7) if you draw a line from T passing through the centre of the circle, it will divide the triangle into two congruent triangles

Perimeter = 2(5+7+9) = 42 in

Answer:

X=5

Y=-2

Step-by-step explanation:

Answer:

x = 5

y = -2

Step-by-step explanation:

Let's solve the system of equations, this way:

-5y + 6x = 40

3y - 8x = -46

******************

-5y + 6x = 40

6x = 40 + 5y

x = (40 + 5y)/6

******************

Substituting x and solving for y in the 2nd equation:

3y - 8x = - 46

3y - 8 * [(40 + 5y)/6] = - 46

3y - (320 + 40y)/6 = - 46

18y - 320 - 40y = - 276 (Multiplying by 6 at both sides)

-22y = - 276 + 320 (Adding 320 at both sides)

-22y = 44

y = -44/22

y = -2

**************************

Solving for x in the 1st equation:

-5y + 6x = 40

-5 * - 2 + 6x = 40

10 + 6x = 40

6x = 40 - 10 (Subtracting 10 at both sides)

6x = 30

x = 30/6

x = 5

To increase the likelihood of selecting a yellow marble Andrew should:

-Add more yellow marbles to the bag

-Remove from the bag 1 green, 1 black, and 2 red marbles

-Triple the number of yellow marbles in the bag

Answer:

B,C,E

Step-by-step explanation:

just did it

Answer:

E. 80

Step-by-step explanation:

First consider exactly what the problem is asking. You have to make a dinner and AT LEAST one of the dishes has to be vegetarian. So then we could have all three be vegetarian (V V V), 2 vegetarian with one meat (V V M), or one vegetarian with 2 meat (V M M). If I can find the number of arrangements possible for each of the possibilities and add them, we should have our answer.

Consider first the all vegetarian option. There are 5 vegetarian meals on the menu and we may choose 3 of them. This will be a combination since the order in which we choose doesn't matter. For example if my 5 vegetarian dishes are salad, hummus, rice, lentils and pasta, it doesn't matter what order I serve them in, since they will all be a part of the meal. Simply put, placing hummus, rice, and lentils on the table is the same as placing rice, lentils and hummus on the table if everybody shares the dishes. If I had specific guests assigned to the each dish then the order would matter, and it would be a permutation. For example if three of Jane's guests, (lets say Mike, Frank, and Bob) are going to have a specific dish, then the arrangement where Mike has rice, Bob has lentils, and Frank has pasta is different from the arrangement where Mike has lentils, Bob has rice, and Frank has pasta. Since there is no mention of a specific order this has to go in, it is safe to assume a combination. So how many ways can we choose 3 vegetarian dishes from 5 options? This will be 5 C 3.

So we found that (V V V) gives us 5 C 3, so lets examine the other remaining cases. (V V M) implies from 5 vegetarian options we can choose 2 and from 4 meat options we choose one. Then (V V M) gives us 5 C 2 * 4 C 1. Likewise for (V M M) we can say 5 C 1 * 4 C 2.

Putting it all together we have 5 C 3 + 5 C 2 * 4 C 1 + 5 C 1 * 4 C 2. 10 + 10*4 +5 *6 =80.

Without a map or structured dataset, it is not possible to provide the eight-digit grid coordinates for benchmark 86 as requested.

The student asked for the eight-digit grid coordinates for benchmark 86, which is circled in red. To determine the eight-digit grid coordinates, we need a map with grid lines or specific information that provides the exact location of benchmark 86. Unfortunately, the data provided does not contain adequate information to pinpoint the exact eight-digit grid coordinates for this benchmark. Grid coordinates are typically derived from a more structured dataset or map rather than the types of numbers presented in the question. Those appear to be an arbitrary sequence of numbers and are not formatted as grid coordinates, which usually consist of an easting and a northing.

Answer:

Find where the expression  [tex]\frac{3}{(x+2)(x-2)}[/tex]

is undefined.

List all of the vertical asymptotes:

[tex]x=2, -2[/tex]

This is what your graph would look like:

Answer:

x  = 12  hours

Step-by-step explanation:

If one pipe fills store pool in 12 hours   in 1 hour will fill 1/12 of the pool

If one pipe fills a store pool in 6 hours in 1 hour will fill 1/6 of the pool

Let call " x " number of hours needed by the third pipe to fills the pool

then in 1 hour  will fill 1/x

The three pipes working together in 1 hour will fill

1/12  +  1/6  + 1/x

Now we know that the three pipes take 3 hours to fill the pool then in 1 hour three pipes will fill 1/3 of the pool, therefore

1/12  +  1/6  + 1/x  = 1/3

( x + 2*x + 12) /12*x  = 1/3   ⇒ ( 3*x +12 )/ 12*x = 1/3

9*x  + 36  = 12*x

- 3*x  = - 36

x  = 36/3

x  = 12  hours

Final answer:

The third pipe, when operating alone, takes 12 hours to fill the pool. This is found by calculating the combined rate of the first two pipes, then the rate of all three, and deducting to find the third pipe's alone rate.

Explanation:

The question asks how long it takes for a third pipe to fill a pool when utilized alongside two other pipes, where one fills the pool in 12 hours, another in 6 hours, and all three together in 3 hours. This is a rate of work problem, commonly encountered in algebra and practical mathematics. To solve, we first find the rates at which each individual pipe fills the pool and then calculate the third pipe's rate.

Determine the rate at which each pipe fills the pool. The first pipe fills the pool at a rate of 1/12 of the pool per hour, and the second at 1/6 of the pool per hour.

Add these rates to determine the combined rate when the two pipes are working together: (1/12) + (1/6) = 1/12 + 2/12 = 3/12 = 1/4. So, the two pipes fill the pool at a rate of 1/4 of the pool per hour together.

When the third pipe is added, all three fill the pool in 3 hours, which means their combined rate is 1/3 of the pool per hour. The rate of the third pipe alone can be found by subtracting the rate of the first two pipes from this combined rate: (1/3) - (1/4) = 4/12 - 3/12 = 1/12.

Therefore, the third pipe fills the pool at a rate of 1/12 of the pool per hour on its own. To find the time it takes for the third pipe to fill the pool by itself, we take the reciprocal of its rate, resulting in 12 hours.

Answer:

0.02 or 2% = Beta

Step-by-step explanation:

Given that,

Risk-free rate = 7 percent

Expected return on the market = 10 percent

Expected return on Security J = 13 percent

Therefore, the beta of Security J is calculated as follows;

Expected return on Security J = Risk-free rate + Beta (Expected return on the market - Risk-free rate)

13 percent = 7 percent + Beta (10 percent - 7 percent)

0.13 - 0.07 = 0.03 Beta

0.06 = 0.03 Beta

0.06 ÷ 0.03 = Beta

0.02 or 2% = Beta

Answer:

Option C

Step-by-step explanation:

6x² +5x + 1

6x² + 3x + 2x + 1

3x(2x + 1) + 1(2x + 1)

(3x + 1)(2x + 1)

Answer: C

Step-by-step explanation: Answer is C

Answer:

im sorry but that question makes o sense

Step-by-step explanation:

Answer:

  y = -(1/12)(x -6)² -2

Step-by-step explanation:

The vertex of the parabola is halfway between the focus and the directrix, so has y-coordinate (-5+1)/2 = -2. The difference in the y-coordinates between the focus and the vertex is ...

  p = -5 -(-2) = -3

An equation of the parabola with vertex (h, k) and focus-vertex distance p can be written:

  y = 1/(4p)(x -h)² +k

For (h, k) = (6, -2) and p = -3, the equation is ...

  y = (-1/12)(x -6)² -2

Answer:

  always true

Step-by-step explanation:

Adding 4-b to both sides of the equation gives ...

  ax = 4

Then dividing by "a" gives ...

  x = 4/a

This is always true when a≠0.

Answer:

The mistake stems from the assumption that angle dab and abc are both 90 and ad = bc and that the perpendicular bisector of dc is different from the perpendicular bisector to ab because they are the same and abcd is a rectangle.

Step-by-step explanation:

If ∡dab = ∡abc and side ab is equal to side bc which are opposite sides, ten then ab is parallel to bc which means the quadrilateral is  parallelogram. Also since two angles of the four angles of the parallelogram are 90 degrees then the parallelogram is a rectangle.

The bisector of one side of a rectangle will also bisect the opposite side of the rectangle. Therefore the bisector of dc is the same as the bisector of ab and it meets ab at the midpoint of ab. Therefore p is now at the midpoint of ab and there are no triangles pad and pbc.

Answer:

Population next year = 1.075p

Step-by-step explanation:

The current population can be represented by 1 p the increase in the population number by next year is 7.5% p or 7.5/100 p that equals to 0.075p. The expression that represents the expected population by next year is:

Population next year = This year population + expected growth

Population next year = 1p + 0.075p = 1.075p

Given Information:

Population rate = 7.5 %

Current population = p

Required Information:

Population next year = ?

Answer:

Population next year = 1.075p

Step-by-step explanation:

The rate of increase in the population is given as 7.5 %

We know that the current population is equal to p

The population in the next year would be the sum of current population and 7.5 % of current population.

Population next year = current population + 7.5% of current population

Population next year = p + 7.5% of p

Population next year = p + 0.075*p

Population next year = p(1 + 0.075)

Population next year = p(1.075)

Population next year = 1.075p

Answer:

constitute meeting the competition.

Step-by-step explanation:

Philip Esten action from the above scenario tries to meet up with the new competition he is encountering.

He operates a mail store where he renders services such as delivering of item overnight, and charging of fax service with each page for a fee of $2.00 for clients. He has a competition in the business environment where he now has direct competitors who offers the same service and product type to clients.

In this case, his competitors tend to attract more customers, both new and Esten old customers, because his competitors are rendering the same services at a cheaper fee to build a better brand of product / services for the store and buying the trust of customers now and for the future.

Esten with the knowledge of how business competition an works, reduces his price of charge to $.50 to attract more people or customers back to his store and tries to drive off the  competitors, knowing quite well that this charges will not cover his cost .