You are offered a 30--day trial period at your dream job. However, the owner of the company is a little unusual so the pay options are non-traditional. They offer you two different pay options for the 30 days:
Option 1: You make $60,000 per day.
Option 2: You make 1 penny the first day, 2 pennies the second day, 4 pennies the third day, 8 pennies the fourth day, etc.
Which is $5,368,709.12 after 30 days of working.

Answer:

x ≥ 1.5

Step-by-step explanation:

2x - 3 ≥ 0 ( add 3 to both sides )

2x ≥ 3 ( divide both sides by 2 )

x ≥ 1.5

List of possible integral roots = 1, -1, 2, -2, 3, -3, 6, -6

List of corresponding remainders = 0, -16, -4, 0, 0, 96, 600, 1764

Check out the table below for a more organized way to represent the answer. The x values are the possible roots while the P(x) values are the corresponding remainders.

====================================================

Explanation:

We'll use the rational root theorem. This says that the factors of the last term divide over the factors of the first coefficient to get the list of all possible rational roots.

We'll be dividing factors of 6 over factors of 1. We'll do the plus and minus version of each. Since we're dividing over +1 or -1, this means that we're basically just looking at the plus minus of the factors of 6.

Those factors are: 1, -1, 2, -2, 3, -3, 6, -6

This is the list of possible integral roots.

Basically we list 1,2,3,6 with the negative versions of each value thrown in as well.

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

From there, you plug each value into the P(x) function

If we plugged in x = 1, then,

P(x) = x^4 - 3x^3 - 3x^2 + 11x - 6

P(1) = (1)^4 - 3(1)^3 - 3(1)^2 + 11(1) - 6

P(1) = 1 - 3 - 3 + 11 - 6

P(1) = 0

This shows that x = 1 is a root, since we get a remainder 0. Do the same for the other possible rational roots listed above. You should find (through trial and error) that x = -2 and x = 3 are the other two roots.

Answer:

c

Step-by-step explanation:

To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.

The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.

Therefore, the fraction of pocket money left can be written as 17/35.

1. Number of athletes did not own any of the three items = 259 - 228

= 31.

2. Number of athletes own a convertible and a TV but not a store = 44 - 9

= 35.

3. Number of athletes own a convertible or a TV = 110 + 91 - 44

= 157.

4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

5. Number of athletes owned at least one type of item = 259 - 31

= 228

6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71

= 118.

The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.

Total number of athletes surveyed = 259

Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228

Number of athletes who did not own any of the three items = 259 - 228 = 31.

The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.

Number of athletes who own a convertible and a TV = 44

Number of athletes who own all three items = 9

Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35

The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.

Number of athletes who own a convertible or a TV = 110 + 91 - 44

= 157.

The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.

Number of athletes own a convertible only = 110 - 15 - 9 = 86

Number of athletes own a TV only = 91 - 44 - 9 = 38

Number of athletes own a store only = 120 - 15 - 43 - 9 = 53

Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

The number of athletes who owned at least one type of item can use the result from part (1).

Number of athletes who owned at least one type of item = 259 - 31

= 228

The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.

Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159

Number of athletes own a TV or a store not a convertible = 13 + 34 +71

= 118.

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The total amount payable at the end of 4 years is 406

In this given sum we are provided with the values of principal , rate of interest , and the number of years , we are asked to calculate the amount payable after 4 years that is the matured amount which is calculated with the addition of the principal amount and the simple interest. For that we had to first find out the amount of interest and then we need to add that with the principal amount to get the matured amount or the amount that is payable at the end of 4 years.

here we have to apply the formulla of simmple interest :

(principal × rate of interest × no. of years )/ 100

In the given sum principal (p) = 350 , rate of interest (r) = 4% pa , no. of years (n) = 4

Simple interest = pnr/100

= (350 × 4 × 4)/100  = 56

Matured Amount = Principal + Interest

= 350 + 56 = 406

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Answer:

x = 7    y = -3

Step-by-step explanation:

x - y = 10   ⇒   x = 10 + y

Substitute  x = 10 + y  into 2x - y = 17:

2(10 + y) - y = 17

20 + 2y - y = 17

y = -3

Substitute the found value of y into x = 10 + y to find x:

x = 10 - 3 = 7

Task:

Enter the function's domain, range, and end behavior.

f(x) = 600(0.55)^x

P.S. So it can be found on the internet.

Answer:

domain: {x | x ∈ R}

range: {y | y > 0}

As x approaches -∞, y approaches +∞

As x approaches ∞, y approaches 0

Step-by-step explanation:

Just to describe the function:

\(600(0.55)^{x}\)

600 is basically the y-intercept, 0.55 indicates that the function is decreasing

You have a horizontal asymptote on the y = 0 and the domain is (-∞, ∞)

the range is (0, ∞) because you have the horizontal asymptote at 0

About "x such that" notation, I am not sure but here it is:

domain: {x | x ∈ R}

range: {y | y > 0}

As x approaches -∞, y approaches +∞

As x approaches ∞, y approaches 0

The marginal frequency of students who chose dancing is 37.

The correct answer to the given question is option 3.

The marginal frequency of students who chose dancing can be calculated by adding up the number of students who chose dancing in each row or column. In this case, we need to add up the number of art students who chose dancing (22) and the number of music students who chose dancing (15), which gives us a total of 37. This is the marginal frequency of students who chose dancing.

Based on the survey results, it appears that a slightly higher percentage of art students prefer dancing (41.5%) compared to music students (31.9%). However, both groups of students seem to be fairly evenly split between dancing and playing sports, with a slight preference for playing sports overall.

It's worth noting that cardiovascular activity is important for overall health and well-being, and both dancing and playing sports can provide great opportunities for exercise and physical activity. Additionally, both activities can also be enjoyable and provide a sense of community and social connection, which is important for middle school students who are still developing their social skills and relationships. Ultimately, the choice between dancing and playing sports will depend on individual interests, preferences, and abilities.

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You can't turn this into an equation because there is nothing that states something is equal to each other. You can turn it into an expression though.

(60÷6​) + b

Answer: Quadrilateral or if thats not right Square or Rectangle

Step-by-step explanation:

Answer:

The angle of elevation from the base to the top of the mountain is 30°.

Step-by-step explanation:

Given: Vertical height of mountain is 650 feet and the distance from the top of the mountain to the base is 1300 feet.

To find: The angle of elevation from the base to the top of the mountain.

Let AB be the height of mountain and BC be the base.

Then, according to question, AB=650 feet and AC=1300 feet.

Let ∠ACB=\(\Theta\).

Then, in ΔABC,

\(sin\Theta=\frac{AB}{AC}\)

⇒\(sin\Theta=\frac{650}{1300}\)

⇒\(sin\Theta=\frac{1}{2}\)

⇒\(\Theta=30\)°

Hence, the angle of elevation from the base to the top of the mountain is 30°.

Answer:

\(a = 40600(1 + \frac{0.009}{1} ) {}^{10} = 40600 \times 1.0937 = 44405.6\)

The reduced price of the item will be $44.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the price of an item has been reduced by 20%. The original price was $55.

The reduced price of the item will be calculated as,

Price  = 55 x ( 100% - 20 %)

Price = 55 x ( 1 - 0.2

Price = ( 55 x 0. 8 )

Price= $44

Hence, the price of the item will be $44.

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The measure of segment DF from the given question is 21

In line geometry, a line is the distance between two points while an angle is the point where two lines intersect.

Given the following parameters

DE = 4x + 10, EF = 2x-1, and DF = 9x-15,

Required

DF

Using the addition postulate

DE + EF = DF

Substitute

4x+10 + 2x -1= 9x - 15

6x + 11 = 9x - 1

6x - 9x =  -1 - 1

-3x = -12

x = 12/3

x = 4

For DF

DF =  9(4) - 15

DF = 21

Hence the measure of segment DF from the given question is 21

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Answer:

\(Probability = 0.00002619\)

Step-by-step explanation:

Given

Let d represents the event that a radar detects an aircraft.

So:

\(P(d) = 0.03\)

Required: Determine the probability that a radar detects three before it fails to detect 1.

This event is represented as: d d d d'

And the probability is calculated as thus:

\(Probability = P(d) * P(d) * P(d) * P(d')\)

Using complement rule:

\(Probability = P(d) * P(d) * P(d) * (1 - P(d))\)

So, we have:

\(Probability = 0.03 * 0.03 * 0.03 * (1 - 0.03)\)

\(Probability = 0.03 * 0.03 * 0.03 * 0.97\)

\(Probability = 0.00002619\)

1.) Probability of getting 1: 0.12 or 12%.

2.) Probability of getting 2: 0.16 or 16%.

3.) Probability of getting 3: 0.25 or 25%.

4.) Probability of getting 4: 0.18 or 18%.

5.) Probability of getting 5: 0.15 or 15%.

6.) Probability of getting 6: 0.14 or 14%.

To calculate the probability of getting a specific number on a fair die, we divide the number of times that number appears by the total number of rolls. In this case, the die was rolled 100 times, and the results are given as follows:

Number: 1 2 3 4 5 6

Times: 12 16 25 18 15 14

To find the probability of getting each number, we divide the corresponding number of times by the total number of rolls (100):

Probability of getting 1 = 12 / 100 = 0.12.

Probability of getting 2 = 16 / 100 = 0.16.

Probability of getting 3 = 25 / 100 = 0.25.

Probability of getting 4 = 18 / 100 = 0.18.

Probability of getting 5 = 15 / 100 = 0.15.

Probability of getting 6 = 14 / 100 = 0.14.

Therefore, the probabilities of getting each number on a fair die, based on the given results of 100 rolls, are approximately:

1: 0.12 or 12%,

2: 0.16 or 16%,

3: 0.25 or 25%,

4: 0.18 or 18%,

5: 0.15 or 15%,

6: 0.14 or 14%.

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Answer:

Step-by-step explanation: evagline has 3/5 of box of nuts.she uses it to fill 6 bowls

The range of possible numbers will be  (-∞ , 16.6] as per the given conditions.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, I’m thinking of a number. When you multiply it by 5 and subtract 3 you will get a number less than 80.

Let "x" be the number

Thus from the given expression

=> 5*x - 3 < 80

add 3 on both sides

=> 5x -3 + 3 < 80 +3

=> 5x < 83divide by 5 into both sides

=> x < 83/5

=> x < 16.6

thus the range of x for the given Condition will be (-∞ , 16.6]

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The conclusion to find out if there has been a significant change in the homework habits of grade-school children is that;

There is insufficient evidence to support the claim that there has been significant change in the homework habits of grade-school children.

The seven steps are below.

Step 1; State the null and alternative hypotheses;

We are given;

Population mean; µ = 8 hours

Thus;

Null hypothesis; H\(_{o}\): µ = 8

Alternative hypothesis; H\(_{a}\) \(\neq\) 8

Step 2. We will set the level of risk that is associated with the null hypothesis;

The level of risk associated with the null hypothesis is simply the level of statistical significance. Thus, α = 0.05 = 5%

Step 3. Select the appropriate test statistic;

The question follows normal distribution and so the test statistic to use is z-test

Step 4. The value of the test statistic would be computed;

Formula for z-score is;

z = (x' - µ)/(σ/\(\sqrt{n}\))

z = (7.4 - 8)/(2.5/\(\sqrt{100}\) )

z = -2.4

Step 5. The value needed for rejection of the null hypothesis would be determined from the z-score table;

From z-score table, with z = -2.4; α = 0.05, two tailed hypothesis;

p-value = 0.0164

Step 6. Compare the p-value with the level of significance;

The p-value is less than the significance value

Since the p-value is less than the significance value, we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that significant change in the homework habits of grade-school children.

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Answer:

First side is: 12cm

Second side is: 36cm

Third side is: 16cm

Step-by-step explanation:

Let x represent the shorter side

Then 3x represents the second side, and

x + 4 represents the third side.

Perimeter of three sides:

P = x + 3x + (x + 4)

Perimeter is 64, so

64 = x + 3x + (x + 4)

64 = 5x + 4

60 = 5x

12 = x

First side is x: 12cm

Second side is 3x: 3(12) = 36cm

Third side is x + 4: 12 + 4 = 16cm

The height of the cylinder whose surface area is given would be = 85 yards.

The cylinder is a type of shape that has three sides which consists of two opposite circles that are joined by a curved surface.

To calculate the height of a cylinder, the formula that should be used is given as follows:

Surface area of cylinder = 2πrh + 2πr²

radius = 29 yards

surface area = 20,761.68 square yards

height = ?

That is ;

20,761.68 = 2×3.14× 29×h + 2×3.14× 29×29

20,761.68 =182.12h + 5281.48

182.12h = 20,761.68-5281.48

182.12h = 15480.2

h = 15480.2/182.12

= 85 yards

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Answer:

the slope is 8

Step-by-step explanation:

the slope is x not sure if its parallel of perpendicular but is i had to gues id guess parallel

Answer:

the slope is 8

the parallel slope is 8

the perpendicular slope is -1/8

\(\text {Hey! Let's Solve this Problem!}\)

\(\text {The First Step is to Convert 1 1/4 into an Improper Fraction:}\)

\(\text {Multiply 1*4 and get 4. Now add 1 and get 5.}\\\text {1 1/4 = 5/4}\)

\(\text {The Final Step is to Add:}\)

\(\text {-3/4+5/4=}\)

\(\text {Your Answer would be:}\)

\(\fbox {1/2}\)

\(\text {Best of Luck!}\)

\(\text {-LimitedX}\)

Hey there!

\(Answer:\boxed{\frac{1}{2}}\)

\(Explanation:\)

Simplify to solve.

\(\boxed{\frac{1}{2}}\text{ is your answer.}\)

Hope this helps!

\(\text{-TestedHyperr}\)

Answer:

20.27

Step-by-step explanation:

Answer:

20.27

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Because C is 1 and D is 4, so 4-1=3.

Answer:

A 3

Step-by-step explanation:

3 is a multiple of all of the numbers

Answer:

3

Step-by-step explanation:

3×7=21

3×8=24

3×15=45

3×10=30

3×14=42

3×20=60

3×28=84

Answer:

130 degrees

Step-by-step explanation:

DE+DA=130