Which function matches the table? Number of Days Rented 1 2 3 4 Rental Cost ($) 12 17 22 27 A. f(x) = 5x B. f(x) = 5 + 5x C. f(x) = 7 + 5x D. f(x) = 12 + 5x

To convert 2077₁₀ to base eight is 4035₈

Since 2077 is in base 10, to convert it to base 8, we successively divide it by 8 and keep the remainder. We divide until we have zero as the dividend then count the remainder from bottom to top.

So, to convert 2077 to base 8, we have

2077 ÷ 8 = 259 r 5

259 ÷ 8 = 32 r 3

32 ÷ 8 = 4 r 0

4 ÷ 8 = 0  r 4

So, counting the remainders from bottom to top, we have 4035₈

So, 2077₁₀ = 4035₈

So, to convert 2077₁₀ to base eight is 4035₈

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A survey was conducted among 40 office staff members to determine their favorite type of take-away food. The results of the survey are summarized in a table.

The survey aimed to gather information about the preferred type of take-away food among the 40 office staff members. The results were compiled into a table, which likely includes different types of take-away food options and the corresponding number of staff members who chose each option as their favorite. Analyzing the table will provide insights into the overall preferences of the office staff regarding take-away food choices. This information can be used for various purposes, such as organizing office events or catering services that align with the majority's preferences. By identifying the most popular type of take-away food among the staff, it becomes easier to meet their preferences and create a positive and inclusive work environment.

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a) In the least-squares line y = 5 - 2x, the slope is -2 and the y-intercept is 5.  b) Since the slope of the line is -2, a change of 1 unit in x would cause a change of 2 units in y. c) When two variables have a negative linear correlation, the slope of the least-squares line is negative.

The least-squares line, also known as the linear regression line, is a straight line that shows the connection between two variables that are linearly related.

A straight line is used to connect two points, and the least-squares line is the line that connects the points with the smallest amount of error or the smallest amount of distance between the points and the line.

The formula for the least-squares line is given by y = mx + b,

where m is the slope of the line and b is the y-intercept.

In the least-squares line

y = 5 - 2x,

the slope is -2, and the y-intercept is 5.

The slope of the line tells us how much y changes when x changes by one unit. In this case, since the slope is -2, a change of 1 unit in x would cause a change of 2 units in y.

When two variables have a negative linear correlation, the slope of the least-squares line is negative.

A negative correlation means that when one variable increases, the other variable decreases.

For example, if we look at the correlation between temperature and snowfall, we would expect a negative correlation. As temperature increases, we would expect snowfall to decrease.

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Answer:

The given equation. 170x - 1000 = 30 (5x - 30) can be classified as an equation with only one solution. x=5

Step-by-step explanation:

First you multiply the parenthesis by 30 to get 170x - 1000 = 150x -900. After this you move the terms together to get 170x - 150x = -900 + 1000. Next you combine the like terms to get 20x = 100. Next you need to get x by itself so you divide both sides by 20 to get x = 5.

Step-by-step explanation:

example:

Answer:

n = 6

Step-by-step explanation:

2n - 32 = 10n - 80

2n - 10n = -80 + 32

-8n = -48

-48/-8 = 6

The percentage of men meeting the height requirement can be calculated by finding the area under the normal distribution curve between the values of 55 inches and 63 inches. To do this, we need to standardize these values using the mean and standard deviation of men's heights.

First, we calculate the z-scores for the height values:

For 55 inches: z = (55 - 67.8) / 3.4 = -3.76

For 63 inches: z = (63 - 67.8) / 3.4 = -1.41

Next, we look up the corresponding areas under the normal curve using a z-table or a statistical calculator. The area between these two z-scores represents the percentage of men meeting the height requirement.

Using a z-table or a calculator, the area corresponding to a z-score of -3.76 is very close to 0, and the area corresponding to a z-score of -1.41 is approximately 0.0823. Therefore, the percentage of men meeting the height requirement is approximately 8.23%.

This result suggests that a relatively small percentage of men meet the height requirement for the amusement park characters. Given that most men do not meet the height requirement, it is likely that the majority of the characters employed at the amusement park are women. This conclusion is based on the information provided about the normal distribution of men's and women's heights and the specified height requirements for the characters.

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Answer:

the correct answer of x is 16

Answer:

6 cups

Step-by-step explanation:

Given that:

Volume of water held in cup when full = 125ml

Number of cups it will take to fill a jug which holds 3/4 L

Converting mL to L:

1000 mL = 1 L

Volume of water in cup when full = 125 / 1000 = 0.125 L

Jug which holds 3/4 L = 0.75 capacity

Hence, number of cups it'll take :

0.75 / 0.125

= 6

It will take 6 cups of 125mL to fill 3/4 L

The p-value associated with the test statistic is 0.018, which is less than the significance level of 10%.

If the p-value is less than the significance level (10%), then the manager can reject the null hypothesis in favor of the alternative hypothesis, which is that the average number of times car owners rotate their tires in a year is less than two.

Based on the sample data of 14 car owners, the mean number of times their tires were rotated in the last 12 months is 1.36, which is less than two. The standard deviation of the sample is 1.16, and the t-test statistic is calculated to be -2.28.

Using a t-distribution table with 13 degrees of freedom (n-1), the critical t-value at a significance level of 10% is -1.771. Since the t-test statistic (-2.28) is less than the critical t-value (-1.771), there is enough evidence to reject the null hypothesis.

Therefore, the manager can conclude that based on this sample data, there is sufficient evidence to suggest that car owners rotate their tires less frequently than the recommended amount in the owner's manual.

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The two buses are initially 515 miles apart and are moving toward each other. They will pass each other around 2:30 P.M.

To solve this problem, we can use the concept of relative speed. The combined speed of the two buses is the sum of their individual speeds, which is 48 + 55 = 103 miles per hour.

We can calculate the time it takes for the buses to meet by dividing the initial distance between them (515 miles) by their combined speed (103 miles per hour):

Time = Distance / Speed

Time = 515 miles / 103 miles per hour

Time ≈ 5 hours

Therefore, the two buses will pass each other approximately 5 hours after they start traveling toward each other. To determine the exact time, we need to consider the starting time (9:30 A.M.) and add 5 hours to it. So, they will pass each other around 2:30 P.M.

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The combination formula can be used to calculate the number of ways that a group of people can be divided into teams of a certain size. In this case, there are 48,620 ways that the 18 people can be divided into 2 teams of 9 people.

To find out how many ways 18 people can be divided into 2 teams of 9 people, we need to use the combination formula. The formula for combination is nCr = n!/r!(n-r)!, where n is the total number of people and r is the number of people in each team.
In this case, n=18 and r=9. Plugging in the values into the formula, we get:
18C9 = 18!/9!(18-9)! = (18x17x16x15x14x13x12x11x10)/(9x8x7x6x5x4x3x2x1)
Simplifying the expression, we get:
18C9 = 48,620
Therefore, there are 48,620 ways that the 18 people can be divided into 2 teams of 9 people.
It is important to note that the order of the teams does not matter. For example, team A consisting of 9 people and team B consisting of the remaining 9 people is the same as team B consisting of 9 people and team A consisting of the remaining 9 people.
In conclusion, the combination formula can be used to calculate the number of ways that a group of people can be divided into teams of a certain size. In this case, there are 48,620 ways that the 18 people can be divided into 2 teams of 9 people.

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Answer:

A

Step-by-step explanation:

You solve for x so,

Y=3-5x

y-3=5x  <----- subtract by 3

3/5+y=x <------ divide by -5

Also (3/5,0) is at the x value

it's the only one that hasn't been with a positive 2

Answer:

X = 3

Step-by-step explanation:

Answer:

15.56%

Step-by-step explanation:

The force applied, F,  to the surface is 90N.

The area, A, of the surface is \(20 cm^2\) = \(0.002m^2\)

The pressure on the surface is:

P = F / A = 90 / 0.002 = 45000 Nm^2

The force is increased by 5N, the new force is 95N.

The surface area is increased by 5 cm^2 = 0.0005 m^2. The new surface area is 0.0025 m^2.

The pressure is now:

P = 95 / 0.0025 = 38000 Nm^2

The percentage decreased is gotten by dividing the difference in the two values by the old value and then multiplying by 100.

=> Difference = 45000 - 38000 = 7000

% decrease is therefore:

= 7000 / 45000 * 100 = 15.56%

There was a 15.56% decrease.

The ratio of the applied force to the area to which the force is applied,

gives the amount of pressure applied.

The outcome decreases by \(\underline{15.\overline 5 \%}\)

Reasons:

\(\mathrm{Pressure, P} = \dfrac{Force, \, F}{Area, \, A}\)

The initial force, F₁ = 5 N

The initial area, A₁ = 20 cm²

\(\mathrm{ } P_1=\dfrac{F_1}{A_1 }\)

\(\mathrm{The \ initial \ pressure \ on \ the \ surface \ is \ } P_1=\dfrac{90 \ N}{0.002 \ m^2} = 45,000 \ Pa\)

The new force, F₂ = F₁ + 5 N = 90 N + 5 N = 95 N

The new area, A₂ = A₁ + 5 cm² = 20 cm² + 5 cm² = 25 cm²

The new pressure after the increase is given by the equation;

\(\mathrm{ } P_2=\dfrac{F_2}{A_2 }\)

\(\mathrm{The \ surface \ pressure \ after \ the \ increase\ is \ } P_2=\dfrac{95 \ N}{0.0025 \ m^2} = \mathbf{38,000 \ Pa}\)

\(Percentage \ change = \dfrac{New \ value - Initial \ value}{Initial \ value} \times 100\)

\(Percentage \ change = \dfrac{38,000 - 45,000}{45,000} \times 100 = 15.\overline 5 \%\)

The outcome decreases by 15.\(\overline 5 \%\)

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Answer:

a = 1

Step-by-step explanation:

The given equation is:

=> 5x+y = 8

Also,

Point = (x,y) = (a,3)

So, x = a , y = 3

Putting this in the above equation

=> 5(a)+3 = 8

=> 5a = 8-3

=> 5a = 5

Dividing both sides by 5

=> a = 1

The Volume of the given Hemisphere is  1071.8 cm³ rounded to 1 decimal place whose radius is 8cm

The Volume of the sphere  is given by the formula 4/3 πr³

The volume of hemisphere is half of sphere

So, The volume of hemisphere is 2/3 πr³

From the given figure it is clear that the radius of the hemisphere is 8cm

Here, we will use the value of π as 3.14 and not 22/7

So, Substituting the values in the formula of Volume of hemisphere

the Volume of hemisphere =2/3 π (8)³

                                      =2/ 3× 3.14 × 512

                                     = 1071.7867 cm³

Hence, the Volume of hemisphere 1071.7867 cm² or 1071.8 cm² rounded to 1 decimal place whose radius is 8cm

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We are comparing the average gain in test scores for two different groups of girls - those assigned to coeducational chemistry classes and those assigned to single-sex chemistry classes. Since these gains are calculated from the data obtained from these specific groups of girls, they represent statistics rather than parameters.

In the given scenario:

The boldface number "12.2" represents a statistic.

The boldface number "15.1" represents a statistic.

A statistic is a numerical value that summarizes a sample of data, while a parameter is a numerical value that summarizes a population.

In this case, we are comparing the average gain in test scores for two different groups of girls - those assigned to coeducational chemistry classes and those assigned to single-sex chemistry classes. Since these gains are calculated from the data obtained from these specific groups of girls, they represent statistics rather than parameters.

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Answer:

This is your answer!

Step-by-step explanation:

The exact length of the curve. y = 3 + 4x^3/2, 0 ≤ x ≤ 1 is L = ∫√(9+108x-144x^(5/2)) / √(9-16x^3) dx, from 0 to 1.

To find the length of the curve, we need to use the arc length formula:

L = ∫√(1+(dy/dx)^2) dx, where y = 3 + 4x^(3/2) and 0 ≤ x ≤ 1.

First, we need to find dy/dx:

dy/dx = (12x^(1/2))/2√(3 + 4x^(3/2))

dy/dx = 6x^(1/2)/√(3 + 4x^(3/2))

Now, we can substitute this into the arc length formula:

L = ∫√(1+(6x^(1/2)/√(3 + 4x^(3/2)))^2) dx, from 0 to 1.

Simplifying the inside of the square root, we get:

L = ∫√(1+(36x)/(3 + 4x^(3/2))) dx, from 0 to 1.

We can simplify this further by multiplying the numerator and denominator of the fraction by (3 - 4x^(3/2)):

L = ∫√(1+36x(3-4x^(3/2))/(9-16x^3)) dx, from 0 to 1.

Expanding the numerator, we get:

L = ∫√((9+108x-144x^(5/2))/(9-16x^3)) dx, from 0 to 1.

Simplifying the expression under the square root, we get:

L = ∫√(9+108x-144x^(5/2)) / √(9-16x^3) dx, from 0 to 1.

We can evaluate this integral using numerical methods, such as Simpson's rule or the trapezoidal rule, to get an approximation of the length of the curve. The exact length of the curve cannot be expressed in a finite number of terms, but it can be approximated to any desired degree of accuracy using numerical methods.

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Answer: The answer is 7

Step-by-step explanation:

Answer: x = 7

Step-by-step explanation:

Subtract 7 on each side to isolate X

7 + x = 14

-7         -7

x = 7

The probability that the mean years of education of this sample is at most 7.6 years is 0.841.

Let X be the mean years of education of this sample. Then X follows a Normal Distribution, N(7.4, 3.4).

We want to find P(X <= 7.6).

Using the Z-Score Table, we find that P(X <= 7.6) = 0.8413.

So, the probability that the mean years of education of this sample is at most 7.6 years is 0.841.

To calculate this, we first find the Z-Score of 7.6

Z = (x - mean) / sd

Z = (7.6 - 7.4) / 3.4

Z = 0.5882

Then, we look up the Z-Score of 0.5882 in the Z-Score Table and find the probability associated with it.

P(X <= 7.6) = 0.8413

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Answer:

D

Step-by-step explanation:

The solution is, the value of x is, D) x ≤ -30.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

given that,

x + 20 ≤ -10

now, we have to solve this,

at first we subtract 20 from both sides, we get,

x + 20 - 20  ≤ -10 -20

or, x  ≤ -30

Hence, The solution is, the value of x is, D) x ≤ -30.

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The value of a and b based on the given table when the number of pairs of tiles is 2 is given by 30 cm and 40 cm respectively.

When,

number of pairs of tiles is 1

Width of each tile = 20 cm

Length of each tile = 30 cm

number of pairs of tiles is 3

Width of each tile = 40 cm

Length of each tile = 50 cm

number of pairs of tiles is 2

Width of each tile, a = 20 cm + width of each tile

= 20 cm + 10 cm

= 30 cm

a = 30 cm

Length of each tile, b = 30 cm + width of each tile

= 30 cm.+ 10 cm

= 40 cm

b = 40 cm

In conclusion, the value of a and b from the above diagram is 30 cm and 40 cm respectively.

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Step-by-step explanation:

x + 3 = 0

x = - 3

f(x) = 2x³ - 4x² - 28x + 6

f(- 3) = 2(- 3)³ - 4(- 3)² - 28 x (- 3) + 6

= 2 x (- 27) - (4 x 9) + 84 + 6

= - 54 - 36 + 90

= - 90 + 90

= 0

Therefore,

x + 3 is factor of 2x³ - 4x² - 28x + 6

To evaluate the expression, we need to use the binomial distribution formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k) where:

- n is the sample size (10 individuals in this case)
- k is the number of individuals who have consumed alcohol (5 in this case)
- p is the probability of an individual consuming alcohol, which is 0.6 according to the problem

If you provide the value of p, I can help you calculate the probability.

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The surface area generated by revolving the curve around the y-axis is 40π.

To find the surface area generated by revolving the curve around the x-axis and y-axis, we can use the formula:

Surface area = 2π ∫\(a^b\) y √(1 + \((dy/dx)^2\)) dx

where y is the function of x in terms of the parameter t, a and b are the lower and upper bounds of t, and dy/dx can be found as dy/dx = (dy/dt) / (dx/dt).

a. When revolving around the x-axis, the function y becomes the radius, so we have:

Surface area = 2π ∫\(0^9\) 5t √(1 + \((5/5)^2\)) dt

= 10π ∫\(0^9\) t dt

= 10π \([t^2/2]_0^9\)

= 405π

Therefore, the surface area generated by revolving the curve around the x-axis is 405π.

b. When revolving around the y-axis, the function x becomes the radius, so we need to express y in terms of x. From the given equation x = 5t, we have t = x/5, and substituting this into the equation y = 5t gives:

y = x

So we have:

Surface area = 2π ∫\(0^{45\)x √(1 + \((1/5)^2\)) dx

= 10π ∫\(0^4\) x dx

= 40π

Therefore, the surface area generated by revolving the curve around the y-axis is 40π.

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