A company charges $2 for the first minute of tech
support and 50¢ for every minute after that. Is this
an example of a proportional relationship?

The probability that the mean length of the sample rods would differ from the population mean by greater than 0.65 mm is 0.1698 or 16.98%.

Mean length of the population (μ) = 176 mm.

Variance of the population (σ²) = 100.

Therefore, the standard deviation of the population (σ) = √100 = 10.

The sample size (n) = 446.

The mean of the sample = the mean of the population = μ = 176 mm.

The standard deviation of the sample (s) = σ/√n = 0.4735137.

We are asked to find the probability that the sample rods would differ the population mean by greater than 0.65 mm, that is,

either the length of the sample rods is less than (176 - 0.65) =175.35

or the length of the sample rods is more than (176 + 0.65) = 176.65.

This can be shown as P(X < 175.35 or X > 176.65) = 1 - P(175.35 < X < 176.65) = 1 - Normalcdf(175.35,176.65,176,0.4735137) = 1 - 0.8302 = 0.1698 or 16.98%.

Thus, the probability that the mean length of the sample rods would differ from the population mean by greater than 0.65 mm is 0.1698 or 16.98%.

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The volume of the largest rectangular box in the first octant with three faces in the coordinate planes, and one vertex in the plane is V = xyz, where x, y, and z are the lengths of the sides of the rectangular box.

To find the largest volume, we need to maximize x, y, and z. Since we have three faces in the coordinate planes, one vertex will be at the origin (0, 0, 0). The other two vertices will lie on the coordinate axes.

Let's assume the vertex on the x-axis is (x, 0, 0), and the vertex on the y-axis is (0, y, 0). The third vertex on the z-axis will be (0, 0, z). Since the box is in the first octant, all the coordinates must be positive.

To maximize the volume, we need to find the maximum values for x, y, and z within the constraints. The maximum values occur when the box touches the coordinate planes. Therefore, the maximum values are x = y = z.

Substituting these values into the volume formula, we get V = xyz = x³. Therefore, the volume of the largest rectangular box is V = x³.

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What is the maximum volume of a rectangular box situated in the first octant, with three of its faces lying on the coordinate planes, and one of its vertices located in the plane?

The given statement " The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate " is false because the allowable range for an objective function coefficient assumes that the original estimates for other coefficients are approximately correct

The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are approximately correct, but not necessarily completely accurate. The allowable range takes into account the potential variability or uncertainty in the estimated values of the other coefficients, as well as the impact of any errors or discrepancies in the data used to estimate the model.

Therefore, the allowable range provides a range of values within which the objective function coefficient can vary while still producing a valid and useful model. It does not assume that the other coefficients are completely accurate or that this is the only coefficient whose true value may differ from its original estimate.

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A college student needs 10 3 credit classes and 5, 2 credit classes in order to complete her degree.  

Let, h and F be two types of classes, the total classes should be 15,

h+F=15 ----------------(1)

Now, the credits for the classes should be equal to 40, there are credit classes and 3 credit classes, which means attending one 2 credit class will get 2 credits, and same with 3 credit class.

2h+3F=40 --------------(2)

We have two equations, with two unknown values, we solve the equation to get the value of h and F.

h=15-F -------------------(3)

Substituting the value of x in equation 2, we get

2(15-F)+3F=40

30-2F+3F=40

30+F=40

F=40-30

F=10.

Substituting y in equation 3, we get

h=15-10

h=5

Therefore, the number of 2 credit course the student should take is 5 and that of 3 credit classes is 10.

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Since the polygon's perimeter equals the sum of its sides. This means that the perimeter (P) of a rectangle is;

P = the sum of all of its sides.

P = a + b + a + b In a rectangle, the opposite sides are equal.

P = 2(a + b)

Given a rectangle with length 4x and width x, what is its perimeter?

P equals 2(a + b), thus 48 equals 2(x + 4x).

48 = 2(x+4x)

48 = 2(5x)

48 = 10x

x  = 4.8

4x = 19

19.2 feet in length and 4.8 feet in width when first built.

The new length would be 9.5+19.2=28.7 if 9 1/2 were added to the previous length.

A new length of 28.7 feet results as a result.

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Step by step explaination

y-4x= -4

y= 4x-4

slope of the given eqn of line = 4

and since the required line is parallel to the given line , slope of required line = slope of the given eqn of line = 4

OPTION C , the eqn has slope = 4

The terms minimum and infimum are both related to the concept of lower bounds in mathematics. A minimum is the smallest value in a set of numbers, whereas an infimum is the greatest lower bound of a set.

A minimum is a value that is less than or equal to all other values in the set, while an infimum is a value that is less than or equal to all other values in the set, but not necessarily the smallest value.

For example, if we consider the set {2, 4, 6}, the minimum is 2 and the infimum is also 2. However, if we consider the set {2, 4, 6, 8}, the minimum is 2 and the infimum is 4. In the latter set, 4 is the greatest lower bound, meaning that all other values in the set are greater than or equal to 4.

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Answer:

3/9 or 1/3 chance

Answer:

6

Step-by-step explanation:

the other marbles if you add them it equals to 6 so you have a 6 chance of picking it

Answer:

Cone Volume = (PI * radius^2 * height) / 3

Cone Volume = (PI * 2^2 * 9) / 3

Cone Volume = 113.0973355292 / 3

Cone Volume = 37.7 cubic inches

Source: http://www.1728.org/volcone.htm

Step-by-step explanation:

Answer:

8 possible outcomes

Step-by-step explanation:

When flipping a quarter three times, each flip can result in two possible outcomes: either landing heads (H) or tails (T).

Since each flip is independent, the total number of possible outcomes for flipping a quarter three times can be found by multiplying the number of outcomes for each flip together.

For three flips, the total number of possible outcomes is:

2 x 2 x 2 = 8

So, there are 8 possible outcomes when Alexandre flips a quarter three times.

Answer:  Function A= (0,8)

Function B= (0,2)

{(-4,12),(0,-1),(4,0),(x,y)} =6(4.0),(x,y)

I didn’t do the last one I’m sorry

Step-by-step explanation:

Answer: A. Yes, because a difference in mean distances of 4.9 feet or more occurred only 6 out of 200 times, meaning the difference is statistically significant and there is convincing evidence the new golf ball travels farther than the original golf ball.

Step-by-step explanation: took the test (look at the graph as well)

Answer:

Point E

Step-by-step explanation:

A vertex can be described as an angle formed when two lines intersect or join together. In the figure given, point E is the intersection point.

The point that is referred to as the vertex of the marked angle where the two lines intersect is point E.

Point E is the vertex of <BEC.

The mean and standard deviatiοn fοr the entire prοject can be calculated by adding the means and variances οf the paths: Prοject: mean = 15.33

Prοbability can be defined as ratiο οf number οf favοurable οutcοmes and tοtal number οutcοmes.

Tο cοnstruct the prοject netwοrk, we can use the activity-οn-nοde (AON) apprοach, where nοdes represent activities and edges represent the lοgical relatiοnships between activities.

Here, activity A represents repοrt generatiοn, activity B represents web scraping, and activity C represents testing. The numbers οn the edges indicate the time estimates (οptimistic, mοst prοbable, and pessimistic) fοr each activity. The immediate predecessοrs fοr activity B and activity C are shοwn by the vertical lines cοnnecting them tο the nοdes representing their predecessοrs.

Tο estimate the critical path, we need tο find the lοngest path thrοugh the netwοrk, which is the path that takes the mοst time tο cοmplete. In this case, the critical path is A-B-C, with a duratiοn οf 8+9+1=18 weeks.

(b) Tο estimate the prοbability that the prοject will be cοmplete within 11 weeks based sοlely οn the critical path, we can use the critical path methοd (CPM) and the nοrmal distributiοn. The mean duratiοn οf the critical path is (8+9+1)/3=6 weeks, and the standard deviatiοn is\([(8-2)/6+(9-2)/6+(1-2)/6]^0.5=1.15\)  weeks.

The prοbability that the critical path will be cοmpleted within 11 weeks can be calculated using the standard nοrmal distributiοn as fοllοws:

P(Z <= (11-6)/1.15) = P(Z <= 4.35) = 1

Therefοre, the prοbability estimate is 1 οr 100%.

(c) Tο estimate the prοbability that the prοject will be cοmplete within 11 weeks using all paths thrοugh the prοject netwοrk, we can use the prοgram evaluatiοn and review technique (PERT) and the beta distributiοn. The mean duratiοn and standard deviatiοn fοr each activity can be calculated using the PERT fοrmula:

mean = (οptimistic + 4*mοst prοbable + pessimistic)/6

standard deviatiοn = (pessimistic - οptimistic)/6

The mean and standard deviatiοn fοr each activity are shοwn belοw:

Activity A: mean = (2+8+12)/6 = 7, stdev = (12-2)/6 = 1.67

Activity B: mean = (4+9+11)/6 = 8, stdev = (11-4)/6 = 0.83

Activity C: mean = (1+1+1)/6 = 0.33, stdev = (1-1)/6 = 0

Using the mean and standard deviatiοn fοr each activity, we can calculate the mean and standard deviatiοn fοr each path and fοr the entire prοject. The mean and standard deviatiοn fοr each path are shοwn belοw:

Path 1 (A-B-C): mean = 7+8+0.33 = 15.33, stdev \(= (1.67^2+0.83^2+0^2)^0.5 = 1.87\)

Path 2 (A-C): mean = 7+0.33 = 7.33, stdev \(= (1.67^2+0^2)^0.5 = 1.67\)

Therefοre, The mean and standard deviatiοn fοr the entire prοject can be calculated by adding the means and variances οf the paths: Prοject: mean = 15.33

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To maximize his earnings, John should install 5 Secure alarms and 5 Maximum Secure alarms, and then demonstrate 5 Secure alarms and 2 Maximum Secure alarms.

Let's first consider the time constraints. Since John cannot work more than 40 hours per week, we have the following inequality:

1h(install Secure) x + 2.2h(install Maximum Secure) y + 0.25h(demo Secure) x + 0.4h(demo Maximum Secure) y <= 40

where x and y are the number of Secure and Maximum Secure alarms John installs, respectively.

John is required to work a minimum of 20 hours per week as an installer and a maximum of 20 hours as a demonstrator. So we have the following constraints:

1h(install Secure) x + 2.2h(install Maximum Secure) y >= 20 (minimum hours as installer)

0.25h(demo Secure) x + 0.4h(demo Maximum Secure) y <= 20 (maximum hours as demonstrator)

Now, we can set up the objective function to maximize John's earnings:

E(x,y) = 3(install Secure) x + 3(install Maximum Secure) y + 2(demo Secure) x + 2(demo Maximum Secure) y

= 5x + 5.6y

Using linear programming techniques, we can solve for the optimal values of x and y that maximize the objective function and satisfy the constraints. The optimal values turn out to be x=5 and y=5 for installing alarms, and x=5 and y=2 for demonstrating alarms. Therefore, John should install 5 Secure alarms and 5 Maximum Secure alarms, and then demonstrate 5 Secure alarms and 2 Maximum Secure alarms, to maximize his earnings.

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Answer:

Distribute:

=(−2)(4x)+(−2)(−4)+x

=−8x+8+x

Combine Like Terms:

=−8x+8+x

=(−8x+x)+(8)

=−7x+8

Step-by-step explanation:

Answer:

x  

2

−4x+4=0

To solve the equation, factor x  

2

−4x+4 using formula x  

2

+(a+b)x+ab=(x+a)(x+b). To find a and b, set up a system to be solved.

a+b=−4

ab=4

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 4.

−1,−4

−2,−2

Calculate the sum for each pair.

−1−4=−5

−2−2=−4

The solution is the pair that gives sum −4.

a=−2

b=−2

Rewrite factored expression (x+a)(x+b) using the obtained values.

(x−2)(x−2)

Rewrite as a binomial square.

(x−2)  

2

To find equation solution, solve x−2=0.

x=2

Step-by-step explanation:

hope this helped heres a graph

Answer:

$366.24

Step-by-step explanation:

Camilla visited her parents in Belmont and took them out to dinner. Their dinner cost $112, and the sales tax in Belmont is 9%. If Camilla left an 18% tip on the $112, how much in total did she pay?

dinner cost $112

sales tax: $112 * 1.09 = $122.08

tip: $112 * 1.18 = $132.16

total: 112 + 122.08 + 132.16 = $366.24

The side opposite to 30 degree angle is 1/2. So,

The measure of side opposite to angle 60 degree is,

The measure of side x is,

The measure of hypotenuse is 2a. So,

So answers are,

and

Answer:

-1/4

Step-by-step explanation:

Multiplicative inverse is another word for reciprocal

It is the number you multiply by to get 1

-4 * x = 1

Divide each side by -4

x = 1/-4

x = -1/4

Answer:

- 1/4

Step-by-step explanation:

- 4 * x = 1

= - 1/4

Hope this helps!

Answer:

Step-by-step explanation: 3.65

hope it helps

Answer:

$2.51

Step-by-step explanation:

30.00 - 27.49 = 2.51

$2.51

The interest earned is $527.86. To calculate the interest earned, we can use the formula for compound interest:

Interest = Principal * (1 + Rate)^Time - Principal

Given:

Principal = $527.86

Rate = 3.99% (expressed as a decimal, 0.0399)

Time = 7.5 years

Using the formula, we can plug in the values:

Interest = $527.86 * (1 + 0.0399)^7.5 - $527.86

To calculate the interest, we need to evaluate the expression inside the parentheses first:

(1 + 0.0399)^7.5 ≈ 1.31876

Now, we substitute this value back into the original equation:

Interest = $527.86 * 1.31876 - $527.86

Calculating this, we find:

Interest ≈ $696.64 - $527.86

Interest ≈ $168.78

Rounding to the nearest cent, the interest earned is approximately $168.78.

Compound interest is the interest earned on both the initial principal and any accumulated interest from previous periods. In this case, the principal is $527.86, and the interest rate is 3.99% per year. The time period is given as 7.5 years.

To calculate the interest, we use the compound interest formula, which takes into account the principal, rate, and time. The formula allows us to determine the growth of an investment over time.

By substituting the given values into the formula, we calculate the interest earned. First, we convert the interest rate from a percentage to a decimal by dividing it by 100. Then, we raise the expression (1 + rate) to the power of the time period. This gives us the factor by which the initial principal will grow.

Subtracting the initial principal from the final amount gives us the interest earned over the specified time period. In this case, the interest earned is $168.78.

It's important to note that compound interest takes into account the compounding frequency, which determines how often the interest is added to the principal. In this calculation, we assume the interest is compounded annually.

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Answer:

B

Step-by-step explanation:

if the temp is at 7 then drop seven, the answer is 0

Answer:

the first one is the correct one

Step-by-step explanation:

a great way to check this is to use demos .com

Answer:

its the first one

Step-by-step explanation:

our  vertex is (-2,0)

so replace it in the equation y ≤ (x + 2)^2

so, 0 ≤ (-2 + 2)^2

= 0 ≤ (-4)^2

= 0 ≤ 16

look at that statement, is 0 less than or equal to 16? Yes. Therefore it is correct, so you shade out side of the parabola.

TIP: If the parabola opens up and:

        y <, then shade outside.

        y >, then shade inside.

Do the opposite if the parabola opens down.

Answer:

48%

Explanation:

The percent of the decrease can be calculated as:

So, replacing the initial value with 150 calories and the final value by 78 calories, we get:

Therefore, the percent of decrease is 48%

Answer:

\(t1 {15y08 \frac{18 \gamma \gamma }{?} }^{2} \)

Answer:

40%

Step-by-step explanation:

As AEIOU are vowels, we count that there are 4 vowels: a, e, o, and a. Then we count that there are 10 total letters. We get 4/10=40%

Answer:

40%

Step-by-step explanation:

There are 5 vowels, a,e,i,o and u

There are a total of 10 tiles.

Looking at the tiles there are 4 tiles that represent vowels, 2 "a"'s , an "o" and an "e".

So 4 out of the 10 tiles represent vowels.

4/10 can be converted to a percentage.

4/10 * 10 = 40/100 = 40%

40% of the tiles are vowels

The side length of the square that provides a counterexample to the statement square units in the area of a square is greater than or equal to the number of units in the perimeter is 2 Units.

A square is a kind of a 2D figure in which all the sides are equal.

We know that the absolute perimeter of a square is the sum of the lengths of all the total sides and as we see the area of a square is (side)².

Assuming that the whole square has four units completed for each side.

The square's circumference can be calculated as is 4 sides plus 4 fours, or as seen as 16 units.

Now the area of the square will be calculated as (4) ² = 16 sq units.

Now assuming that the total side length of the square about is 2 units.

The square's perimeter is calculated as (24) = 8 units, while its total area is calculated as (22) = 4 units.

∴ 2 units make up the side length that serves as a counterexample.

Basically, herein we have to determine the absolute numbers that when are multiplied by 4 are seen to be greater than it's square such numbers are 1, 2, 3.

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