find the parametric equations for the tangent line to the curve x=t4−1,y=t5+1,z=t3 at the point (15, 33, 8). use the variable t for your parameter.

Answer:

Money in the cash box is $150

Step-by-step explanation:

Let

x = money in the cash box

1/5 of the money in a cash box is 30 dollars

1/5 of x = $30

1/5 * x = 30

1/5x = 30

Divide both sides by 1/5

x = 30 ÷ 1/5

= 30 × 5/1

= 150/1

x = $150

Money in the cash box is $150

The simplified radical for the given equation is 2√3.

The given equation is \(\frac{3}{x} =\frac{x}{4}\).

Radical of any number is the same as the root of the number. The root can be a square root, cube root, or in general, it is nth root. Thus, any expression or number that uses a root is known as a radical.

To compute for the values of x given the proportion, we can cross-multiply both sides of the equation as follows:

\(\frac{3}{x} =\frac{x}{4}\)

⇒x×x=3×4

⇒x²=12

⇒x=±√12

From this, we can see that the solutions for the equation are the positive and negative roots of 12.

By simplifying the radical, we get √12 = √(2² x 3) = 2√3

Therefore, the simplified radical for the given equation is 2√3.

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Answer:

30/105 = 2/7

0.2857

Step-by-step explanation:

In the steady-state condition of the two-server (M/M/2) queueing system with the given steady-state probabilities, the arrival rate is 1 customer per time unit, the utilization of each server is 1/2, and the average number of customers in the system is infinite (∞).

In a two-server (M/M/2) queueing system, the notation M/M/2 represents an exponential interarrival time distribution, an exponential service time distribution, and 2 servers.

The steady-state probabilities in this system are given as p0 = 1/16, p1 = 4/16, p2 = 6/16, p3 = 4/16, and p4 = 1/16.

To solve the problem, we need to calculate the arrival rate and the utilization of the system.

1. Arrival Rate (λ): We know that the arrival rate is 2 customers per time unit.

Since this is a two-server system, each server can handle one customer at a time.

Therefore, the total arrival rate is divided equally among the servers, so the arrival rate for each server is λ/2 = 2/2 = 1 customer per time unit.

2. Utilization (ρ): The utilization of the system is the average fraction of time that each server is busy.

In a steady-state condition, the utilization can be calculated using the following formula:

  ρ = λ / (2μ)

  where μ is the service rate per server.

In an M/M/2 system, the service rate per server is the same as the arrival rate because it follows an exponential service time distribution. Therefore, μ = λ = 1.

Substituting the values, we have:

  ρ = 1 / (2 * 1) = 1/2

  So, the utilization of each server is 1/2.

3. Average Number of Customers in the System (L): The average number of customers in the system can be calculated using Little's Law:

  L = λ * W

  where W is the average time a customer spends in the system.

In an M/M/2 system, the average time a customer spends in the system can be calculated as:

  W = 1 / (μ - λ)

  Substituting the values, we have:

  W = 1 / (1 - 1) = 1 / 0 = ∞

Since the utilization (ρ) is 1/2, which is less than 1, the average time a customer spends in the system is infinite (∞).

Therefore, the average number of customers in the system (L) is also infinite (∞).

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Answer:

40:15 simplified is, (i divided by 5) 8:3

Ratio is when you have a number to a number just put them together but put a colon between them to make it a ratio, thats all ;D. It's basically a fraction.

But you can also simplify ratios just like fractions because they are fractions!

Answer:

D. 8:3

Step-by-step explanation:

40/15

Simplify:

8/3

First pick: Random apple

2 out of the 5 apples are red. Therefore, the probability of choosing a red apple is:

Second pick: Red apple removed

We're left with 4 apples, one of which is red.

Therefore, the probability of choosing the red apple from this bowl is:

To get the probability of the two events happening right next to each other, we mulitply both probabilities:

Meaning that the probability that both apples chosen will be red is 1/10, or 10%

Answer:

14

Step-by-step explanation:

\(\frac{14}{7}\) + 5 + \(\frac{21}{3}\)

= 2 + 5 + 7

= 14

Answer

Sorry i answered the wrong question

Answer:

division

Step-by-step explanation:

division so as to find the value of x

Answer:

y = 5/8x +1

Step-by-step explanation:

Hope this helps!

An equation for the line of best fit is y = 5x.

The y-intercept of the line of best fit is equal to (0, 0).

The size of a store which Feline Delights could expect to sell 20 bags per day is 4,000 square footage.

Feline Delights could expect to sell 20 bags per day in an 11,000 square foot store.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (45 - 30)/(9 - 6)

Slope (m) = 15/3

Slope (m) = 5

At data point (6, 30), a linear equation in slope-intercept form for this line can be calculated as follows:

y - y₁ = m(x - x₁)

y - 30 = 5(x - 6)

y = 5x - 30 + 30

y = 5x

When y = 20, the store size is given by;

20 = 5x

x = 20/5 = 4

In thousands, we have:

x = 4,000 square footage.

When x = 11,000 square footage, the number of bags is given by;

y = 5x

y = 5(11)

y = 55 bags.

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The shoe sizes of 20 students at a college in Jamaica vary between 5 and 10.

The shoe sizes of 20 students at a college in Jamaica. The provided data shows a range of shoe sizes, including 5, 6, 7, 8, 10, and some fractional sizes such as 6.5 and 8.5. The range of shoe sizes indicates the diversity among the students in terms of foot measurements.

It's interesting to note that the shoe sizes don't follow a strict pattern, as there are fractional sizes included. This suggests that the students have individual foot dimensions and preferences when it comes to shoe sizes. The wide range of sizes reflects the varying needs and characteristics of the student population.

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There are 9 possible schedules to play basketball such that dave can play on monday or wednesday or both which is union of two set .

so this question seems like we have to take union of ways of palying on monday or wednesday

let n(m) be number of ways of playing on monday

n(w) be number of ways of playing on wednesday

we have to find n(m∪w)

n(mUw) = n(m) +n (w) - n(m∩ w)

so n(m) = \(4_C__2\) as one day is now fixed which is monday so we have 4 available days and 2 days to play.

n(m) = \(4_C__2\)  = 6

similary n(m) = n(w) = 6

now  n(m∩w) = \(3_C__1\) as now we have  2 fixed day and we have 3 day remaining and only one day to play.

n(m∩w) = \(3_C__1\) =3

now n(mUw) = n(m) +n (w) - n(m∩ w)

=> 6 + 6 -3

=> 12 - 3

so n(mUw) = 9

so we have 9 schedules to paly keeping condition given in the question.

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The given statement is False. A test statistic based on point estimation is not used to construct the decision rule which defines the rejection region.

In hypothesis testing, a test statistic is calculated using sample data and a specific hypothesis to assess the strength of evidence against the null hypothesis. The decision rule, which determines whether to reject or fail to reject the null hypothesis, is based on the test statistic's distribution under the null hypothesis, rather than the point estimate itself.

The construction of the decision rule involves selecting a significance level (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The rejection region is determined based on the chosen significance level and the distribution of the test statistic. If the calculated test statistic falls within the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.

Point estimation, on the other hand, is used to estimate an unknown parameter of interest, such as the population mean or proportion, based on sample data. It involves calculating a single value (point estimate) that represents the best guess for the parameter value. The point estimate is not directly involved in constructing the decision rule or defining the rejection region in hypothesis testing.

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False. A test statistic based on point estimation is not used to construct the decision rule that defines the rejection region.

The process of hypothesis testing involves constructing a decision rule to determine whether to accept or reject a null hypothesis based on sample data. The decision rule is typically defined using a critical region or rejection region, which is a range of values for the test statistic.

Point estimation, on the other hand, is a method used to estimate an unknown population parameter based on sample data. It involves calculating a single value (point estimate) that serves as an estimate of the population parameter.

While point estimation and hypothesis testing are both important concepts in statistics, they serve different purposes. Point estimation is used to estimate population parameters, whereas hypothesis testing involves making decisions based on sample data.

The decision rule for hypothesis testing is typically constructed based on the significance level (alpha) and the distribution of the test statistic, such as the t-distribution or the standard normal distribution. The test statistic is calculated using sample data and compared to critical values or calculated p-values to determine whether to reject the null hypothesis.

Therefore, the statement that a test statistic based on point estimation is used to construct the decision rule defining the rejection region is false.

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Answer:

my bro you gotta put the table down

Step-by-step explanation:

Answer:

x≤21

Step-by-step explanation:

x/3≤7

Multiply both sides by 3

3x/3≤7×3

Simplify

x≤21

Hope this helped!!!

the answer is -43.89

Answer:

-19.57

Step-by-step explanation:

you can also write this equation like this (3.3 x -1.9) (7 x -1.9)

(3.3 x -1.9)= -6.27

(7 x -1.9)= -13.3

now u subtract them

-6.27-13.3 = -19.57

The number of terms in the given arithmetic sequence is n = 10. Using the given first, last term, and the common difference of the arithmetic sequence, the required value is calculated.

The general form of the nth term of an arithmetic sequence is

an = a1 + (n - 1)d

Where,

a1 - first term

n - number of terms in the sequence

d - the common difference

The given sequence is an arithmetic sequence.

First term a1 = \(1\frac{1}{2}\) = 3/2

Last term an = \(2\frac{1}{2}\) = 5/2

Common difference d = 1/9

From the general formula,

an = a1 + (n - 1)d

On substituting,

5/2 = 3/2 + (n - 1)1/9

⇒ (n - 1)1/9 = 5/2 - 3/2

⇒ (n - 1)1/9 = 1

⇒ n - 1 = 9

⇒ n = 9 + 1

∴ n = 10

Thus, there are 10 terms in the given arithmetic sequence.

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Disclaimer: The given question in the portal is incorrect. Here is the correct question.

Question: If the first and the last term of an arithmetic progression with a common difference are \(1\frac{1}{2}\), \(2\frac{1}{2}\) and 1/9 respectively, how many terms has the sequence?

x = time goal

16% = .16

.16 x = 32

x = 32/.16 = ___________ minutes

Jesse' weekly reading time is an illustration of ratio and proportion.

Jesse' weekly reading time is 200 minutes

Represent the reading time with x.

16% of his weekly reading time is given as 32 minutes

This is represented using the following equation

\(16 \% \times x = 32\)

Express 16% as decimal

\(0.16\times x = 32\)

Divide both sides by 0.16

\(x = 32/0.16\)

\(x = 200\)

Hence, Jesse' weekly reading time is 200 minutes

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Answer:

C. 4

Step-by-step explanation:

A pancake is circular in shape

Hence, the area of a circle = πr²

HenceThe corner shop charges

a) $12 for a 3-inch personal pancake.

For personal pancake

r = 3 inches

πr² = π × 3²

= 28.274333882 square inches

= 28.3 square inches

b) The largest pancake is a 6-inch pancake that costs $20.

For Largest pancakes

r = 6 inches

πr² = π × 6²

= 113.09733553 square inches

Approximately = 113.1 square inches

How many times larger is the area of the largest pancake than the personal pancake?

This is calculated as :

Largest pancake/Personal pancake

= 113.1/28.3

3.9964664311 inches

Approximately = 4

Option C is the correct option

Answer:

4

Step-by-step explanation:

Answer:

Not solutions.

Step-by-step explanation:

-5x+6y=-5

6y=-5+5x

6y=5x-5

y=5/6x-5/6

-5/6 is about -0.833

And the slope is 5/6.

So for every x there is 5/6y.

This means (1, 4) won't work cause it's too low.

Also 5/6*6=5. this is too low too.

So they aren't solutions.

Answer:

-1/2y+1/2x

Step-by-step explanation:

when you times -1/2 times you get -1/2 but when you get -1/2y- -1/2x

but when your working with integers if there is two negetive signs together than you will add      

The solution set of the equation will be x = - 1, or x = - 11.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

To solve the equation x² + 12 x = -11, you can calculate this using the following steps:

x² + 12  x = -11

x² + 12 x + 11 = 0

(x + 1)  (x + 11) = 0

1. x = - 1

2. x = - 11

Therefore, solution set of the equation will be x = - 1, or x = - 11.

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Answer:

D.  (39.6) or 39.0

Step-by-step explanation:

See the attached worksheet.

Two right triangles are formed in the diagram.  Use the pythagorean theorem on both, starting with the lower triangle, since two of the sides are known and the third (d) may be calculated.  

1.  From the first (bottom) triangle, we find that d is 36.66.

2.  Using this value of d in the upper triangle provided a length for x of 39.6, closest to answer option D at 39.0

If boat is heading towards a lighthouse, whose beacon-light is 119 feet above the water, the distance from point A to point B is approximately 973 feet.

To find the distance from point A to point B, we can use trigonometry and the fact that the angles of elevation from both points are known.

Let x be the distance from point A to the lighthouse, and y be the distance from point B to the lighthouse. We can set up two equations using tangent function:

tan(5) = 119/x

tan(18) = 119/y

We can solve for x and y by isolating them in each equation:

x = 119/tan(5) ≈ 1343.44 feet

y = 119/tan(18) ≈ 370.79 feet

Therefore, the distance from point A to point B is approximately 1343.44 - 370.79 = 972.65 feet.

We rounded the final answer to the nearest foot, which is 973 feet.

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Answer:

The data is more spread out so their is a greater variability in the data.

Step-by-step explanation:

The Mean absolute deviation is large, then the data is more spread out  and there is greater variability in the data.

Mean absolute deviation is "collected data set is the average of absolute deviations from the center point of the data set".

According to the question,

Formula for Mean absolute deviation = summation of ( absolute value of   xₙ - x⁻ divided by number of data values),     where ' xₙ' is the input data values and 'x⁻ ' is mean of the given data values .

When the mean absolute deviation is large number then the data spread out more and the variability is greater in data.

Hence, the Mean absolute deviation is large then there is greater variability in the data.

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a. 44.4% of the time each service desk is idle.

b. The probability that both service clerks are busy is 0.22 or 22%.

c. The probability that both service clerks are idle is 11.1%.

d. On average, 0.67 customers are waiting in line in front of each service desk.

e. A customer takes, on average, 5.33 minutes to get serviced from the moment they join the queue (i.e., waiting plus service time).

a) The arrival rate is 1 customer every 6 minutes. Therefore, 10 customers arrive at each service desk every hour. The service rate is 1 customer every 4 minutes, which means that a service desk can handle 15 customers every hour.

The utilization rate of each service desk = arrival rate/service rate = (10/60) ÷ (15/60) = 2/3 Average number of customers in the system at any time (queue + service) = utilization/(1 - utilization) = (2/3)/(1 - 2/3) = 2

Therefore, the average number of customers in the queue is the average number of customers in the system minus the average number of customers in service:Average number of customers in the queue = 2 - 2 = 0

Therefore, each service desk is idle for 60% - 15.6% = 44.4% of the time.

b) The probability of a service desk being busy is equal to its utilization rate = 2/3.

Therefore, the probability of both service clerks being busy is:P(both busy) = (2/3)² = 4/9 = 0.44

c) The probability of a service desk being idle is equal to 1 - utilization rate = 1 - 2/3 = 1/3.

Therefore, the probability of both service clerks being idle is:P(both idle) = (1/3)² = 1/9 = 0.11 or 11%.

d) We can use Little's Law to calculate the average number of customers in the queue:

Average number of customers in the queue = arrival rate x average waiting time in queue Average waiting time in queue = average number of customers in queue / arrival rate = 0 / (10/60) = 0 Average number of customers in the queue = 0 Therefore, on average, 0.67 customers are waiting in line in front of each service desk.

e) The average time a customer spends in the system (waiting + service) is equal to the average number of customers in the system divided by the arrival rate:

Average time in system = average number of customers in system / arrival rate Average number of customers in system = utilization/(1 - utilization) = (2/3)/(1 - 2/3) = 2 Average time in system = 2 / (10/60) = 12/10 = 1.2 minutes = 72 seconds The service time is 4 minutes. Therefore, the average waiting time is:

Average waiting time = average time in system - service time = 1.2 - 4 = -2.8 minutes We can't have negative waiting time, so the actual waiting time is 0.

Therefore, a customer takes, on average, 5.33 minutes (4 minutes of service + 1.33 minutes of waiting) to get serviced from the moment they join the queue.

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Answer:

y = 2x + 7

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

180 = 90 + 40 + (4x + 10)

180 = 130 + (4x + 10)

4x + 10 = 180 - 130

4x + 10 = 50

4x = 50 - 10

4x = 40

x = 40/4

x = 10

Answer:

x = 10

Step-by-step explanation:

An euclidean triangle is defined to have sum of all 3 interior angles equal to 180°.

In the given triangle, we know three measurement:

You may be wondering, where does 90° come from. The answer is you can find it by looking if a triangle has a little square symbol or not. If it does, the measurement will always be 90°.

Now since we know that sum of 3 interior angles must equal to 180° in euclidean triangle. Therefore, sum up three of measurement then set to 180°.

\(\displaystyle{90 + 4x+10 + 40= 180}\)

Evaluate and solve for the x-variable:

\(\displaystyle{90 + 4x+10 + 40= 180}\\\\\displaystyle{4x+140 = 180}\\\\\displaystyle{4x=180-140}\\\\\displaystyle{4x=40}\\\\\displaystyle{x=10}\)

Therefore, the value of x is 10

To find the absolute extrema of the function f(x) = 3x - 216x² - 5 on the domain [-7,7], we need to evaluate the function at the critical points and endpoints of the domain.

First, let's find the critical points by taking the derivative of f(x) and setting it equal to zero: f'(x) = 3 - 432x. Setting f'(x) = 0 and solving for x: 3 - 432x = 0; 432x = 3; x = 3/432 = 1/144.  Since the domain is [-7, 7], we need to check the function at the critical point x = 1/144, as well as at the endpoints x = -7 and x = 7. Now, let's evaluate the function at these points: f(-7) = 3(-7) - 216(-7)² - 5 = -1462. f(1/144) = 3(1/144) - 216(1/144)² - 5 ≈ -5.010 . f(7) = 3(7) - 216(7)² - 5 = -10592. The function has an absolute minimum value at x = 1/144, and its value is approximately -5.010.

Therefore, the correct choice is: A. The absolute minimum is -5.010, which occurs at x = 1/144.

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