If 30,15,90 and x are in proportion find the value of x

Answer:

Since the decoration is in the shape of a triangle, we can use the formula for the area of a triangle to solve for its height. The area of a triangle is given by:

Area = (1/2) x base x height

Let's call the height of the decoration h. We know that the base after firing is 9 inches, so we can plug in the given values and solve for h:

Area = (1/2) x 9 x h

Area = 4.5h

We don't know the exact area of the decoration, but we do know that the decoration maintains its shape after firing. This means that the ratio of the areas before and after firing is the same, and so is the ratio of the heights and bases. Since the height and base are proportional, we can write:

h / 15 = 9 / 10

Simplifying the equation, we get:

h = (9/10) x 15

h = 13.5

Therefore, the height of the finished decoration is 13.5 inches.

On a control chart, Control limits separates common from assignable causes of variation option C.

Shewhart charts, after Walter A. Shewhart, are another name for control charts. It is a statistical process control tool that aids in tracking process advancements over time. For instance, hospital management decides to utilise a solution technique in order to shorten the time required to admit a patient.

The process flow diagram for how patients are admitted to the hospital is first created. The average amount of time it takes to admit a patient each day is then measured. Lastly, plot the process variables across time on a control chart.

This control chart's goals are to identify any "special" reasons of variation as well as to document any process improvements.

Learn more about Control limits:

https://brainly.com/question/23821364

#SPJ4

The furnsale7 data set appears to take the form of a panel data structure.

Panel data is a type of longitudinal data that combines observations over multiple time periods for the same individual or group.

This type of data contains multiple observations for the same unit over time and provides valuable insight into changes that occur over time.

Panel data can provide valuable insights into long-term trends and changes in behavior or trends in a population. Panel data can also be used to study economic growth and development, market trends, and consumer behavior.

To know more about data structure click on below link:

https://brainly.com/question/29487957#

#SPJ11

The order quantity should be 4 bottles.

There are 6 bottles of paroxetine 10 mg in stock, and the par level is 4 bottles, while the maximum quantity is 10 bottles. The question is asking how many bottles should be ordered.

This can be found by calculating the difference between the current stock level and the par level and then adding this difference to the current stock level. If the result exceeds the maximum quantity, the order quantity is equal to the difference between the maximum quantity and the current stock level.

Otherwise, the order quantity is equal to the difference between the current stock level and the par level.In this case, the difference between the current stock level and the par level is 6 - 4 = 2 bottles. Adding this difference to the current stock level gives us a total of 6 + 2 = 8 bottles.

Since 8 is less than the maximum quantity of 10, the order quantity is 8 - 4 = 4 bottles. Therefore, 4 bottles should be ordered to maintain the par level of 4 bottles. Therefore, the order quantity should be 4 bottles.

To know more about Quantitative refer here :

https://brainly.com/question/15712531

#SPJ11

This tree diagram shows all possible orders in which Ryan can read the 3 books, including reading the mystery book (M) first, the history book (H) second, and the biography (B) last, as well as reading the biography first, the mystery second, and the history last.

Mystery is an intriguing and often baffling phenomenon or situation. It is something that is not easily explained or understood and often involves a puzzle or secret that needs to be solved. It can be an event, an entity, or a situation that evokes curiosity, suspense, and a desire to uncover the truth. Mystery can be found in everyday life, literature, films, and other forms of entertainment. It is often used to create a sense of anticipation and wonder, and can be a powerful tool in storytelling. Mystery can also be used to explore deeper truths and to connect with our own inner mysteries.

To learn more about mystery
https://brainly.com/question/25734188
#SPJ1

Complete Question is attached below:

The extreme values of the function f(x, y, z) = x^2 + y^2 + z^2, x^2 + y^2 + z^2 + xy = 27 are minimum = 0 and maximum = 18

Given that

f(x, y, z) = x^2 + y^2 + z^2, x^2 + y^2 + z^2 + xy = 27

To find the extreme values of the function f(x, y, z) subject to the given constraint, we can use the method of Lagrange multipliers.

Defining the Lagrangian function L as follows:

L(x, y, z, λ) = f(x, y, z) - λ(g(x, y, z))

where g(x, y, z) is the constraint function and λ is the Lagrange multiplier.

In our case, we have:

f(x, y, z) = x^2 + y^2 + z^2

g(x, y, z) = x^2 + y^2 + z^2 + xy - 27

So, our Lagrangian function becomes:

L(x, y, z, λ) = x^2 + y^2 + z^2 - λ(x^2 + y^2 + z^2 + xy - 27)

To find the extreme values of f(x, y, z) subject to the constraint g(x, y, z) = 0, we need to solve the following system of equations:

∂L/∂x = 0

∂L/∂y = 0

∂L/∂z = 0

∂L/∂λ = 0

g(x, y, z) = 0

Taking the partial derivatives of L with respect to x, y, z, and λ, we get:

∂L/∂x = 2x - λ(2x + y) = 0

∂L/∂y = 2y - λ(2y + x) = 0

∂L/∂z = 2z - λz = 0

∂L/∂λ = x^2 + y^2 + z^2 + xy - 27 = 0

From the third equation, we get:

2z - λz = 0

z(2 - λ) = 0

So, either z = 0 or λ = 2.

If z = 0, then from the first two equations, we get:

2x - λy = 0

2y - λx = 0

Multiplying the first equation by y and the second equation by x, we get:

2xy - λy^2 = 0

2xy - λx^2 = 0

Subtracting the second equation from the first, we get:

λ(x^2 - y^2) = 0

Since λ cannot be zero, we have x^2 = y^2 and x = y

Similarly, if λ = 2, then from the first two equations, we get:

2x - 2y = 0

x = y

Substituting x = y into the constraint equation, we get:

2x^2 + x^2 = 27

x^2 = 9

x = ±3

So, the possible critical points are:

(3, 3, 0)

(-3, -3, 0)

(0, 0, 0)

Recall that

f(x, y, z) = x^2 + y^2 + z^2

So, we have

f(3, 3, 0) = 3^2 + 3^2 + 0^2 = 18

f(-3, -3, 0) = -3^2 + -3^2 + 0^2 = 18

f(0, 0, 0) = 0^2 + 0^2 + 0^2 = 0

Hence, the minimum is 0 and the maximum is 18

Read more about Lagrange multipliers at

https://brainly.com/question/10479355

#SPJ1

The p-value is (0.0297)

To test the hypothesis that jumping does not affect the girls' breath-holding times, we will conduct a paired t-test using the given data. Here's a step-by-step explanation:

Solution:

1. Calculate the difference between relaxed and jumping times for each girl:
(27-20), (49-43), (31-28), (22-21), (23-25), (45-43), (37-35), (29-32)
The differences are: 7, 6, 3, 1, -2, 2, 2, -3

2. Compute the mean and standard deviation of the differences:
Mean = (7+6+3+1-2+2+2-3)/8 = 16/8 = 2
Standard Deviation = sqrt[((7-2)^2+(6-2)^2+(3-2)^2+(1-2)^2+(-2-2)^2+(2-2)^2+(2-2)^2+(-3-2)^2)/7] = sqrt(42/7) = sqrt(6)

3. Calculate the t-statistic:
t = (Mean - Hypothesized Mean) / (Standard Deviation / sqrt(N))
t = (2 - 0) / (sqrt(6) / sqrt(8)) = 2 / (sqrt(6) / 2.828) ≈ 2 / 0.748 ≈ 2.675

4. Determine the p-value using the t-distribution table or calculator for a two-tailed test with 7 degrees of freedom (N-1) at the 5% level:
The p-value is 0.0297 (rounded to four decimal places).

Since the p-value (0.0297) is less than the significance level of 0.05, we reject the null hypothesis that jumping does not affect the girls' breath-holding times, on average.

To know more about Hypothesis:

https://brainly.com/question/31319397

#SPJ11

The statements when converted to unit rates are $1.20 per lap and $37.50 per hour

To compare the pricing options, we can convert each to a unit rate, which is a rate with a denominator of 1.

This allows us to compare the cost of each option per lap or per hour.

i. $30 for 25 laps:

To find the unit rate, we can divide the total cost by the number of laps:

Unit rate = $30 ÷ 25 laps = $1.20 per lap.

ii. $75 for 2 hours:

To find the unit rate, we can divide the total cost by the number of hours:

Unit rate = $75 ÷ 2 hours = $37.50 per hour.

So, the unit rate for option i is $1.20 per lap and the unit rate for option ii is $37.50 per hour.

By comparing the unit rates, we can determine which pricing option is more cost-effective based on the number of laps or hours Alex wants to ride.

Read more about unit rates at

https://brainly.com/question/19493296

#SPJ1

Answer:  The area of the smaller circle is [tex]65.6cm^{2}[/tex].

Step-by-step explanation:

A = [tex]\pi r^{2}[/tex], r is the radius.

1. Find out the diameter of the small circle.

[tex]\frac{1}{3}(27)= 9[/tex]

2) Find out the radius, r.

[tex]radius = \frac{diameter}{2} =\frac{9}{2} =4.5[/tex]

3) We plugin r = 4.5 into the formula to solve the area of the smaller circle.

[tex]A=\pi r^{2}=\pi (4.5)^{2} =65.6cm^{2}[/tex]

If the objective function coefficient for variable 1 decreases by 20, the solution will shift in the direction of the decrease in the objective function coefficient. It means that the optimal solution that was obtained previously will no longer remain optimal, and the new optimal solution will be found with the new objective function coefficient.

In linear programming, the objective function determines the maximum or minimum value that can be attained in the solution, subject to the constraints. The constraints in the problem can be either equalities or inequalities, which limit the range of values that the decision variables can take on.

The change in the objective function coefficient will change the direction of the optimal solution, and it may affect the feasibility of the solution. It means that some constraints may no longer be satisfied, or some variables may become infeasible.

In such cases, it will be necessary to revise the constraints or the variables to ensure the feasibility of the solution.

The solution can also be affected if the constraints of the problem change. The new constraints may limit the range of values that the variables can take on, or they may add new variables to the problem. These changes can affect the feasibility of the solution, and it may require the problem to be solved again to obtain the new optimal solution.


To know more about linear programming, refer here:

https://brainly.com/question/30763902#

#SPJ11

There is not enough evidence to suggest that the difference between the two population means is statistically significant at the 5% significance level.

To test the hypothesis that the difference between two population means is zero, the researcher can use a two-sample t-test. The test statistic is calculated as the difference between the sample means divided by the standard error of the difference.

In this case, the sample means are 106.4 and 99.2, and the standard error of the difference is 6.1. Therefore, the test statistic is (106.4 - 99.2) / 6.1 = 1.18.

To decide whether to reject the null hypothesis that the difference between the two population means is zero, the researcher needs to compare the test statistic to the critical value. The critical value needed to reject the null hypothesis at a 5% significance level with 2 degrees of freedom (n1 + n2 - 2 = 2) is 2.09.

Since the test statistic of 1.18 is less than the critical value of 2.09, the researcher fails to reject the null hypothesis.

To learn more about statistics click on,

https://brainly.com/question/14000767

#SPJ4

The probability that a randomly selected event of washing dishes will take a person between 12 and 15 minutes is 0.33 or 33%.

Uniform distribution is a probability distribution where all outcomes are equally likely. In this case, the time it takes to wash dishes is uniformly distributed between 8 and 17 minutes. This means that any time between 8 and 17 minutes is equally likely to occur.

To find the probability that a randomly selected event of washing dishes will take a person between 12 and 15 minutes, we need to find the area under the curve of the uniform distribution function between 12 and 15 minutes.

Since the distribution is uniform, the area under the curve between 12 and 15 minutes is simply the width of the interval divided by the total width of the distribution. Mathematically, we can express this as:

P(12 ≤ X ≤ 15) = (15 - 12) / (17 - 8)

P(12 ≤ X ≤ 15) = 3 / 9

P(12 ≤ X ≤ 15) = 0.33 or 33%.

To know more about probability here

https://brainly.com/question/11234923

#SPJ4

The decision that most clearly reflects a lack of understanding of the concept of sunk costs is "You study eight hours for a final exam even though there is no way now that you can pass the course".

Sunk costs refer to any costs that have already been incurred and cannot be recovered. Sunk costs are irrelevant in decision-making because they are already gone and cannot be recovered. Decision-makers must only consider future costs and benefits when making decisions.

A lack of understanding of sunk costs may result in individuals making decisions based on past costs rather than future costs and benefits. Decision-making that is influenced by sunk costs may result in inefficient resource allocation and lost opportunities.

Individuals must ignore sunk costs and instead focus on future costs and benefits to make effective decisions.

In the given options, "You study eight hours for a final exam even though there is no way now that you can pass the course" is the decision that most clearly reflects a lack of understanding of the concept of sunk costs.

Even though the student has already spent 8 hours studying, the sunk costs are irrelevant because the student cannot pass the course now. The student should focus on future costs and benefits and use the remaining time to study for other courses.

To know more about sunk costs:

https://brainly.com/question/29488541

#SPJ11

The percentage of alcohol in the vat after an hour will be 4.8%.

Explanation:

Given that a vat with 900 gallons of beer contains 4% alcohol (by volume), beer with 6% alcohol is pumped into the vat at a rate of 9 gal/min and the mixture is pumped out at the same rate. We need to find the percentage of alcohol after an hour.

Let's consider V be the volume of the vat and x be the percentage of alcohol in the vat. Now, the total amount of alcohol in the vat will be Vx.

Let A be the volume of alcohol added in the vat per minute by the pump. Now the volume of alcohol in the vat after a minute will be Vx + A and the volume of the mixture will be V+ 9.

Now the volume of alcohol in the mixture will be (Vx + A)×(x%) and the total amount of alcohol in the mixture will be Vx(x%) + 9A×(6%).

So, the volume of alcohol in the mixture after a minute will be (Vx(x%) + 9A×(6%))/(V + 9).

The rate of change of x will be given by (Vx(x%) + 9A×(6%))/(V + 9) - x/(V + 9). On solving this we get the differential equation:

dx/dt = 0.06 - 0.000067x

On solving the differential equation we get:

x = 80 + 8200/(75e^(0.000067t))

At t = 60 minutes, x = 80 + 8200/(75e^(0.000067×60)) = 4.8%.

Therefore, the percentage of alcohol in the vat after an hour will be 4.8%.

To learn more about volume, refer below:

https://brainly.com/question/1578538

#SPJ11

Therefore, based on this collection of data during a significance level of 0.05, there is insufficient proof to draw the conclusion that the average annual precipitation in the Amazonian rain forest is less than 200 cm.

Hypothesis The amount of pleasure increases with daily solar exposure. The presumed reason in this case and the factor that is independent is sun exposure. The expected impact, or dependent variable, is the degree of happiness.

To determine if the data provide sufficient that the annual rainfall in the Amazon rainforest is different than 200 cm, we can perform a hypothesis test with the following hypotheses:

Null hypothesis: The true mean annual rainfall in the Amazon rainforest is equal to 200 cm.

Alternative hypothesis: The true mean annual rainfall in the Amazon rainforest is different than 200 cm.

We can use a two-sided t-test with a significance level of 0.05 to test this hypothesis.

We must first determine the population mean and standard variation.

x = (188 + 232 + 210 + 198 + 202 + 193 + 219 + 202 + 252 + 156 + 184 + 222)/12 = 202.17 cm

Sample standard deviation, s = 26.770 cm

Next, we can calculate the t-statistic:

t = (x - μ) / (s / sqrt(n)) = (202.17 - 200) / (26.770 / sqrt(12)) = 0.491

Using a t-distribution table with 11 degrees of freedom (n-1), at a significance level of 0.05, we find the critical values to be ±2.201. Since the calculated t-statistic of 0.491 is within the range of -2.201 to 2.201, we fail to reject the null hypothesis.

Therefore, there is not sufficient evidence to conclude that the annual rainfall in the Amazon rainforest is different than 200 cm based on this sample data at a significance level of 0.05.

To know more about Hypothesis visit:

https://brainly.com/question/25263462

#SPJ1