suppose you fill a tall topless tin can with water, and then punch a hole near the bottom with an ice pick. the water leaks quickly at first, then more slowly as the depth of the water decreases. in engineering or physics, you will learn that the rate at which water leaks out is directly proportional to the square root of its depth, y.

On average Carmen earned $38.8 per week of profit and for 12 weeks the profit earned is $465.6.

What is average?

In everyday terms, an average is one number chosen to represent a list of numbers; it is often the sum of the numbers divided by the number of numbers in the list (the arithmetic mean).

The profit earned by Carmen in her first week = -$44.50

The profit earned by Carmen in her second week = -$26.25

The profit earned by Carmen in her third week = $80.50

The profit earned by Carmen in her fourth week = $88.75

The profit earned by Carmen in her fifth week = $95.50

The average profit earned by Carmen is = sum of profit earned / number of weeks profit earned

Substitute the values into the equation -

Average = [(-44.50) + (-26.25) + 80.50 + 88.75 + 95.50] / 5

Average = 194/5

Average = 38.8

The avearge profit per week is $38.8

To find the profit Earned by Carmen in 12 weeks use the arithmetic operation of multiplication -

Profit Earned = 12 × Average profit per week

Substitute the values in the equation -

Profit Earned = 12 × 38.8

Profit Earned = 465.6

Therefore, the profit earned is $465.6.

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Answer:465.6

Step-by-step explanation:

Answer:

66

Step-by-step explanation:

the difference of 54 and 32 is 54 - 32 = 22

the difference of 8 and 5 is 8 - 5 = 3

then

22 × 3 = 66

The batter ran a distance of 0.112 kilometers or approximately 112 meters.

A mathematical number known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.

A baseball diamond is made up of four bases, and the distance a batter runs for a single is from home plate to first base, then first base to second base, then second base to third base, and finally third base back to home plate.

So the total distance the batter runs is 4 times the distance from home plate to first base, which is 28 meters.

28 meters x 4 = 112 meters

To convert meters to kilometers, divide by 1000:

112 meters / 1000 = 0.112 kilometers

Thus, the batter ran 0.112 kilometers or approximately 112 meters.

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The critical F value for a sample of 6 and 4 degrees of freedom at a .10 two-tailed significance level can be found using a F-distribution table. The exact value depends on the specific table used.

For the comparison between Mark and Debbie, we would need to perform an F-test for equality of variances to determine if there is more variation in Mark's data. The null hypothesis is that the variances are equal, and the alternative hypothesis is that the variance of Mark's data is greater. The test statistic would be the ratio of the larger variance to the smaller variance, with the degrees of freedom being the smaller of the two sample sizes minus 1.

A .05 significance level means that we reject the null hypothesis if the p-value is less than .05. The p-value can be found using an F-distribution table or a statistical software.

The conclusion would depend on whether the p-value is less than .05 or not.

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The length of PX is 1.56.

The Pythagorean Theorem is a mathematical principle that relates the lengths of the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

c² = a² + b²

The Pythagorean Theorem is one of the most famous and widely-used theorems in mathematics, and is a fundamental principle in geometry. It is used to find the length of one side of a right triangle when the lengths of the other two sides are known, and is also used to test whether a triangle is a right triangle.

Since YP is perpendicular to AB, we have right triangle APY with AP as hypotenuse and PY as the height.

Using the Pythagorean theorem, we can find the length of AP:

AP² = AY² + PY²

AP² = 4.7² + 1.4²

AP² = 22.09

AP = 4.7

Similarly, since ZP is perpendicular to BC, we have right triangle CPZ with CP as hypotenuse and PZ as the height.

Using the Pythagorean theorem, we can find the length of CP:

CP² = CZ² + PZ²

CP² = 3.2² + PZ²

CP² = 10.24

CP = 3.2

Since PX is perpendicular to AB, we have right triangle BPX with BP as hypotenuse and PX as the height.

Using the Pythagorean theorem, we can find the length of BP:

BP^2 = AP^2 + CP^2

BP^2 = 4.7^2 + 3.2^2

BP^2 = 26.69

BP = 5.15

Finally, using the Pythagorean theorem, we can find the length of PX:

PX^2 = BP^2 - PY^2

PX^2 = 5.15^2 - 1.4^2

PX^2 = 2.46

PX = 1.56

Therefore, the length of PX is 1.56.

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The solution of the given differential initial value problem is

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).

Given is the initial value problem -

y''' + 10y'' + 25y' = 0

We can write the -

[tex]$25 \frac{d}{d x} y{\left(x \right)} + 10 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$[/tex]

The given differential equation can be solved and written as -

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6)

Therefore, the solution of the given differential initial value problem is

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).

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The total manufacturing cost assigned to Job P is $84,240.

The total manufacturing cost consists of direct material, direct labor, variable overhead, and fixed overhead costs.

The variable manufacturing costs include direct materials, direct labor, and variable overhead while the fixed overhead costs are period costs related to the production process.

                                                              Molding    Fabrication      Total

Machine hours used                                4,200         2,520           6,720

Fixed manufacturing overhead           $16,800    $25,200     $ 42,000

Fixed manufacturing overhead per hr    $4              $10

Variable manufacturing overhead

per machine-hour                               $ 1.40           $ 2.20

                                         Job P       Job Q

Direct materials           $ 21,840    $ 13,440

Direct labor cost        $ 35,280    $ 12,600

Actual machine hours used:

Molding                           2,890          1,340

Fabrication                       1,010          1,480

Total                                3,900        2,820

Actual Manufacturing Costs (Job P):

                                                             Job P

Direct materials                                   $21,840

Direct labor costs                               $35,280

Overheads:                        

Variable                                               $5,460 (3,900 x $1.40)

Fixed:

Molding = $11,560 ($4 x 2,890)

Fabrication = $10,100 ($10 x 1,010)   $21,660

Total manufacturing costs               $84,240

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Answer:

The zero in the equation y = 2x + 8 is when x = -4. When x = -4, y = 0.

The joint probability distribution function for exponential random variables with pdf f(x) = 0.5e^(-0.5x), x ≥ 0, find P(X > 1,Y > 4) is, e^(-5/2).

The X and Y are independent variables, so probability distribution function of X is same as that of Y.

The joint probability distribution function for independent variables is,

[tex]\int \int f(x)f(y) dx dy[/tex]

where f(x) and (y) are the probability distribution function in x and y respectively.

In this question, X>1 and Y>4, so the limits of integration for X goes from 1 to infinity and for Y it goes from 4 to infinity.

[tex]\int_4^\infty \int_1^\infty 0.5 \times 0.5 \times e^{-0.5x} e^{-0.5y} dx dy\\= 0.25\int_4^\infty e^{-0.5y} dy \int_1^\infty e^{-0.5x} dx\\= 0.25 \times [-2e^{-0.5y}]_4^\infty \times [-2e^{-0.5x}]_1^\infty \\= 0.25 \times \dfrac{2}{{e}^2} \times \dfrac{2}{\sqrt{e}}[/tex]

The integral is, e^(-5/2).

The joint probability distribution function is, e^(-5/2).

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--The complete question is, If X and Y are independent exponential random variables with pdf f(x) = 0.5e^(-0.5x), x ≥ 0, find P(X > 1,Y > 4).--

Answer:

Q 1 : Solution:

Let the height of the building be h.

We know that tan(60) = h/9 (angle of elevation formula)

h = 9tan(60) = 9sqrt(3)/3 = 3*sqrt(3) = 3.464101615 m (approx)

Q 2 : Solution:

Let the height of the pole be h.

Let the shorter segment be x, and the longer segment be 9x.

We know that tan(theta) = x/(20) = 9x/(20+h) (angle subtended formula)

By cross multiplying and simplifying, we get:

x = (20h)/(h+180)

The ratio of the segments is x:9x = 1:9, so x = (20h)/(h+180) = 1/10 * h

h = 10x = (20h)/(h+180)

h^2 + 180h - 20h^2 = 0

h(20-h) = 0

h = 0 or h = 20

Since the pole has a height, h = 20m is not possible, so the height of the pole is h = 178.8m

The questions that are appropriate for the teacher to ask her population are:

How many hours of sleep do you get per night?

On average, how long does it take you to complete your homework?

What time do you leave for school in the morning?

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The survey is conducted among the seventh grade students so the valid question their teacher would have asked them is:

How many hours of sleep do you get per night?

On average, how long does it take you to complete your homework?

What time do you leave for school in the morning?

while the other two questions are invalid as it the students are young and they are not legal to vote also it is not necessary that they would arrive to school by car.

Hence, the questions that are appropriate for the teacher to ask her population are:

How many hours of sleep do you get per night?

On average, how long does it take you to complete your homework?

What time do you leave for school in the morning?

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Answer:6

Step-by-step explanation:

The two numbers are 3 and 7.

Let the two numbers be x and y.

Considering the first statement :

x + y = 10 ...........................(1)

Considering the second statement:

x - y = 4   ............................(2)

Adding equations (1) and (2):

x + y + x - y = 10 + 4

              2x = 14

                x = 7

Substituting the value of x in equation (1):

           7 + y = 10

                 y = 10 - 7

                 y = 3

Therefore, the value of the two numbers is 3 and 7.

For reference:

https://www.cliffsnotes.com/study-guides/algebra/algebra-i/word-problems/number-problems-with-two-variables

Using the system of equations we get the values of 3 digit number as:

238

Given:

The sum of the digits of a three-digit number is 13.

The tens digit, t, is 1 more than the hundreds digit, h. The units digit, u, is 3 more than the sum of the tens and hundreds digits.

we are asked to determine each digit of the given number:

we frame the equation as:

tens digit (t) = 1+h

hundreds digit (h) = h

units digit (u) = 3+(t+h)

hence,

h + (1+h) + (3+(t+h)) = 13

open the brackets.

h+1+h+3+(t+h)=13

substitute t value from the above mentioned state.

h+1+h+3+((1+h)+h)=13

h+1+h+3+1+h+h=13

arrange the like terms and add.

4h + 5 = 13

4h = 13-5

4h=8

h = 8/4

h = 2

hence we get the hundreds digit as 2.

now substitute it to get t and u value.

t = 1+h

t = 1+2

t = 3

tens digit = 3

u = 3+(t+h)

u = 3+(3+2)

u = 3+5

u = 8

units digit = 8

Therefore , the solution of the given problem of linear equation comes out to be total amount collected is $4956.

The foundation for a linear regression curve is the equation y=mx+b. B is the slope, and m is the y-intercept. The previous sentence is sometimes referred as a "mathematical equation involving two variables," even though that y or y are separate components. Two variables make up bivariate linear equations. There are no known solutions to application issues involving linear equations. Y=mx+b is the equation for a single set of equations.

Here,

Given :

Pupil : price per ticket is $8

teacher :  price per ticket is $20

Thus ,

Let the x be the total amount of teacher is :

So,

Pupil collected 416$ more than teachers total amount is :

Pupil total amount = 416 + x

So,

Total tickets sold is 1/4 of the ticket sold :

=> 1/4y * 20 = x

=> 5  = x/y

=>x = 5y

So,

=> 416 + 5y = 3/4 * 8 y

=> 416 + 5y = 6y

=> y = 516 tickets were sold

Thus ,

=> 1/4 * 516 =  129

=> 129 * 20 = 2580

For pupil is :

=> (516 -219) * 8

=> 2376

Total amount collected is => 2580 + 2376 = 4956

Therefore , the solution of the given problem of linear equation comes out to be total amount collected is $4956.

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The number of pounds of $9 nuts he must used, 126

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Randall wants to mix 21 lb of nuts worth $2 per lb,

with some nuts worth $9 per lb

He wants to make a mixture worth $8 per lb

The number of pounds of $9 nuts must he use = ?

Suppose, the number of pounds of $9 = x

Then, According to given condition,

Average price in a mixture  =  (9x + 21 x 2)/x +21

                                              =  8

(9x + 21 x 2)/x +21 = 8

9x + 42 = 8(x + 21)

9x + 42 = 8x + 168

9x - 8x = 168 - 42

x = 126

Hence, the number of pounds of $9 nuts is 126

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The length t of the triangle side is 44 mm

What is the trigonometric ratio?

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.

according to law of cosines,

t² = 41² +54² - 2 (41)(54) cos x

t² = 41² +54² - 2 (41)(54) ( 3/5)

t² =  1681 + 2916 - (13284/5)

t² =  1681 + 2916 - (13284/5)

t² =  4597 - 2656.8 =1940.2

t = ±√1940.2 = ±44 mm

length is positive

The length t of the triangle side is 44 mm

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The factor by which g([tex]x[/tex]) grows over the interval from 14 to 16 is 1.1429.

The factor is a number that can be divided evenly into another number. For example, 2, 3, 5 and 10 are all factors of 10. When two or more numbers are multiplied together, each number is a factor of the product.

The factor by which g(x) grows over the interval from 14 to 16 can be determined by calculating the ratio of the values of g(x) at the endpoints of the interval.

At x = 14, g(x) = 4(14) = 56

At x = 16, g(x) = 4(16) = 64

The factor by which g(x) grows over the interval from 14 to 16 is 64/56 = 1.1429.

This means that g(x) grows by a factor of 1.1429 over the interval from 14 to 16.

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The value of h such that the matrix is the augmented matrix of a consistent linear system is -2

From the question, we have the following parameters that can be used in our computation:

6 -3 h

-12 6 4

For a consistent system of linear equation, the equations are the equivalent

So, we have

6x - 3y = h

-12x + 6y = 4

Divide the second equation by -2

6x - 3y = -2

By comparing the equations, we have

h = -2

Hence, the solution of h is -2

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Answer:

nothing

Step-by-step explanation:

Answer:

Step-by-step explanation:

nothing

Confidence interval refer a range of estimates for an unknown parameter and here unknown parameter is percentage of residents support the increase. So, the correct answer is option(c), i.e., More than 40 percent of the residents support the increase.

We have, A random sample of residents in city J, about whether they supported raising taxes to increase bus service for the city and sample is based on survey.

Significance level = 95%

Confidence interval = (0.46,0.52)

Confidence interval: A confidence interval, in statistics, defines to the probability that a population parameter will fall between two set values. Therefore, the population parameter i.e., the proportion lies in range of between 0.46 to 0.52. Therefore the actual population proportion of people who support the increase is surely greater than 40%, but always be less than 52%. So, out of five options, option (c) is that satisfied this condition. That is more than 40% of the residents support the increase, implies the option( C) is the correct answer.

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Step-by-step explanation:

The graph would represent a straight line that slopes downwards and passes through the point (2,1).

Answer: The shape of the distribution of the age of first heart attack in the US population who have had at least one heart attack is likely to be positively skewed, with the majority of cases occurring in older age groups and a relatively small number of cases occurring in younger age groups. The frequency of heart attacks generally increases with age, reaching a peak in the older age groups.

Step-by-step explanation:

The meer-kitty survey feedback tab has limitations in its data. The survey results must have at least 120 unique responses to be considered useful and aligned with the business objective. The current data, however, only has 40 total responses, with 11 of them coming from one user. This skews the results and makes it difficult to accurately analyze the feedback.

To address these limitations, it is recommended to remove the duplicates, in this case the 11 responses from one user, and focus on the remaining 29 unique responses. This will provide a clearer picture of the survey results and a more accurate representation of the feedback. By doing so, the analysis of the data will be better aligned with the original business objective and provide more valuable insights.

It is important to consider the limitations of the data when conducting any type of analysis, especially when it comes to surveys and feedback. By taking the necessary steps to ensure the data is as accurate and reliable as possible, the results of the analysis will be more meaningful and relevant to the business.

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Answer:

-5

Step-by-step explanation:

First, find the solutions to the quadratic equation.

[tex]3x^2+15x+9=0\\3(x^2+5x+3)=0[/tex]

Since this is not factorable, use the quadratic formula and simplify.

x = (-5±[tex]\sqrt{(5)^2-4(1)(3)}[/tex])÷2(1)

x = (-5±[tex]\sqrt{13}[/tex])÷2

So x1 = (-5+[tex]\sqrt{13}[/tex])÷2 and x2 = (-5-[tex]\sqrt{13}[/tex])÷2

Now just sub it into the equation and simplify:

(-5+[tex]\sqrt{13}[/tex])÷2 + (-5-[tex]\sqrt{13}[/tex])÷2

= [tex]\frac{-5+\sqrt{13} + (-5)-\sqrt{13}}{2}[/tex]

= [tex]\frac{(-5)+(-5)+\sqrt{13}-\sqrt{13} }{2}[/tex]

= [tex]\frac{-10}{2}[/tex]

= -5

Answer:

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Answer:

1) Given

2) Multiplication Property of Equality

3) 3x + 6 = 24     Distributive Property of Addition

4) 3x = 18     Subtraction Property of Equality

5) x = 6     Division Property of Equality

Step-by-step explanation:

[tex]\begin{array}{|l|l|}\cline{1-2}\vphantom{\dfrac12} \rm Statements & \rm Reasons\\\cline{1-2}\vphantom{\dfrac12}\frac{3(x+2)}{4}=6& \rm Given\\\cline{1-2}\vphantom{\dfrac12}3(x+2)=24&\text{Multiplication Property of Equality}\\\cline{1-2}\vphantom{\dfrac12}3x+6=24&\text{Distributive Property of Addition}\\\cline{1-2}\vphantom{\dfrac12}3x=18&\text{Subtraction Property of Equality}\\\cline{1-2}\vphantom{\dfrac12}x=6&\text{Division Property of Equality}\\\cline{1-2}\end{array}[/tex]

Given:

[tex]\dfrac{3(x+2)}{4}=6[/tex]

Apply the Multiplication Property of Equality by multiplying both sides by 4:

[tex]\implies 3(x+2)=24[/tex]

Apply the Distributive Property of Addition:

[tex]\implies 3 \cdot x + 3 \cdot 2=24[/tex]

[tex]\implies 3x+6=24[/tex]

Apply the Subtraction Property of Equality by subtracting 6 from both sides:

[tex]\implies 3x+6-6=24-6[/tex]

[tex]\implies 3x=18[/tex]

Apply the Division Property of Equality by dividing both sides by 3:

[tex]\implies \dfrac{3x}{3}=\dfrac{18}{3}[/tex]

[tex]\implies x=6[/tex]

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

For all numbers, a, b, and c:

Multiplying a number by a group of numbers added together is the same as multiplying each number separately:  

For all numbers, a, b, and c:

For all numbers, a, b, and c:

Answer:

Please type or attach a math question to be answered.

Answer:

About extravagance philosophy

The length of the bases for the trapezoid are

shorter base is 3 in and the longer base is 7 in

The formula for area of trapezoid is

= 1/2 sum of bases * height

base of the trapezoid

20 = 1/2 sum of bases * 4

1/2 sum of bases = 5

sum of bases = 10

The relationship between the bases

longer base = 2 * shorter base + 1

sum of bases = longer base + shorter base

sum of bases = 2 * shorter base + 1 + shorter base

sum of bases = 3 shorter base + 1

substituting will result to

10 = 3 shorter base + 1

10 - 1 = 3 shorter base

9 = 3 shorter base

shorter base = 3 in

longer base = 2 * shorter base + 1

longer base = 2 * 3 + 1

longer base = 7 in

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