A constant head permeability test is performed on a soil that is 2 cm x 2 cm square and 2.5 cm long. The head difference applied during the test is 18 cm, and 5 cm3is collected over a time of 100 sec. a) Compute the permeability based on these test conditions and results b) A falling head test is to be done on the same soil specimen in teh same time (t1 - t2

The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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Answer:

The two expressions are equivalent, The value of both expressions when t = 5 is 32, and The value of both expressions when t = 3 is 24

Step-by-step explanation:

4 (3 + 3) = 4(3) + 12

4(6) = 12 + 12

24 = 24

4(5 + 3) = 4(5) + 12

4(8) = 20 + 12

32 = 32

Answer:

A,E,F

Step-by-step explanation:

i did the test

Answer:   A≈1015.4

Step-by-step explanation:

A=2πrh+2πr2=2·π·8·12.2+2·π·82≈1015.36275

Answer:

407 mm²

Step-by-step explanation:

The formula for the surface area of a clyinder is: A = 2\(\pi\)r · (r + h)

Plugging in the given values, we have: A = 2\(\pi\)4 · (4 + 12.2)

A = 2\(\pi\)4 · (4 + 12.2)

A = 2\(\pi\)4 · 16.2

A = 2(3.14)4 · 16.2

A = 406.944

A = 407 (rounded)

hope this helps!

x = 301/56

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expression

Given the algebraic expression,

\(3\frac{1}{8} \div (x - 4 \frac{7}{28} ) = \frac{17}{18} + 1 \frac{5}{6} \)

Step 1:

Simplify the expression by converting the mixed numbers into improper fractions:

25/8 ÷ ( x - 119/28) = 17/18 + 11/6

Step 2: Simplify the right side of the equation

25/8 ÷( x - 119/28) = 17/18 + 33/18

25/8 ÷( x - 119/28) = 50/18

Step 3: Multiply both sides of the equation by (x - 119/28)

25/8 = 50/18 × (x - 119/28)

Step 4: Multiply both sides of the equation by (18/50)

25/8 × (18/50) = (x - 119/28)

Step 5: Simplify the left side of the equation

9/8 = (x - 119/28)

Step 6: Add 119/28 to both sides of the equation

9/8 + 119/28 = x

Step 7: Calculate the value of x:

x = 9/8 + 119/28

= 63/56 + 238/56

= 301/56

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Answer:

64

Step-by-step explanation:

ummmmmmmmmmmmmmm

The mode will not change.

Given data,

58,60,53,54,60,35,58,60

Outlier is the value in a set of data that much higher or lower than other values in data.

from given data, outlier is 35.

Mode is the value in a set of data that occurs more frequently in set of data.

from given data, 60 occurs more frequently.

Hence, 60 is the mode of data.

If outlier is removed from the data set then it will not affect the mode of the data

Thus, the mode will not change.

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The degree of the power function represented in the table f(x) is 2.

In order to find the degree of the power function represented in the given table, you must find the difference of the y-values.

The second difference is illustrated as:

2 - 6 = -4.

-2 - 2 = -4

-6 - (-2) = -4

This illustrates that the second differences are constant.

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What is the degree of the power function represented in the table?

1

2

3

4

x h(x)

−2 −8

−1 −2

0 0

1 −2

2 −8

Answer:

7

Step-by-step explanation:

Let a and b be the sides of the equilateral triangle and the regular hexagon respectively as shown in figures (1) and (2).

The area of the equilateral having side a is

\(A_T= \frac {\sqrt3}{2}a^2\cdots(i)\)

Now, join all the 6 corner points of the regular hexagon to the center of the hexagon as shown in figure (3).

As there are 6 equal sides, so angle subtended by each side at the center is 360/6=60 degrees.

Considering the triangle POR:

\(\angle POR= 60\) degree [angle at center]

As sides PO=RO, so \(\angle OPR = \angle ORP = 60\) degree.

Hence, triangle POR is an equilateral triangle.

Similarly, all the remaining 5 triangles are equilateral triangles.

So, the area of hexagon = 6 x Area of triangle POR

As the length of sides of the triangle POR is b,

so the area of the triangle POR \(= \frac {\sqrt3}{2}b^2\).

Hence, the area of the regular hexagon,

\(A_H = 6 \times \frac {\sqrt3}{2}b^2\cdots(ii)\)

As the equilateral triangle and a regular hexagon have the same area, so from the equations (i)and (ii), we have

\(A_T=A_H\\\\\frac {\sqrt3}{2}a^2=6 \times \frac {\sqrt3}{2}b^2\\\\\Rightarrow a^2=6b^2\\\\\Rightarrow \frac {b^2}{a^2}=\frac 1 6\\\\\Rightarrow \frac {b}{a}=\frac {1}{\sqrt 6}\cdots(iii)\)

Given that the ratio of the side length of the regular hexagon to the side length of the equilateral triangle, b/a= m/√n.

On comparing with the equation (iii), we have

m=1 and n=6

Hence, m+n=1+6=7.

The value of the function F(3) will be 1/125. It is obtained by putting the value 3 in the place of x.

A connection between independent variables and the dependent variable is defined by the function. Functions help to represent graphs and equations.

A function is represented by the two variables one is dependent and another one is an independent function. The relation between them is shown as y if dependent and x is the independent variable.

F(x)=(1/5)ˣ

F(3)=(1/5)³

F(3)=1/125

Hence, the value of the function F(3) will be 1/125.

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The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:

\(c^2 = a^2 + b^2 - 2ab*cos(C)\)

In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:

\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)

49 = 16 + 25 - 40*cos(C)

49 = 41 - 40*cos(C)

40*cos(C) = 41 - 49

40*cos(C) = -8

cos(C) = -8/40

cos(C) = -0.2

To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:

C = arccos(-0.2)

Using a calculator, we find that C ≈ 101.54 degrees.

Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

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The option (b) set y equal to a constant other than zero to get the curve of points where the slope is that constant.

A slope field is a visual representation of the slopes of a function's derivative at different points on the xy-plane. The slope at a particular point in the xy-plane is given by the derivative of the function at that point.

To match the given equations with their corresponding slope fields, you need to analyze the behavior of the slopes and isoclines. An isocline is a curve in the plane along which the slope of a function is constant. Isoclines are useful in constructing slope fields by hand, as they help in determining the slope at different points.

To start with, set y equal to zero and observe how the derivative behaves along the x-axis. Similarly, set x equal to zero and observe the behavior of the derivative along the y-axis. These observations will give you an idea of the direction and magnitude of the slope at different points in the xy-plane.

Next, consider the curve in the plane defined by setting y' = 0. This curve represents the points in the picture where the slope is zero. These points are known as critical points or equilibrium points. They are essential in analyzing the stability and behavior of a system.

These curves are called isoclines and can be used to construct the slope field picture by hand.

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Complete Question:

Match the following equations with their slope field. Clicking on each picture will give you an enlarged view. While you can probably sove this problem by guessing, it is useful to try to predict characteristics of the slope field and then match them to the picture Here are some handy characteristics to start with- you will develop more as you practice. Set y equal to zero and look at how the derivatiwe behaves along the x axis. Do the same for the y axis by setting x equal to 0. Consider the curve in the plane defined by setting y' = 0-this should correspond to the points in the picture where the slope is zero. Setting y equal to a constant other than zero gives the curve of points where the slepe is that constant. These are called isoclines, and can be used to construct the slope field picture by hand.

The number of minutes that the players spend running bases during each hour of practice is the constant of proportionality of the proportional relationship.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

In the context of this problem, the variables x and y are given as follows:

The equation for the constant is given as follows:

k = y/x.

Representing the hourly time spent running times, you can calculate it taking any point (x,y) on the graph of the function.

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Determining the interval (represented by n); randomly selecting a number between 1 and n; and including each nth element in your sample, are the steps in Systematic Sampling.

This is further explained below.

Generally, Systematic sampling is a statistical procedure that involves the selection of items from an ordered sample frame. It is used in the survey methodology known as survey methodology. The equiprobability approach is the kind of systematic sampling that is used the most often.

In conclusion,  The procedures involved in Systematic Sampling are as follows: determining the interval, which is denoted by the number n; picking a number at random that falls between 1 and n and incorporating every nth element in your sample.

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Answer:

I assume it would be 15 loves of banana bread.

Step-by-step explanation:

if you do 8 loves of pumpkin bread, you get $24 profit.

If you do 15 loves of banana bread, you get $37.50 in profit.

To maximize the profit of $38 , baker should make 12 loaves of banana bread and 2 loaves of pumpkin bread.

" Linear inequalities are defined as algebraic expression which are related with the sign of inequality."

According to the question,

'x' represents the number of loaves of banana bread

'y' represents the number of loaves of pumpkin bread

As per the given condition,

Total profit  on making bread \('P' = 2.50x + 4.00y\)     ____(1)

Linear inequalities are

\(2x + 3y\leq 30\\\\x+ 2y \leq 16\)

By solving linear inequalities we get,  

\(x= 12\\ \\y =2\)

As shown in the diagram drawn , point of intersection  is (12,2) for the given inequality.

Substitute the value of 'x' and 'y' in (1) to get the maximize profit ,

Maximize profit ' P' \(= 2.50(12) + 4 (2)\)

                          \(= 30 + 8\\= \$38\)

Hence, to maximize the profit of $38 , baker should make 12 loaves of banana bread and 2 loaves of pumpkin bread.

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Answer:

B

Step-by-step explanation:

Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.

Answer:

18 Bowls of Candy

Step-by-step explanation:

Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.

Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.

Now, we can calculate the total number of bowls of candy:

Total bowls of candy = (Number of bags) x (Bowls per bag)

Total bowls of candy = 6 bags x 3 bowls per bag

Total bowls of candy = 18 bowls

Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.

Answer:

2

Step-by-step explanation:

14·\(\frac{1}{7}\)=2

Answer:

2

Step-by-step explanation: 1/7th's of 14 is 2.

1/7 x 14 = 2.

Answer:

  3.33×10⁴

Step-by-step explanation:

You can use the hint, or you can use a common exponent. Here is the latter case.

  (3.9×10⁴) -(5.7×10³) = (3.9×10⁴) -(0.57×10⁴) = (3.9 -0.57)×10⁴

  = 3.33×10⁴

_____

With a little practice, you can see the effect on exponents of moving the decimal point. Here, we have ...

  5.7×10³ = (0.57×10)×10³ = 0.57×(10×10³) = 0.57×10⁴

__

When adding or subtracting in scientific notation, all that is required is that the exponents of all the numbers be the same. The hint says make all the exponents be 0. Above, we have chosen to make them all be 4. You could also use 3:

  (3.9×10⁴) -(5.7×10³) = (39×10³) -(5.7×10³) = (39 -5.7)×10³

  = 33.3×10³ = 3.33×10⁴

Answer:

± (1 ÷ 9)

Step-by-step explanation:

Data provided in the question

Since  3 is added to the absolute value and -9

The result is 4

Now this information should be transformed in a mathematical equation

Let us assume be x so the product of the number and -9 be -9x

Fo rthe absolute value we use the mode. Thus the required expression is:

3 + |-9x|

Given that the result is 4

So, it would be

3 + |-9x| = 4

Now Solving the above equation which is given below:

|-9x| = 4-3

|-9x| = 1

here we will remove the mode by introducing ± sign which is shown below:

-9x = ± 1

-9x = 1 or -9x = -1

x = -1/9

or

x = \(\frac{1}{9}\)

Therefore, the value of x is ± (1 ÷ 9).

Answer:

m - 3.2

Step-by-step explanation:

If the nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. The estimated number of fish in the lake is 35 fish.

Let x represent the estimated number of fish in the lake

Hence,

x /10 = 7/2

Cross multiply

2x = 10 × 7

2x = 70

Divide both side by 2x

x =70/2

x = 35 fish

Therefore 35 is the number of fish.

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Answer:

2 1/2

Step-by-step explanation:

5/8 divided by 1/4 is 2 1/2

Answer:

Based on the diagram, we can see that the triangle formed by the line segment with length 8 and the two dashed line segments is a right triangle with a 45° angle. This means that the other two angles of the triangle are also 45° each.

Using the properties of 45°-45°-90° triangles, we know that the length of the hypotenuse is equal to the length of either leg times the square root of 2. Therefore, we have:

x = 8 / sqrt(2) = 8 * sqrt(2) / 2 = 4 * sqrt(2)

So the value of x is option B: 8√2 / 2 or simplified, 4√2.

Answer:

770,400

Step-by-step explanation:

770,400 seconds

Answer:

Marcel's and Stephanie's taxable incomes are less than their annual salaries because they both have a series of tax deductions

Step-by-step explanation:

Based on the trend of the increase in children born out of wedlock, if this trend keeps increasing, the year with 67% of babies born out of wedlock will be 2055 .

In 1990, the 28% of children were born out of wedlock and this trend was increasing by 0.6% per year.

If the trend continues, the number of years till 67% of children born out of wedlock will be:

= (67%  - 28%) / 0.6%

= 65 years

The year will be:

= 1990 + 65

= 2055

The first part of the question is:

According to the National Center for Health Statistics, in 1990, 28% of babies in the United States were born to parents who were not married. Throughout the 1990s, this percentage increased by approximately 0.6 per year.

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The simple interest formula is A = P(1+r t) then the value of t =33.2210 years.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

The simple interest formula is equal to

A = P(1+r t)

where, A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

P = $ 3300

A = $ 10700

r = 6.75 % = 6.75 / 100 = 0.0675

substitute in the formula above

$10700 = 3300(1+0.0675 t)

simplifying the above equation, we get

Divide both sides by 3300

\($\frac{3300(1+0.0675 t)}{3300}=\frac{10700}{3300}$$\)

Simplifying the above equation, we get

\($1+0.0675 t=\frac{107}{33}$$\)

Subtract 1 from both sides

\($1+0.0675 t-1=\frac{107}{33}-1$$\)

Simplifying the above equation, we get

\($0.0675 t=\frac{74}{33}$$\)

Divide both sides by 0.0675

\($\frac{0.0675 t}{0.0675}=\frac{\frac{74}{33}}{0.0675}\)

\($t=\frac{74}{2.2275}$\)

t = 33.2210 years

Therefore, the value of t exists 33.2210 years.

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The linear inequality with the solution set (2,-5), (-5,-5), (-5,5), (5,5), (5,-2) are x ≤ 5 and y ≤ 5

The solution set is given as

(2,-5), (-5,-5), (-5,5), (5,5), (5,-2)

We can see that the highest y value in the above ordered pairs is 5

So, we have

y ≤ 5

Also, we can see that the highest x value in the above ordered pairs is 5

So, we have

x ≤ 5

Hence, the linear inequality with the solution set is x ≤ 5 or y ≤ 5

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