you are bored at a lunch meeting and decide to place a raisin in your glass of water. the raisin swells to twice its original size. relative to the water, the raisin must have been:

The required answer is fail to reject a null hypothesis.

What is Null hypothesis?

The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is feasible to determine the probability that the null hypothesis is correct using statistical testing.

Given that:

α = 0.05

then

z0.05 = 1.645

Hence, the rejection region is {z < −1.645}.

Hence, The required answer is fail to reject a null hypothesis.

To know more about Null hypothesis visit,

https://brainly.com/question/4436370

#SPJ4

The equation of a line with slope m and y-intercept is Y = mx + b. (0,b). y = 7x + 4 is the equation of the line with slope of 7 and y-intercept equals to 4?

Since the slope of the line is 7 and the y-intercept is 4, the equation of the line can be written as y = 7x + 4.

The equation of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept. In mathematics, the slope or gradient of a line is a numerical representation of the line's steepness and direction.

In the equation y = 7x + 4, 7 is the slope of the line and 4 is the y-intercept. This means that the line has a slope of 7 and the y-intercept is 4.

Learn more about slope here

https://brainly.com/question/3605446

#SPJ4

Answer:

Step-by-step explanation:

So if one bit of the length, is half the size of the other bit then we can make the following equation, for x being the length of rope:

x + 2x = 66

3x = 66

x = 22

That is the length, of the smaller one (half the big one), so 2x = 44. Hence d) is your answer.

Hope I helped!

Answer:

2 ways below

Step-by-step explanation:

To complete the triangle, you would need to bend the other end of the strip of metal so that it is also 10 inches from the first bend. One way to do this would be to measure 10 inches from the first bend and mark the spot, then use a bending tool to carefully bend the metal at the mark.

Another way would be to hold the metal strip against a ruler or measuring tape, aligning the first bend with the 10-inch mark, then use the bending tool to make the second bend at the 20-inch mark. In either case, the resulting triangle would have two equal sides that are 10 inches long, and a base that is 8 inches long.

the maximum volume of the swimming pool in cubic feet = 29744[tex]ft^{3}[/tex]

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder or a sphere.

Different shapes have different volumes. In 3D geometry, we have studied the various shapes and solids such as cubes, cuboids, cylinders, cones, etc., that are defined in three dimensions. For all these shapes, we are going to learn to find the volume.

Volume of a solid is measured in cubic units. For example, if dimensions are given in meters, then the volume will be in cubic meters. This is the standard unit of volume in the International System of Units (SI). Similarly, other units of volume are cubic centimeters, cubic feet, cubic inches, etc.

given that

the combined surface area of the floor of the pool and the four sides is $4800$ square feet.

each side (there are 4)   =  4   x w x w

and the bottom                     w x w              

 total surface area   5 w^2 = 4800

 w = depth = 30.984 ft

 volume= 30.984^3 = 29744.89[tex]ft^{3}[/tex]

To learn more about  volume:

https://brainly.com/question/1578538

#SPJ4

The flour will last for about 11 days.

What is equation ?

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

An equals sign is a part of a mathematical expression referred to as an equation. A lot of equations include algebra. In math, algebra is employed when you don't know the precise amount to calculate.

Suppose, the flour will last for x days.

She uses 15 pounds of flour each day.

So, the total amount of flour used in x days 15x pounds.

Given that, she has 157.86 pound of flour.

So, the equation will be

15 x = 157.86

x = 157.86 / 15

 = 10.524

 ≈ 11

Thus, the flour will last for about 11 days.

To learn more about equation from the given link  

brainly.com/question/22688504

#SPJ1

Answer:

To find the area of a parallelogram, we can use the formula A = bh, where A is the area, b is the base, and h is the height. In this case, we are given that the area is 60 square units, so we can use this information to find the value of b and h for each of the options given.

Option A: 12 15 10

In this option, we can see that the base is 12 units and the height is 15 units, so we can plug these values into the formula to find the area: A = 12 * 15 = 180 square units. This is much larger than the given area of 60 square units, so option A cannot be correct.

Option B: 10 10.2 6

In this option, we can see that the base is 10 units and the height is 6 units, so we can plug these values into the formula to find the area: A = 10 * 6 = 60 square units. This matches the given area of 60 square units, so option B could be correct.

Option C: 15 15 12

In this option, we can see that the base is 15 units and the height is 12 units, so we can plug these values into the formula to find the area: A = 15 * 12 = 180 square units. This is much larger than the given area of 60 square units, so option C cannot be correct.

Option D: 6 6 10

In this option, we can see that the base is 6 units and the height is 10 units, so we can plug these values into the formula to find the area: A = 6 * 10 = 60 square units. This matches the given area of 60 square units, so option D could be correct.

Therefore, the correct answer is either option B or option D.

"Copy an angle" construction has been performed.

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays.  Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

Observe that angles BAC and TSR are same.

This means, construction is done to copy the angle BAC.

So, "copy an angle" construction has been performed.

To learn more about the angle from the given link

https://brainly.com/question/25716982

#SPJ1

It will be less than 26 °C as water has a relatively higher specific heat than sand is true statement about the final temperature of water.

Temperature is a unit used to represent hotness or coolness on any of a number of scales, including Fahrenheit and Celsius. According to temperature, heat energy will naturally move from a hotter (body with a higher temperature) to a colder (body with a lower temperature) (one at a lower temperature).

Given,

In an experiment, equal amounts of water and sand were heated under a lamp. The initial and final temperatures of each were recorded. A partial record of the temperature is shown.

Experimental Record

Substance Initial Temperature Final Temperature

Sand 20 °C 26 °C

Water 20 °C

The quantity of heat energy absorbed by one unit of a substance when its temperature rises by one unit is measured as the substance's specific heat.

This allows you to calculate the equation for a substance's specific heat:

Specific heat equals heat / (mass Δ T)

Given that both samples have the same amount (mass) and that all of the heat from the lamp is applied to them, you can assume that the specific heat of the samples will be as follows:

particular heat is equal to constant / ΔT.

Therefore, the two quantities are inversely connected.

Since sand has a lower specific heat than water, the sand on the shore of a beach is warmer during the day. When walking on a sandy beach on a bright day, your feet get scorched since it's hotter than the ocean.

When equal amounts of water and sand are heated as per the experiment's instructions, water will increase in temperature more slowly and, as a result, reach a lower end temperature than sand. This is because water has a higher specific heat than sand. This is the second option; because water has a substantially higher specific heat than water, the end temperature of water is less than 26°C.

To learn more about temperature, visit:

https://brainly.com/question/11317988

#SPJ1

Answer:

To determine the garbage per capita, we need to divide the total waste generated by the population. In 2005, the total waste generated was 8.618 x 10^8 pounds and the population was 2.76 x 10^5 people, so the garbage per capita in that country in 2005 was 3.12 pounds per person. This can be calculated as follows:

8.618 x 10^8 pounds / 2.76 x 10^5 people = 3.12 pounds/person

Alternatively, we can rewrite the population in scientific notation to make the calculation easier:

8.618 x 10^8 pounds / (2.76 x 10^5) people = 8.618 x 10^8 pounds / (2.76 x 10^3 x 10^2) people

Now we can cancel out the common factors of 10^2 from the numerator and denominator to get the final result:

8.618 x 10^8 pounds / (2.76 x 10^3 x 10^2) people = 8.618 x 10^8 pounds / (2.76 x 10^3) people

= 8.618 x 10^5 pounds / (2.76) people

= 3.12 pounds/person

This shows that in 2005, the garbage per capita in that country was 3.12 pounds per person.

Answer:

350 miles

Step-by-step explanation:

62 : 100 = 217 : x

x = 217 · 100 / 62

x = 21 700 / 62

x = 350

The limiting matrix is [tex]\bar{P}[/tex]=[tex]\left[\begin{array}{ccc}0.75&0.25\\0.75&0.25\\\end{array}\right][/tex].

Mathematicians frequently refer to "transition matrices" in a variety of situations. The term "change of coordinates matrix" is occasionally used in the context of linear algebra. As an alternative term for a stochastic matrix, or a matrix that describes transitions, it is employed in the theory of Markov chains. Use row operations to try to create the identity matrix to the left while augmenting the matrix of the second basis with the matrix of the first basis. Afterward, the transition matrix will be on the right. Row 1 should be multiplied by 1 as follows: R1=R1 R 1=-R 1 R1=R1.

The given transition matrix is:

P=[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex]

Let S=[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex] =[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}0.9a+0.1b\\0.3a+0.7b\\\end{array}\right][/tex]=[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]

Here, 0.9a+0.1b=0, 0.3a-0.3b=0

So, a=b

a+b=1

a=b=1/2

S=[tex]\left[\begin{array}{ccc}0.5\\0.5\\\end{array}\right][/tex]

This S is called the stationary matrix

P=[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex]

P=det[tex]\left[\begin{array}{ccc}0.9-\lambda&0.1\\0.3&0.7-\lambda\\\end{array}\right][/tex]=0

λ²-1.6λ+0.6=(λ-1)(λ-0.6)=0

λ₁=1, λ₂=0.6

x=[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]

Px=λx

[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex] =1[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]

0.9a+0.1b=a

a=b

v₁=[tex]\left[\begin{array}{ccc}1\\1\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex] =0.6[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]

0.9a+0.1b=0.6a

b=-3a

v₂=[tex]\left[\begin{array}{ccc}1\\-3\\\end{array}\right][/tex]

V=[tex]\left[\begin{array}{ccc}1&1\\1&-3\\\end{array}\right][/tex]

V⁻¹=(1/4)[tex]\left[\begin{array}{ccc}3&1\\1&-1\\\end{array}\right][/tex]

D=[tex]\left[\begin{array}{ccc}\lambda_{1} &0\\0&\lambda_{2}\\\end{array}\right][/tex]

D=[tex]\left[\begin{array}{ccc}1&0\\0&0.6\\\end{array}\right][/tex]

P=VDV⁻¹

Pⁿ=VDⁿV⁻¹

[tex]\bar{P}[/tex]=[tex]\left[\begin{array}{ccc}0.75&0.25\\0.75&0.25\\\end{array}\right][/tex]

This is the required limit matrix.

To know more about transition matrix, visit:

https://brainly.com/question/15071670

#SPJ4

The domain and the range are {0.5, 1.25, 2.0, 2.5} and {50, 100, 200, 225, 300}

The relation is not a function

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

Time (in minutes)      (x)  0.5   1.25   2.0   2.0   2.5

Distance (in meters) (y)   50   100   200  225  300

The domain is the list of the x values (without repetition)

So, we have

Domain = {0.5, 1.25, 2.0, 2.5}

The range is the list of the y values (without repetition)

So, we have

Range = {50, 100, 200, 225, 300}

For a relation to be a function, the x values must not be repeated for different y values

From the table, we have: (2.0, 200) and (2.0, 225)

The x value 2.0 is repeated for y values 200 and 225

Hence, the relation is not a function

Read more about domain and range at

https://brainly.com/question/2264373

#SPJ1

The slope of ½ is 0. A line with a zero slope is neither rising nor falling when seen from left to right or the other way around. Simply put, the slope of a horizontal line is zero.

y=m x + b, where m is the slope and b is the y-intercept, is the slope-intercept form.

where y= 0 and

y = m x + b

The slope is 0 when expressed in the slope-intercept form, or m = 0.

A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).

Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.

For more information on slope kindly visit to

https://brainly.com/question/16941905

#SPJ4

The number of children and adults that swam at the public pool is

331 and 23.

An equation is a mathematical statement of two expressions connected by an equal sign.

Example:

2x + 5 = 9 is an equation.

We have,

The total number of people = 354.

Cost for children = $1.50

Cost of adults = $2.25

Total amount = $548.25

Now,

Number of children = x

Number of adults = y

Now,

x + y = 354 _____(1)

x = 354 - y ____(2)

1.50x + 2.25y = 548.25 _____(3)

Putting (2) in (3).

1.50 (354 - y) + 2.25y = 548.25

531 - 1.50y + 2.25y = 548.25

0.75y = 548.25 - 531

0.75y = 17.25

y = 17.25/0.75

y = 23

Now,

x = 354 - y

x = 354 - 23

x = 331

Thus,

The number of children is 331.

The number of adults is 23.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

Answer:

100 km

Step-by-step explanation:

The answers to all the subparts using equations are shown:

(A) pair of linear equations: y + 40 = x and x + y = 110

(B) 75 minutes every day of swimming.

(C) The given statement is false as a result.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, (A):
Y indicates the volume of swimming

X denotes the quantity of tennis.

Making two equations now:

y + 40 = x

x + y = 110

(B)

X in the other equation is changed to match the first equation.

Please plug this in:

y + 40 + y = 110

2y = 70

35 minutes of swimming equals Y.

Including: 35

35 + 40 = 75 minutes every day of swimming.

(C)

No, given that equation: 70 + (70 - 40) = 100

This statement is false as a result.

Therefore, the answers to all the subparts using equations are shown:

(A) pair of linear equations: y + 40 = x and x + y = 110

(B) 75 minutes every day of swimming.

(C) The given statement is false as a result.

Know more about equations here:

https://brainly.com/question/28937794

#SPJ1

Answer: 175

Step-by-step explanation: So the formula for finding the area of a rhombus is A= 1/2 d1+d2. So, we multiply 14 x 25 to get 350, then we divide by 2, and get 175!  I hoped this helped you solve your problem :)

a)There are [tex]2^m^n[/tex] possible relation

b)Similarly [tex]n^m[/tex]

c)[tex]\frac{n^m}{2^m^n}[/tex]

a)Set A has m elements and set B has n elements

Firstly determine the number of elements A*B by using the multiplication rule

Number of elements[tex]=A*B=m*n=mn[/tex]

For each element, [tex]A*B[/tex] we have two option

First element 2 ways

Second element 2 ways

mn element 2 ways

By using the multiplication rule

[tex]2*2*2......=2^m^n }[/tex]

Then there are [tex]2^m^n[/tex] possible relation

b)Similarly [tex]n^m[/tex]

c)[tex]\frac{n^m}{2^m^n}[/tex]

Learn more about relation from

https://brainly.com/question/15395662

#SPJ4

By using testing of hypothesis, it can be concluded that

There is a systematic error in atleast one of the methods

First option is correct

What is testing of hypothesis?

Suppose there is a data at hand and there is a hypothesis to be tested. Testing of hypothesis determines whether the given hypothesis can be supported with the data at hand.

A t test can be used to compare results from two different methods.

Here, the difference in the results is significant, it means that

So the null hypothesis has to be rejected

There is a systematic error in atleast one of the methods

First option is correct

To learn more about testing of hypothesis, refer to the link-

https://brainly.com/question/15980493

#SPJ4

Complete Question

The complete question has been attached

The proof of  AB ≅ CD is given below.

What is triangle?

Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed by a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.

Given:  BD and AC bisect each other.

So, AE = AC  and BE = ED

Consider the triangles  ΔAEB and , ΔECD

Given,

AE = EC                         ...S

BE = ED                         ....S

Here, lines BC and AD intersects at point E, so

 m ∠AEB = m ∠DEC               ....A

Therefore, from SAS congruency,

ΔAEB ≅ ΔECD

Hence,  AB ≅ CD

To know more about triangle, click on the link

https://brainly.com/question/25215131

#SPJ1

Answer:

y = - [tex]\frac{1}{2}[/tex] x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x - 4 ← is in slope- intercept form

with slope m = 2

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , then

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute (4, - 1 ) into the partial equation

- 1 = - 2 + c ⇒ c = - 1 + 2 = 1

y = - [tex]\frac{1}{2}[/tex] x + 1 ← equation of perpendicular line

The limit of a function is a value of the function as the input of the function gets closer to some number.

We know that, a limit is a value toward which an expression converges as variable approaches certain values.

The limit of a function at m point is nothing but the value that the function approaches as its argument(variable) approaches m.

When a function is said to have a limit L at point p if it is possible to make the function arbitrarily close to L by choosing values to point p.

It is a value of the function as the input of the function gets closer to some number.

Therefore, the limit of a function is nothing but a value of the function as the input of the function gets closer to some number.

Learn more about the limit of a function here:

https://brainly.com/question/7446469

#SPJ4

Answer: Your answer will be 12.57.

Step-by-step explanation:

Using the formulas

C=2 x π x r

d=2 x r

Solving for C.

C = πd = π·4 ≈ 12.56637

Answer:

B

Step-by-step explanation:

by plugging in f, you can see that B, is the only correct answer

A fails at values greater than or equal to  f = 2

C fails for all values

and D fails for all values

B works for all given values

2(1) + 3 = 5

2(2) + 3 = 7

2(3) + 3 = 3

2(4) + 3 = 11

2(5) + 3 = 13

The force that it will take if applied perpendicular at 30° = 58 N

According to the formula of torque = τ and force = F,

τ =  r x F x sinθ --- equation 1

Given, F = 100 N , r = 0.2 m (r = radius)

We have to find the force when θ (angle) = 30°

Putting value in equation 1,

τ = 0.2 x 100 x sin (30°)

τ = 10 Nm

Value of torque from here = 10 Nm

Now to calculate the force perpendicular at 30° the equation will change as,

τ = r x F x cosθ --- equation 2

10 = 0.2 x F x cos 30°

Taking τ on the right side and F on left,

F = 10/ (0.2 x cos 30°)

F = 57.73 N

F = 58 N

Therefore, The force that it will take if applied perpendicular at 30° = 58 N

To learn more about this question on forces and torque,

https://brainly.com/question/14126857

#SPJ4

Answer:3

Step-by-step explanation: