A consumer agency wants to determine which of two laundry detergents, A or B, cleans clothes better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale from 1–10, with 1 being the least clean to 10 being the most clean. The difference in mean ratings (A – B) was determined to be 1.5. Assuming there is no difference in the two detergents, 200 simulated differences in sample mean ratings are displayed in the dotplot.



Using the dotplot and the difference in mean ratings from the samples, is there convincing evidence that the one detergent is better than the other?

Yes, because a difference in mean rating of 1.5 or more occurred only 23 out of 200 times, meaning the difference is statistically significant and there is convincing evidence that A is more effective than B.
Yes, because a difference in mean rating of 1.5 or more occurred only 23 out of 200 times, meaning the difference is statistically significant and there is convincing evidence that B is more effective than A.
No, because a difference in mean rating of 1.5 or less occurred 167 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.
No, because a difference in mean rating of 1.5 or more occurred 23 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.


answer is D

The volume of the solid given is 125/24 and is constrained by the planes z = x, y = x, x + y = 5, and z = 0.

The capacity of an object is expressed in terms of volume. The quantity of space a three-dimensional item takes up can also be referred to as volume.  It is sometimes referred to as the vessel's "capacity" or "volume." infant milk bottle with milliliter measuring indications and juice bottle with a 1 liter capacity.

Given

The bounds for z are 0 ≤ z ≤ x.

The bounds in the xy-plane are x ≤ y ≤ 5 - x and x in [0, 5/2]

So, V = ∫∫ (x - 0) dA

= ∫(x = 0 to 5/2) ∫(y = x to 5 - x) x dy dx

= ∫(x = 0 to 5/2) x (5 - 2x) dx

= ∫(x = 0 to 5/2) (5x - 2x^2) dx

= (5x^2/2 - 2x^3/3) {for x = 0 to 5/2}

=  125/24.

The volume of the solid given is 125/24 and is constrained by the planes z = x, y = x, x + y = 5, and z = 0.

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Answer:

y =x+3

y =-x²+[?]

Find the gradient;

What is the formula for the gradient of a graph?

Finding the gradient of a straight-line graph

X2 = 2

Y2 = 7

ΔX = 4

ΔY = 3

θ = 36.869897645844°

Equation of the line:

y = 0.75x + 5.5

When x=0, y = 5.5

When y=0, x = -7.3333333333333

OR

X2 = -6

Y2 = 1

ΔX = -4

ΔY = -3

θ = 216.86989764584°

Equation of the line:

y = 0.75x + 5.5

When x=0, y = 5.5

When y=0, x = -7.3333333333333

The measure of  angle B is m ∠B = 107°.

What is similar triangles?

Triangles that are similar in shape but differ in size are known as similar triangles. Examples of related objects include all equilateral triangles and squares with any side length. To put it another way, if two triangles are similar, then their corresponding angles and sides are congruent and equal in size.

Given:   Δ NPZ ~ Δ HBZ

As the triangles NPZ and triangle HBZ are similar that means the corresponding angles are congruent.

⇒ ∠N = ∠H,  ∠P = ∠B,  ∠Z = ∠Z

Since,

∠P = (8x - 37)°,  ∠Z = 42°,  ∠H = (2x - 5)°

⇒ 2x - 5 = ∠H,  ∠B = 8x - 37,  Z = 42°

Since, the sum of three angles of triangle is 180°.

⇒              ∠H + ∠B + ∠Z = 180°

(2x - 5)° + (8x - 37)° + 42° = 180°

                10x - 42° + 42° = 180°

                                  10x = 180°

                                     x = 18°

So,

∠B = (8x - 37)° = 8(18) - 37 = 144 - 37 = 107°.

Hence, the measure of  angle B is m ∠B = 107°.

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The perimeter of ΔAEB is 18.5 feet.

A triangle's other two sides are divided in the same proportion if a line drawn parallel to either one of its sides intersects the other two sides at two different spots.

As,  side AB║DF hence we will use Triangle Proportionality theorem to calculate the length of side AE.

Since, AE/AD = EB/ BF

AE/2 = 7.2/8.4

AE = 6.5 feet

So, the perimeter of ΔAEB is

= AE + EB + BE

=6.5+4.2+7.8

=18.5 ft.  

Hence, the perimeter  is 18.5 feet.

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Answer:

16/11

Step-by-step explanation:

Let x = 1.45454...

Multiply both sides by 100:

100x = 145.454...

Subtract both sides by x:

100x - x = 145.454... - x

100x - x = 145.454... - 1.45454...

99x = 144

x = 144/99

The term can be simplified in lowest as 16/11. Hence, 1.45454... can be written as the ratio of two integers of 16/11

The value of m ∠ Q is 23°.

What are complementary angles?

Because the three angles of a triangle sum up to 180° and the right angle has already taken up 90°, the two non-right angles in a right-angled triangle are complementary. We say two angles "Complement" one other when their sums equal 90 degrees.

Here, we have

Given: m ∠ P = (12x + 7), m ∠ Q = (6x - 7), and ∠ P and ∠ Q are complementary angles.

The sum of the measures of two complementary angles is 90°.

So, m∠P + m∠Q = 90°

Substitute 12x+7 for m∠P and 6x−7 for m∠Q.

12x+7 + 6x−7 = 90°

18x = 90°

x = 5°

To find m∠Q, substitute 5 for x in 6x−7.

6×5 - 7 = 23°

m ∠ Q = 23°

Hence, the value of m ∠ Q is 23°.

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Using PEDMAS to solve the mathematical expression given, the value is 2

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It is an acronym used to remember the order of operations in math problems. It is also sometimes referred to as Order of Operations.

In this problem, we will need to use and apply the rules of PEMDAS.

We will need to break this into different components and then bring them together afterwards.

[(3/5 + 0.425 - 0.005) ÷ 0.1] / [30.5 + 1/6 + 3(1/3)] + [6(3/4) + 5(1/2)] / [(26 ÷ 3(5/7)] - 0.05

This becomes ;

[10.2 / 34] + [12.25 / 7] - 0.005

We can further resolve this into

2.05 - 0.005

And then we just subtract the values from one another

2.05 - 0.005 = 2

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According to the solving by  using substitution method the  x and y are x = 6/5 and y = -8/5 respectively.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable through one equation is substituted in the second equation in this procedure, as the name implies.

given equations are 2x+4y = 4 and -2x+ y = -4

Now, simplifying -2x+y = -4

-2x+y = -4

∴ y = -4 + 2x

i.e. y = 2x - 4

By substitution method,

y = 2x - 4 in other given equation 2x+4y = 4,

 2x+4y = 4

 2x+4(2x - 4) = 4

∴ 2x + 8x - 8 = 4

∴ 10x = 4 + 8

∴10x = 12

∴ x = 12/10

∴ x = 6/5

Now ,

substituting x = 6/5 in y = 2x - 4,

 y = 2(6/5) - 4

∴ y = - 8/5

∴ x = 6/5  &  y = - 8/5.

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The fractions of the numbers are found as follows:

To divide a number by the nth power of 10, the decimal digit in the number is moved n units to the right.

The fraction that represents 10% of a number is given as follows:

10/100 = 1/10.

Meaning that the number is divided by 10, which is the first power of 10, and thus the decimal digit is moved one unit right in the number.

The fraction that represents 1% of a number is given as follows:

1/100.

Meaning that the number is divided by 100, which is the second power of 10, and thus the decimal digit is moved two units right in the number.

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Answer:

Hey there! So the square root of 38 can be simplified by breaking it down into simpler parts. We can use a technique called prime factorization. We need to find the largest perfect square that is a factor of 38 and extract it from the square root. So, we can express 38 as 219 and that means we have 2^2=4 as the largest perfect square. Therefore, we can simplify the square root of 38 as 2sqrt(19).

It can't be simplified anymore, but it gives us a more manageable form. Let me know if you have any more questions, I'm happy to help!

________________________________________________________

A perfect square is a number that can be written in the form of n^2 (n raised to the power of 2) for some whole number n. For example 4, 9, 16, 25 and 36 are perfect squares. A way to determine if a number is a perfect square is by taking the square root of that number, if the result is a whole number it's a perfect square. Also, you can check it by finding the prime factorization of the number, if each of the prime factors appears in even power, it's a perfect square.

There are a few techniques that can make simplifying square roots quicker and easier:

Recognizing perfect squares (as described above) and extracting them from the square root

Using prime factorization to simplify the square root

Recognizing when the square root can be written as a rational number (a fraction of two integers)

Another way to approach is to factorise the radicand and combine any pairs of identical factors out from the square root.

Please let me know if you have any other questions on this topic or any other topic I could help with.

√38 is the simplest representation of the square root of 38.

The square root of a number is a value that, when multiplied by itself, gives the original number.

In the case of √38, we are looking for a number that, when multiplied by itself, equals 38.

Since 6 multiplied by itself is 36 and 7 multiplied by itself is 49, we can conclude that the square root of 38 lies between 6 and 7.

We cannot find a whole number that satisfies the equation √38 = x, where x is an integer.

Therefore, we express the square root of 38 as an irrational number, meaning it cannot be expressed as a simple fraction or a terminating or repeating decimal.

Hence, √38 is the simplest representation of the square root of 38.

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The Additive inverse of 3/2 is -2/3.

Additive Reciprocal

An additive reciprocal is a number that is added to a given number to bring the sum to zero. For example, adding -3 to the number 3 will result in zero. So the additive reciprocal of 3 is -3. In our daily life, we come across situations where we cancel the value of a quantity by forming its additive reciprocal.

Additive Reciprocal in Fraction:

The additive reciprocal of the fraction a/b is -a/b and vice versa. This is because a/b + (-a/b) = 0. The additive reciprocal of a positive fraction is the same fraction with a negative sign, but for negative fractions the additive reciprocal is the same fraction without a negative sign.

Given, the number is 2/3

We have to find the additive inverse of the given number.

In mathematics, the additive inverse of a number ‘a’ is the number that, when added to ‘a’, yields zero.

So, 2/3 + (-2/3)= 0

Therefore, the additive inverse of 2/3 is -2/3.

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Coordinate (0,1) of y-intercept implies that a line or curve cross the Y axis

at 1.

The location of a point on the cartesian coordinate plane where a straight line or curve line as well as a plane crosses the Y axis is called Y-intercept. The coordinate of y-intercept is expressed as (0, y). This y value is y-intercept. The X coordinate of y intercept is zero.

In case of an equation of line while writing in slope-intercept form it is denoted by b such as y = mx+ b

in the above equation, b is y-intercept and m is the slope.

The y -intercept given by coordinate (0, 1) defines that a straight-line or curve line cross the Y axis at 1. The x coordinate of y -intercept is always zero because over the Y axis there is no value of X.

The y-intercept can have negative or positive value.

Suppose we have an equation of line 4x + 8y + 10 = 0

                                we will write it in a slope-intercept form

                                     8y = -4x - 10

                                     y = - 4x/8 - 10/8

                                    y = -1/2x - 5/4

In the above equation - 5/4 or -1.25 is the y-intercept that means the line crosses the Y-axis at -1.25

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Answer:

a₄ = - 2

Step-by-step explanation:

to calculate a term in the sequence subtract 5 from the previous term

give first term a₁  = 13 , then

a₂ = a₁ - 5 = 13 - 5 = 8

a₃ = a₂ - 5 = 8 - 5 = 3

a₄ = a₃ - 5 = 3 - 5 = - 2

The equation is y = 1000 - 10x, where y is the number of blankets sold and x is the price in dollars.

This equation represents the relationship between the number of blankets sold (y) and the price of each blanket (x). The equation starts with the total number of blankets Christina has to sell (1000) and then subtracts 10 for every $1 increase in the price of the blanket. This means that as the price of the blanket increases, the number of blankets sold will decrease by 10 for every $1 increase. For example, if Christina charges $50 for a blanket, the number of blankets sold would be 500 (1000 - (10x50)).

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You went to the supermarket to buy 10 bananas. Each banana weighed 50 grams. If the price for bananas was $6.50 per kilogram, how much would you have to pay?

You do 10 x 50 = 500                     /                      Your bananas weigh 500g

$6.50 halved is $3.25                     /                       So $3.25 for 500g

So your answer is $3.25

Hope this helps! :)

The stem represents the tens place and the leaves represent the unit place of each data point, allowing for easy visualization of the distribution of the data.

A stem-and-leaf plot is a type of graph used to display the distribution of a set of data. It is a way to show the frequency of different values in a dataset. In this case, it is showing the number of days of snowfall at a winter sports resort for each of the past 171717 years.

Continuous and discrete data distributions are the two main forms found in statistics. Continuous data is information having a wide range of possible values. When measuring this kind of information, such weight or temperature, a scale is frequently used. A histogram is another tool for representing continuous data.

The complete question will be :

The stem and leaf plot shows the number of days of snowfall at a winter sports resort for each of the past years. represents a year with days of snowfall. Here is the five-number summary for these data Five-number summary According to the - IQR rule for outliers, how many high outliers are there in the data set?

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Answer:

0

Step-by-step explanation:

Pyramids have been a symbol of great architecture inventions of the mankind. Egyptian People were the first once to design pyramids on a very large level.

Let a be the Side of Area of base of Pyramid . The base of a pyramid is a square shaped quadrilateral

The Volume of the Pyramid with base area   and height  is given by the equation (1)

[tex]Volume = (1/3)Ah....(1)[/tex]

[tex]A = a^{2}[/tex]

[tex]a = Side[/tex]

A = [tex]a^{2}[/tex] = [tex]44cm^{2}[/tex]

[tex]h = 12.6[/tex]

Putting these values in equation (1) we get

[tex]Volume = (1/3)X44X12.6[/tex]

[tex]Volume[/tex] [tex]= 184.8cm^{3}[/tex]

Hence , the volume of the pyramid is 184.8cm³

Answer:yes

Step-by-step explanation:

yes

Answer:

Starbursts = 12 dollars

M&M = 2 dollars

1. Make Startbursts and M&Ms into "x"

(a) 1x + 2x = 12

2. 3*1= 3

4+2x=12

(b) 4 packs

This expression has no defined meaning. It is not a valid mathematical expression.

− [infinity] [infinity] is not a valid mathematical expression so it has no defined meaning.

The expression − [infinity] [infinity] is not a valid mathematical expression, and thus it has no defined meaning. It is not a valid mathematical expression because it contains two symbols, infinity and negative infinity, which do not interact with each other in any meaningful way. Infinity is a concept that is used to represent an unbounded or infinitely large value, while negative infinity is a concept used to represent a value that is infinitely small. When combined, these two symbols do not represent any meaningful mathematical quantity. Therefore, the expression − [infinity] [infinity] has no defined meaning.

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Answer:

66

Step-by-step explanation:

a^5

Answer:

16 929

Step-by-step explanation:

a1 = 22      d = 11     a 54  = 605

Sum = 54 ( 22 + 605) /2 = 16 929  

The height of an acute triangle can be calculated using the Pythagorean Theorem. The formula for this theorem is a2 + b2 = c2, where a and b are the two legs of a right triangle and c is the hypotenuse.

To find the height of an acute triangle, we must first identify the two legs of the triangle. The length of the two legs can be determined by measuring the lengths of the three sides of the triangle. Once we have the lengths of the two legs, we can apply the Pythagorean Theorem to calculate the length of the hypotenuse.

Once the length of the hypotenuse is determined, we can use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle. This formula states that the square of the height of the triangle is equal to the square of the hypotenuse minus the square of the two legs. So, to find the height of an acute triangle, we first measure the lengths of the three sides, then use the Pythagorean Theorem to calculate the hypotenuse, and finally use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle.The height of an acute triangle can be calculated using the Pythagorean Theorem. The formula for this theorem is a2 + b2 = c2, where a and b are the two legs of a right triangle and c is the hypotenuse. To find the height of an acute triangle, we must first identify the two legs of the triangle. The length of the two legs can be determined by measuring the lengths of the three sides of the triangle. Once we have the lengths of the two legs, we can apply the Pythagorean Theorem to calculate the length of the hypotenuse.

Once the length of the hypotenuse is determined, we can use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle. This formula states that the square of the height of the triangle is equal to the square of the hypotenuse minus the square of the two legs. So, to find the height of an acute triangle, we first measure the lengths of the three sides, then use the Pythagorean Theorem to calculate the hypotenuse, and finally use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle.

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After making the subject of [tex]$n^2=4 \mathrm{~d}+t^3 / t^3$[/tex] could be [tex]$\mathrm{t}=\sqrt[3]{4 d / n 2-1}$[/tex]

An expression is a combination of symbols, such as numbers and operators, that represent a computation or a value. Expressions can be used to perform calculations, assign values to variables, and control the flow of a program. They are a fundamental concept in computer programming.

Simplification is the process of making an expression or equation simpler, while still maintaining its meaning or function. This can be done by combining like terms, combining or removing unnecessary elements, or applying mathematical rules or identities.

For example, in algebra, simplifying an expression might involve combining the coefficients of similar terms (such as 2x + 3x = 5x), or factoring out a common factor from multiple terms (such as 2x^2 + 4x = 2x(x+2)).

Glven expression,

[tex]$$\begin{aligned}& n^2=4 \mathrm{~d}+t^3 / t^3 \\& n^2=4 \mathrm{~d} / t^3+t^3 / t^3 \\& n^2=4 \mathrm{~d} / t^3+1 \\& n^2-1=4 \mathrm{~d} / t^3 \\& t^3=4 \mathrm{~d} / n^2-1 \\& \mathbf{t}=\sqrt[3]{4 d / n 2-1}\end{aligned}$$[/tex]

Hence after making [tex]$\mathbf{t}$[/tex] the subject of[tex]$n^2=4 \mathrm{~d}+t^3 / t^3$[/tex] could be

[tex]$$\mathrm{t}=\sqrt[3]{4 d / n 2-1}$$[/tex]

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a) The flowchart for the congruency of triangles is given below.

b) The triangles are congruent as DQ ≅ XZ, PQ ≅ XY, and ∠PQD ≅ ∠ZXY.

What is congruency?

The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal.

In the given diagram, it can be seen that -

Line segment DQ = Line segment XZ.

Similarly, Line segment PQ = Line segment XY.

Since, the two sides of the triangle are equal, hence the third side must also be equal.

Line segment PD = Line segment ZY.

Also, in the diagram it can be seen that ∠PQD ≅ ∠ZXY.

Therefore, the triangles PDQ and ZXY are equal and congruent.

The flowchart for the same is given below.

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The percent increase is 50%.

The percentage increase in a quantity is the rate of difference in the old and new value to the old value, express in percentage.

i.e percentage increase = (old value - new value)/ old value

If the new quantity were be have decreased, then the percentage decrease can also be determined.

Considering the given question, the percentage increase can be determined by;

old quantity = 8

new quantity = 4

So that,

percentage increase = (old value - new value)/ old value

                                   = (8 - 4)/ 8 *100%

                                   = 4/ 8 * 100%

percentage increase = 50%

The percent increase is 50%.

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Personal assets are the list of things which are owned by any person for the present or the future use such as house , saving accounts, Cash etc.

Therefore, the personal assets represent the valuable  items owned by any individual for present or the future use.

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The value of the sequence is (c) 13, 25, 37, 49

The definition of the sequence is given as

a(1) = 13

a(n) = a(n - 1) + 12

The above definitions imply that we simply add 12 to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a(2) = 13 + 12 = 25

a(3) = 25 + 12 = 37

So, the sequence is 13, 25, 37

Hence, the value is (c)

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Note that It is not a good idea to guess what a value on a graph might be if it is beyond the points that are already plotted. The reason for this is that the guess might not be accurate. Generally, it is better to stay within the defined data limits.

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

Because they display information quickly and readily, graphs and charts are powerful visual aids. It's no surprise that graphs are widely utilized in print and electronic media. Data can often be easier understood when displayed as a graph rather than a table since the graph might illustrate a pattern or comparison.

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Answer:

x = 8

Step-by-step explanation:

x + 4 = 12

Subtract 4 from both sides

x = 8

Let's check

8 + 4 = 12

12 = 12

So, x = 8 is correct!

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Answer:

The slope of line r is -3/4

Step-by-step explanation:

First, let's find the slope of line q. We can find the slope by finding the change in y over change in x.

[tex]\displaystyle{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Therefore, substitute in:

[tex]\displaystyle{m=\dfrac{8-4}{6-3}}\\\\\displaystyle{m=\dfrac{4}{3}}[/tex]

Therefore, the slope of line q is 4/3. Since we want to find the slope of line r and we know by the given that line r is perpendicular to line q. By the definition of perpendicular line is [tex]\displaystyle{m_1m_2=-1}[/tex].

Let [tex]m_1[/tex] be slope of the line q which is 4/3. Therefore, substitute in and solve for [tex]m_2[/tex] (slope of line r)

[tex]\displaystyle{\dfrac{4}{3}m_2=-1}\\\\\displaystyle{4m_2=-3}\\\\\displaystyle{m_2=-\dfrac{3}{4}}[/tex]

Therefore, the slope of line r is -3/4

The first ferry's speed is 18.5 mph and the second ferry, which is slower, travels at 13.5 mph.

Let x represent the first ferry's speed.

The second, slower ferry's speed is then x-5 (since 5 miles per hour slower)

First ferry time equals distance/speed equals

50/x

Time spent on the second ferry:

50 / x - 5

The difference in times is 1 hour because the second ferry departs an hour earlier.

50 / x - 5 - 50/x = 1

50x - 50(x - 5) = x (x - 5 )

250 = x² - 5x

x² - 5x - 250 = 0

(x - 10 )(x + 5) = 0

x = 18.5 - 13.5

Speed can never be detrimental.

Therefore, the first ferry's speed is 18.5 mph.

and the second ferry, which is slower, travels at 13.5 mph.

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