wei kiat is 4 times as old as hafiz. Find the ratio of Wei kiat's age to hafiz's age. pls help​

The reflection of Z (5 1/2, 3) across the x-axis is (5 1/2, -3).

Here,

The given point is Z (5 1/2, 3).

We have to find the point of reflection of Z (5 1/2, 3) across the x-axis.

What is Reflection across x-axis?

A point after reflection across the x-axis, the x- coordinate remains the same but y - coordinate is taken to be the additive inverse.

Now,

Since, The given point Z (5 1/2, 3) is lie on first coordinate.

Hence, The reflection of the point Z (5 1/2, 3) is lie on the third coordinate.

And, In the third coordinate the x-coordinate is positive and y-coordinate is negative.

Since, The rule of the reflection across x- axis is,

(x, y) → (x, -y)

So, The reflection of the point Z (5 1/2, 3) across the x - axis = (5 1/2, -3)

Therefore, The reflection of Z (5 1/2, 3) across the x-axis is (5 1/2, -3).

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Answer:

W = 8cm

L = 19cm

Step-by-step explanation:

The first step to solving these problems is always writing the information that is given into 2 equations.

Piece of info #1: Length is 5cm less than 3 times the width

Piece of info #2: Perimeter (of the rectangle, which has 4 sides) is 54cm

Turing these into equations...

Equation 1) L = 3*W - 5

Equation 2a) L+L+W+W = 54

Let's simplify that second equation:

Equation 2b) 2L+2W = 54

Now, we just solve the system of two equations by substitution. Take the known value of L from equation 1 and substitute it in for the value of L in equation 2b:

2*(3*W-5)+2W = 54

Now we solve for W:

6W - 10 + 2W = 54

8W - 10 = 54

8W = 64

W = 64/8

W = 8 cm

Now that we know W, we can substitute its value into either equation 1 or equation 2 to find L. Here, I'll randomly choose equation 1.

Equation 1) L = 3*W - 5

L = 3*8 - 5

L = 24-5

L = 19 cm

Answer:

AC = 12 cm

Step-by-step explanation:

AB=9 centimeters, you figure out what times what is 9. in this case, it is 3 for A and B. Then you go to BC=12 and 3 for B and 4 for C making it 12 So AC would equal 3x4.

The interval which describes the range of the provided function x^2 + 2 is negative infinity to two (-∞,2).

Domain of a function is the set of all the possible input values which are valid for that function. Range of a function is the set of all the possible output values which are valid for that function.

The given function is,

\(f(x) = x^2 + 2\)

The domain of this function is all real numbers. As the quadratic function has the constant value of 2. The vertex of the function is at 0,-2. Thus, the range of this function is,

\(y\in R, y\geq -2\)

Thus, the interval which describes the range of the provided function x^2 + 2 is negative infinity to two (-∞,2).

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The f(x) has a degree of 1, hence it is linear in nature while g(x) is a polynomial function because of the third degree.

The key features that they have in common are the y-intercept, domain, and range

Linear equations are equations that has a degree of 1 while polynomial equations are equations that has a degree of 2 and above.

Given the following functions

f(x) = –4x + 5 and;

g(x) = x^3 + x^2 – 4x + 5

Since the f(x) has a degree of 1, hence it is linear in nature while g(x) is a polynomial function because of the third degree.

The key features that they have in common are the y-intercept, domain and range

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The values of

AB = 9cm

BP = 7.2 cm

AP = 5.4 cm

The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

AB = √15² -12²

AB = √225 - 144

AB = √81

= 9cm

Using similar triangles theorem;

15/9 = 12/BP

represent BP by x

15x = 12 × 9

15x = 108

x = 7.2

Using Pythagorean theorem

AP = √ 9²-7.2²

AP = √81- 51.84

AP = √ 29.16

AP = 5.4

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Discrete values are the data values which are quantitative and the number of values is finite or countable.

What is discrete data?

In a count involving integers, there are only a finite number of potential values. It is impossible to break this kind of data into separate components. Discrete data consists of discrete variables that are non-negative, finite, numerical, and countable.

We are given interval, discrete, categorical and continuous values.

Of these, we need to find that which type of data values are quantitative and the number of values is finite or countable.

Interval data is quantitative but not countable because interval can range from infinity to infinity.

Discrete data is both quantitative and countable.

Categorical data is qualitative and not quantitative.

Continuous data is quantitative but not finite.

Hence, discrete values are the data values which are quantitative and the number of values is finite or countable.

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Answer:

1436.8 in³

Step-by-step explanation:

Volume of sphere = (4/3)πr³

r = 7

---> (4/3)π(7)³ = 1436.8 in³

Have a great day :)

Answer:

The volume of the sphere is A.

Answer:

49/9  or 5 4/9

Step-by-step explanation:

Answer:   8 4/9

Step-by-step explanation: Hope this helps :)

The lateral surface area of a rectangular prism is 2(l + w)h sq units.

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces).

The lateral surface area of a rectangular prism is given by

Where l, w, and h are the length, width, and height, respectively. To find the lateral surface area, we need the values of l, w, and h.

Without these values, it is not possible to determine the lateral surface area of the rectangular prism.

Therefore, the lateral surface area of a rectangular prism is 2(l + w)h sq units.

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The length of each piece of ribbon is 0.1 meters and the discount percentage is 75%

From the question, we have the following parameters

Length of the coaxial cable = 4/5 meters

Also, from the question;

We have

Number of pieces = 8

The length of each piece from the cable is the quotient of the Length of the coaxial cable and the number of pieces

This is represented as

Length of each piece = Length of the coaxial cable/Number of pieces

So, we have

Length of each piece = (4/5)/8

Evaluate the quotient

Length of each piece = 0.1

Hence, the length is 0.1 meter

Here, we have

Original price = $45.00

Purchased amount = $11.25

The discount is calculated as

Purchased amount = Original price * (1 -discount)

So, we have

11.25 = 45 * (1 - discount)

So, we have

1 - discount = 0.25

Evaluate

Discount  0.75

This gives

Discount = 75%

So, the discount is 75%

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In this probability case, the correct statements are:

A) There are 2 black socks.

C) There is at most 1 gray sock.

E) It is likely that a black sock is selected.

D) It is impossible to select a red sock.

Given that the probability of selecting a  black, white, or gray sock is 1, we can deduce that the total number of socks in the bag is "16".

Statement A  is correct because it state s that there are 2 black socks.

Statement C  is correct because it states that there is at most 1 gray sock, which means there can be either   0 or 1 gray sock.

Statement E   is correct because it states that it is likely to select a black sock.   Since the probability of selecting a white sock is 3/4, the probability of selecting a black  sock is higher  than that.

Statement   D is correct because  it states that it is impossible to select a red sock. The given information does not  mention any red socks, so the probability of selecting a red sock is 0.

Statement B is incorrect because it states that there are 12 white socks.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

A bag contains 16 socks.One sock is chosen at random.The probability of selecting a black,white,or gray sock is 1.The probability of selecting a white sock is 3/4.Selecting a gray sock is less likely than selecting a black sock.Which statements describe the situation?Choose all the correct answers.

A There are 2 black socks.

C There is at most 1 gray sock.

E It is likely that a black sock is selected.

B There are 12 white socks.

D It is impossible to select a red sock.

Answer:

69

Step-by-step explanation:

if it bisects that mean both angles are equal which tells us we can just divide the whole angle by 2

angle BOA is 138

so when you divide 138 by 2 you get 69

hope it helped

please mark brainiest

288 ounces of water are left in the water tank.

What is arithmetic?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots

Here, we have

Given: Tom has a water tank that holds 5 gallons of water. tell me this is water for my footing to fill six bottles they each hold 16 ounces and a picture that holds one over 2 gallons.

1 gallon = 128 ounces, 2 gallon = 256 ounces

6 bottles × 16 ounces = 96 ounces

2 gallon + 96 ounces = 256 + 96 ounces = 352 ounces

5 gallon = 5 × 128 = 640 ounces

= 640 - 352 = 288 ounces

Hence,  288 ounces of water are left in the water tank.

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To determine whether the furnace will be adequate for a 1,400 square foot house with a 9-foot ceiling, we need to calculate the volume of the house and compare it to the volume the furnace is designed to heat.

The volume of the house can be found by multiplying the square footage by the ceiling height:

1,400 sq ft x 9 ft = 12,600 cubic feet

Since the furnace is designed to heat 10,000 cubic feet, and the house has a volume of 12,600 cubic feet, the furnace may not be adequate for heating the house. The furnace is not capable to heat the entire house.

The ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) do not correspond to the intervals where the graph of f(x) is decreasing. The pairs (1, -2) and (-3, -18) are the correct ones.

To determine where the graph of f(x) is decreasing, we need to examine the intervals where the function's derivative is negative. The derivative of f(x) is given by f'(x) = -3x^2 - 8x + 3.

Now, let's evaluate f'(x) for each of the given x-values:

f'(-1) = -3(-1)^2 - 8(-1) + 3 = -3 + 8 + 3 = 8

f'(2) = -3(2)^2 - 8(2) + 3 = -12 - 16 + 3 = -25

f'(0) = -3(0)^2 - 8(0) + 3 = 3

f'(1) = -3(1)^2 - 8(1) + 3 = -3 - 8 + 3 = -8

f'(-3) = -3(-3)^2 - 8(-3) + 3 = -27 + 24 + 3 = 0

f'(-4) = -3(-4)^2 - 8(-4) + 3 = -48 + 32 + 3 = -13

From the values above, we can determine the intervals where f(x) is decreasing:

f(x) is decreasing for x in the interval (-∞, -3).

f(x) is decreasing for x in the interval (1, 2).

Now let's check the ordered pairs in the table:

(-1, -6): Not in a decreasing interval.

(2, -18): Not in a decreasing interval.

(0, 0): Not in a decreasing interval.

(1, -2): In a decreasing interval.

(-3, -18): In a decreasing interval.

(-4, -12): Not in a decreasing interval.

Therefore, the ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) are not located in the intervals where the graph of f(x) is decreasing. The correct answer is: (1, -2), (-3, -18).

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Note the complete and the correct question is

Q- Consider the function below, which has a relative minimum located at (-3, -18) and a relative maximum located at 1/3, 14/27).

\(f(x) = -x^3 - 4x^2 + 3x\).

Select all ordered pairs in the table which are located where the graph of f(x) is decreasing: Ordered pairs: (-1, -6), (2, -18), (0, 0),(1 , -2), (-3 , -18), (-4. , -12)

Answer:

Step-by-step explanation:

Using elimination method:

2x - y = 7

3x + y = 3

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

5x = 10

Divide both sides of the equation by 5

\( \frac{5x}{5} = \frac{10}{5} \)

Calculate

\(x = 2\)

Now, substitute the given value of X in the equation

3x + y = 3

\(3 \times 2 + y = 3\)

Multiply the numbers

\(6 + y = 3\)

Move constant to R.H.S and change it's sign

\(y = 3 - 6\)

Calculate

\(y = - 3\)

The possible solution of this system is the ordered pair ( x , y )

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

Check if the given ordered pair is the solution of the system of equation

\(2 \times 2 - ( - 3) = 7\)

\(3 \times 2 - 3 = 3\)

Simplify the equalities

\(7 = 7\)

\(3 = 3\)

Since all of the equalities are true, the ordered pair is the solution of the system

Hope this helps..

Best regards!!

Answer:

The total interest earned at the end of the year was $ 820, and the interest generated by the total deposited was 10.25%.

Step-by-step explanation:

Given that last year, Manuel deposited $ 7000 into an account that paid 11% interest per year and $ 1000 into an account that paid 5% interest per year, and no withdrawals were made from the accounts, to determine what was the total interest earned at the end of year and what was the percent interest for the total deposited, the following calculations must be performed:

7000 x 0.11 + 1000 x 0.05 = X

770 + 50 = X

820 = X

8000 = 100

820 = X

820 x 100/8000 = X

82,000 / 8,000 = X

10.25 = X

Therefore, the total interest earned at the end of the year was $ 820, and the interest generated by the total deposited was 10.25%.

The function that best models this scenario is C of x equals 3.75 times x if x is less than 5 and 3.25x plus 5 if x is greater than 6.

Let the number of hours be illustrated as x. In this situation, local city park rents kayaks for $3.75 per hour. This will be:

= 3.75 × x

= 3.75x

Also, customer rents for four or more hours, the cost is only $3.25 per hour, plus a $5 processing fee. This will be illustrated as:

= 5 + (3.25 × x)

= 5 + 3.25x

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Answer:

2( x + 1) = 18

2x + 2 = 18

2x = 16

x = 16/2 = 8

174 number of students must be in the 8th grade class.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that The eight grade class is planning a trip to Washington, D.C. this spring.

They need a minimum of 75 people to attend in order to reserve busses.

1/3 of the 8th grade class plus 17 parent chaperones have signed up and this is enough to satisfy the requirement,

We need to find the number of students must be in the 8th grade class

1/3x+17≤75

Subtract 17 on both sides

1/3x≤58

x≤174

Hence, 174 number of students must be in the 8th grade class.

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The value of integral is 3.

Let's evaluate the integral over the positive half of the interval:

∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx

Let u = 4 + 3sin(x), then du = 3cos(x) dx.

Substituting these expressions into the integral, we have:

∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du

Using the power rule of integration, the integral becomes:

∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]

Evaluating the definite integral at the limits of integration:

(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))

(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0

So, the value of integral is

= 3-0

= 3

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Answer:

\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)

Step-by-step explanation:

First, compute the indefinite integral:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)

To evaluate the indefinite integral, use the method of substitution.

\(\textsf{Let} \;\;u = 4 + 3 \sin x\)

Find du/dx and rewrite it so that dx is on its own:

\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)

Rewrite the original integral in terms of u and du, and evaluate:

\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)

Substitute back u = 4 + 3 sin x:

                            \(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

Therefore:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.

Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.

\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)

Therefore, the curve of the function is:

So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.

Integrate the function between -π and -π/2.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)

Integrate the function between -π/2 and π/2:

\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)

Integrate the function between π/2 and π.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)

To evaluate the definite integral, sum A₁, A₂ and A₃:

\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)

Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:

\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the given expression cannot be zero.

Answer:

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

Both cars will make same distance but the first one will be on road for 3 more hours.

Let the number of hours the first car in travel be x.

Then set an equation:

There is a Weak positive association between the amount of goals scored and the number of wins a hockey team has. Most of the data points fall between 4 goals scored and 5  number of wins. Causation cannot be established because their relationship was not in a controlled setting.

When if a relationship between two variables is said to be  negative, it is one that does not just necessarily mean that the association is weak. Although though both variables tend to increase in reaction to one another, a weak positive correlation depicts that the relationship is not very strong.

Therefore, even though  the data tells us that there is a weak positive relationship that exist between the two variables, it is vital to know that that correlation does not equal causation.

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Answer:

8

Step-by-step explanation:

the value of x is 8 because the sides are the same

Answer:

x = 590/11

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

50 + x + 10 + 8x + 2x = 650

Step 2: Solve for x

Answer:

x= 590/11

Step-by-step explanation:

Fyi you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free.

Answer:

Option A: Axis of symmetry: x = -0.5; Vertex: (-0.5, 0.75); f(x) = x2 + x + 1

Step-by-step explanation:

1) The axis of symmetry of quadratic graph is the vertical line that divides the graph curve into two congruent halves. In this case, it is: x = -0.5

2) Vertex is the point at which the graph curve changes direction or simply coordinates of the crest or trough of the curve.

The graph given has a trough with the coordinates: x = -0.5, y = 0.75. This is (-0.5, 0.75)

3) The roots of a quadratic equation are the points where the curve crosses the x-axis. In this case, it doesn't cross and so we have imaginary roots.

Now, formula for line of symmetry is; x = -b/2a

Thus; -b/2a = -0.5 or -b/2a = -1/2

Thus, b = 1 and a = 1

Our first and second terms will now be;

x² + x

Looking at the options, the only one with x² + x as it's first 2 terms is option A.

Thus, the complete equation will be x² + x + 1

Answer:

NO

Step-by-step explanation:

The objective of this surveys is to determine if the two surveys will reach a similar conclusion.

From the data given, we have  two test surveys here:

The survey is to measure the effect of an advertising campaign for a certain brand of detergent.

Now in the first survey; interviewers ask house- wives whether they use that brand of detergent and in the second survey  the interviewers ask to see what detergent is being used.

Let assume that the brand name of the detergent is KLIN ;

From this disparities of statement ; we anticipate that they will reach different conclusion. This is because; from the first survey people will either respond to the fact that they use the brand detergent (KLIN) or do not used the brand detergent. But in the second survey; when being asked to see what detergent that is being used. There are greater chance that they will bring out the detergent that is commonly used  which will eventually result to the same detergent .