In a sociological survey, one was interested in estimating the percentage who had used cocaine in a population. Questions of this nature are sensitive and therefore the randomized response technique was used. A regular die was used to randomly distribute the questions. Respondents had to stand behind a screen and read the following instructions:
1) Roll the die once and if it shows 1 or 2 answer the question.
" Have you used cocaine at any time in the past year? "
2) If the die shows 3, 4, 5 or 6 answer the question.
"Does the die show an even number of dots?"
840 people took part in the survey and 314 yes and 526 no were received. Estimate the proportion who have used cocaine in the past year.
Answer with a proportion ie a number between 0 and 1. Use 4 correct decimal places.

Answer:

the answer could be: 1,2,3,4,5,6,7. If you are not sure about the answer than substitute the number that you pick and solve as if it was a normal equation.

Step-by-step explanation:

4-(3*x)<25

example:

4-(3*1)<25

4-3<25

1<25

Answer:

9

Step-by-step explanation:

No. of rolls Mark have =

[tex] \frac{288}{32} = 9[/tex]

pls mrk me brainliest

Answer:

10

Step-by-step explanation:

5+10=15

15×2=30

so the answer to your question is 10

Answer:

x = 10.

Step-by-step explanation:

Given: Two times the sum of 5 and some number is 30. What is the number?

First, write the equation:

2(5 + x) = 30

Simplify the brackets with distribution property:

10 + 2x = 30

Then collect like terms:

2x = 30 - 10

Finally, calculate:

2x = 20   (Divide both sides by 2)

x = 10

The solution is that the three consecutive even integers are 8, 10, and 12.

Let's assume the first even integer to be x. Since we are looking for three consecutive even integers, the second even integer will be x + 2, and the third even integer will be x + 4.

According to the problem statement, 3 times the first even integer is equal to 2 times the third even integer, which can be written mathematically as:

3x = 2(x + 4)

Solving for x, we get:

3x = 2x + 8

x = 8

Therefore, the first even integer is 8, and the second and third even integers are 10 and 12, respectively.

We can verify that 3 times the first even integer is indeed equal to 2 times the third even integer:

3(8) = 24

2(12) = 24

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The patient has formula feedings through a feeding tube. She is given 250 ml every 4 hours (0400, 0800, 1200, 1600, 2000, 2400) around the clock. The nurse gives 100 ml of water after each feeding.

The intake of the patient from 2300 to 0700 would be 750 ml.

The formula for calculating the patient's intake from 2300 to 0700

The formula to calculate the patient's intake from 2300 to 0700 is the following:

7 hours after 2300 ⇒ 7+24 - 23 = 8 hours before 0800

Thus, the patient's intake from 2300 to 0800 would be:

From 2300 to 2400 = 250 ml

From 2400 to 0400 = 250 ml

From 0400 to 0800 = 250 ml

From 0800 to 0700 = 100 ml (as it is less than 4 hours)

Total Intake = 250 ml + 250 ml + 250 ml + 100 ml = 850 ml

Intake from 2300 to 0700 = Total intake - Intake from 0800 to 0700

Intake from 0800 to 0700 = 100 ml

Total Intake = 850 ml - 100 ml = 750 ml

Therefore, The patient is receiving formula feedings through a feeding tube, administered every 4 hours (at 0400, 0800, 1200, 1600, 2000, and 2400). Following each feeding, the nurse administers 100 ml of water. It can be calculated that the patient's total intake during the period from 2300 to 0700 would be 750 ml.

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Answer:

Surface area of the sheet: 296 square meters

Area of tank: 480 cubic meters

Step-by-step explanation:

Don't forget your units!

"determine the iron sheet required for the fabrication" is asking for the surface area of the rectangular prism.

This is found by adding the five sides of the prism. The top side is excluded because it is open.

Front and back: 2(12m * 5m) = 120m^2

Left and right: 2(8m * 5m) = 80m^2

Floor: (12m * 8m) = 96m^2

120m^2 + 80m^2 + 96m^2 = 296m^2

The volume is found using standard methods. The open top does not have an impact here.

12m * 8m * 5m = 480m^3

The experimental probability that Sue will hit the bullseye on her next toss is 2/7.

What is the experimental probability?

The proportion of outcomes where a specific event occurs in all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.

Here, we have

Given: Sue is playing darts. So far, she has hit the bullseye 4 times and missed the bullseye 10 times.

We have to find the experimental probability that Sue will hit the bullseye on her next toss.

experimental probability = 4/(4+10) = 4/14 = 2/7

The next toss = P = 2/7

Hence,  the experimental probability that Sue will hit the bullseye on her next toss is 2/7.

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The probability that at least two policies will pay out before the insured parties have reached age 61 is 0.3400.

The answer is as follows: The expected number of policies that will pay out before the insured parties have reached age 61 isE(x) = np = 12 × 0.05 = 0.6Therefore, the expected number of policies that will pay out before the insured parties have reached age 61 is 0.6.b) The variance of the number of policies that will pay out before the insured parties have reached age 61 isVar(x) = np(1-p) = 12 × 0.05(1-0.05) = 0.570Therefore, the variance of the number of policies that will pay out before the insured parties have reached age 61 is 0.570.c) To find out the probability that at least two policies will pay out before the insured parties have reached age 61, we can use the complement rule that is:P(X ≥ 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)P(X = 0) = (0.95)^12 = 0.2835 (probability that none of the 12 policies will pay out before the insured parties have reached age 61)P(X = 1) = 12C1(0.05)(0.95)^11 = 0.3765 (probability that only one of the 12 policies will pay out before the insured parties have reached age 61)Therefore,P(X ≥ 2) = 1 - P(X = 0) - P(X = 1) = 1 - 0.2835 - 0.3765 = 0.3400Therefore, the probability that at least two policies will pay out before the insured parties have reached age 61 is 0.3400.

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Answer: To determine which size is the better buy, we need to calculate the cost per ounce for each size, taking into account the coupon for the regular size.

For the regular size, the cost per ounce is:

$8.00 / 20 oz = $0.40 per oz

With the $1.00 coupon, the cost for the regular size becomes:

$8.00 - $1.00 = $7.00

So the cost per ounce for the regular size with the coupon is:

$7.00 / 20 oz = $0.35 per oz

For the economy size, the cost per ounce is:

$10.00 / 40 oz = $0.25 per oz

Therefore, the economy size is the better buy as it costs only $0.25 per oz compared to $0.35 per oz for the regular size with the coupon.

Step-by-step explanation:

If a point has polar coordinates (4, - (3pi)/4) with the angle measured in radians, two additional polar representations of the points are  (4, 5pi/4) and (4, -11pi/4)

To find two additional polar representations of the point (4, - (3pi)/4), we need to add and subtract integer multiples of 2pi from the angle measure while keeping the same radius.

First, let's add 2pi to the angle measure:

(4, - (3pi)/4 + 2pi) = (4, 5pi/4)

This gives us a new polar representation of the same point with a positive angle measure within the interval [-2pi, 2pi].

Next, let's subtract 2pi from the angle measure:

(4, - (3pi)/4 - 2pi) = (4, -11pi/4)

This gives us another polar representation of the same point with a negative angle measure within the interval [-2pi, 2pi].

Therefore, the three polar representations of the point (4, - (3pi)/4) are:

(4, - (3pi)/4)

(4, 5pi/4)

(4, -11pi/4)

Each of these polar representations describes the same point in the polar coordinate system, but with a different angle measure.

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The area under the standard normal curve between z=-2.30 and z=1.8  by using the cumulative distribution function is 0.957.

Finding the area under the standard normal curve between two points requires the use of the cumulative distribution function. This function is given by the formula:

F(z) = 1/2 (1 + erf(z/√2))

Where erf is the error function.

We will use this formula to find the area under the standard normal curve between z=-2.30 and z=1.8.

The area under the standard normal curve between z=-2.30 and z=1.8 can be found using the following equation:

Area = F(z2) - F(z1)

Where z1 is the lower bound of the area and z2 is the upper bound of the area.

For our example, z1 = -2.30 and z2 = 1.8.

We can plug these values into the equation to find the area under the standard normal curve between z=-2.30 and z=1.8:

Area = F(1.8) - F(-2.30)

We can then use the cumulative distribution function to find the values for F(1.8) and F(-2.30):

F(1.8) = 1/2 (1 + erf(1.8/√2)) = 0.966

F(-2.30) = 1/2 (1 + erf(-2.30/√2)) = 0.009

Substituting these values into the equation:

Area = 0.966 - 0.009

Area = 0.957

Therefore, the area under the standard normal curve between z=-2.30 and z=1.8 is 0.957.

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The variance of a fair die that has been rolled 14 times and the number of faces that appear exactly three times is 2.33.

The variance of X can be calculated using the following formula:
Var(X) = Σ(P(X=x)*(x-μ)²)/N
Where Σ represents the summation of all possible outcomes, P(X=x) is the probability of an event occurring, x is the possible outcome, μ is the mean of all possible outcomes, and N is the number of trials.

In this case, the number of possible outcomes of a fair die is 6, and since the die has been rolled 14 times, N = 14. To calculate the mean, we use the formula μ = ΣP(X=x)*x, and in this case, the mean would be 3 since each face appears exactly 3 times.

Therefore, Var(X) = Σ(P(X=x)*(x-3)²)/14. We can then calculate the variance of X by substituting in the probabilities for each face: P(X=1) = 1/14, P(X=2) = 1/14, P(X=3) = 1/14, P(X=4) = 1/14, P(X=5) = 1/14, and P(X=6) = 1/14.

This yields a variance of 2.33, as calculated below:
Var(X) = (1/14 * (1-3)² + 1/14 * (2-3)² + 1/14 * (3-3)² + 1/14 * (4-3)² + 1/14 * (5-3)² + 1/14 * (6-3)²)/14
= 2.33.

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Answer:

-5m - 10

Step-by-step explanation:

1/3(3m+6)-2(3m+6)

= 1m + 2 - 6m - 12

= -5m - 10

So, the answer is -5m - 10

Answer:

-5(m+2)

Step-by-step explanation:

1/3(3m+6)-2(3m+6)

combine like terms

-5/3(3m+6)

Distribute

-5m - 10

common factor

-5(m+2)

Answer:

[tex]0.523[/tex]

Step-by-step explanation:

Total number of respondents = 313 + 286 = 599

Number who responded yes = number running a red light

[tex]\text P(\text {ran a red light)}}\\\\=\dfrac{\text{Number who ran a red light}}{\text{Total number of respondents}}\\\\= \dfrac{313}{599}\\\\= 0.52253[/tex]

Rounded to 3 decimal places the probability is [tex]0.523[/tex]

Answer:

17/125

Step-by-step explanation:

0.136×1000÷1×1000=136/1000

136/1000=17/125

Multiplying two numbers written in scientific notation can be done by multiplying their coefficients and adding their exponents, such as [tex](2.75 x 10^-2)[/tex] x [tex]10^(-2+8)[/tex] = [tex]6.875 x 10^6[/tex].

What does an expression mean?

Instead of using estimates produced at random, it is better to use rolling integer variables that can be increasing, decreasing, or blocking. They could only help one another by sharing tools, information, or solutions to issues.

In the given question,

(2.75 x [tex]10^-2[/tex]) (2.5 × [tex]10^8[/tex]) X​

To multiply two numbers written in scientific notation, you can simply multiply their coefficients and add their exponents. So:

(2.75 x [tex]10^-2[/tex]) (2.5 × [tex]10^8[/tex]) = (2.75 x 2.5) x [tex]10^(-2+8)[/tex] = 6.875 x [tex]10^6[/tex]

The result is 6.875 x 10⁶, which is the sum of (2.5 x 10⁸) and (2.75 x 10⁻²).

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The dictionary cost $36 if Merisa spent 3÷4 of her money on a dictionary. She spent 1÷2 of the remainder on a calculator.

What is Algebraic expression ?

In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a quantity or a relationship between quantities.

Let M be the total amount of money Merisa had before she made any purchases.

Merisa spent 3÷4 of her money on a dictionary, which means she spent 1÷4 of her money on the calculator and other expenses.

So, the amount of money she had left after buying the dictionary is:

M - 3÷4 M = 1÷4 M

She then spent 1÷2 of the remainder on a calculator, so:

(1÷2) (1÷4 M) = 1÷8 M

Let's call the cost of the calculator C.

We know that the dictionary cost $30 more than the calculator, so:

D = C + $30

We can now set up an equation to solve for C:

C + $30 = 3÷4 M

C = 3÷4 M - $30

And we also know that:

C = 1÷8 M

We can substitute the second equation into the first equation and solve for M:

1÷8 M + $30 = 3÷4 M

3÷4 M - 1÷8 M = $30

5÷8 M = $30

M = $48

So, Merisa had $48 before she made any purchases.

We can now use this to find the cost of the dictionary:

D = C + $30

D = (1÷8 M) + $30

D = ($6) + $30

D = $36

Therefore, the dictionary cost $36.

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Sol wants to paint 146.28 square feet of the wall light green.

The problem states that Sol has to paint 365.7 square feet of wall space, but he wants to paint only a fraction of the total area light green. The fraction he wants to paint light green is given as 0.4.

To find out how many square feet of the wall he wants to paint light green, we need to multiply the total area of the wall by the fraction of the area he wants to paint light green.

So, we can calculate the area of the wall that Sol wants to paint light green as:

Area of wall to be painted light green = 0.4 x 365.7

= 146.28 square feet

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a) Number of roots in the given polynomial is three.

b) Possible rational roots of the given polynomial are {±1, ±2, ±3, ±6, ±9, ±18}

c) The roots of the given polynomial are {2, 3i, -3i}.

Given polynomial is `P(x) = x³ - 2x² + 9x - 18`.a) Number of roots in the given polynomial is three. b) Possible rational roots of the given polynomial are expressed in the form of `p/q`, where p is a factor of the constant term `-18` and q is a factor of the leading coefficient `1`.Constant term of the given polynomial is `-18`. The factors of `-18` are 1, 2, 3, 6, 9, and 18. Leading coefficient of the given polynomial is `1`. The factors of `1` are ±1.∴ Possible rational roots of the given polynomial are {±1, ±2, ±3, ±6, ±9, ±18}.c) Let us check whether the possible rational roots satisfy the given polynomial. To check the roots, we can use synthetic division, which is an efficient method to check the roots of a polynomial. When `x = -1` is substituted in the given polynomial, we get P(-1) = (-1)³ - 2(-1)² + 9(-1) - 18= -1 + 2 - 9 - 18= -26, which is not equal to `0`.When `x = 1` is substituted in the given polynomial, we get P (1) = 1³ - 2(1)² + 9(1) - 18= 1 - 2 + 9 - 18=-10, which is not equal to `0`.

When `x = -2` is substituted in the given polynomial, we get  P(-2) = (-2)³ - 2(-2)² + 9(-2) - 18= -8 + 8 - 18 - 18= -36, which is not equal to `0`.When `x = 2` is substituted in the given polynomial, we get P(2) = 2³ - 2(2)² + 9(2) - 18= 8 - 8 + 18 - 18= 0, which is equal to `0`.∴ `x = 2` is a root of the given polynomial. By using synthetic division method, we can find the remaining two roots. x - 2 | 1 - 2 9 - 18| | 2 0 18| | 1 0 9 0|Therefore, the factors of the given polynomial are `(x - 2)(x² + 9)`.The quadratic factor, `x² + 9`, does not have any real roots, as the discriminant is negative.∴ The roots of the given polynomial are {2, 3i, -3i}.

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The sοlutiοn οf the given prοblem οf quadrilateral cοmes οut tο be DC  = 12 .

In mathematics, a rectangle is a fοur-sided οbject with fοur cοrners. Either "quad" οr "array οf inventive ideas" are Latin terms that were used tο cοin the phrase (meaning "side"). Fοur cοrners, fοur areas, and fοur cοrners are the three cοmpοnents οf a rectangle. Cοnvex and cοncave are the twο primary varieties οf cοnvex and cοncave fοrms. Cοnvex quadrilaterals alsο include the subdivisiοns οf trapezοids, geοmetric shapes, angles, rhοmbuses, and squares.

Here,

Assuming that ABCD is a trapezοid with parallel sides AB and CD, we can use the knοwledge that the perimeter οf a trapezοid is equal tο the sum οf its οppοsite sides tο cοnstruct the fοllοwing equatiοn:

=> AB = 52 + CD = BC + AD

Assuming AB = 13 and BC = 15, the equatiοn can be simplified as fοllοws:

=>  13 + CD + 15 + AD = 52

=>  CD + AD = 24

=> DC  = 12

Hοwever, we are unable tο determine the length οf DC οr AD withοut additiοnal details regarding the angles οr side lengths οf the trapezοid. As a result, there is nο clear sοlutiοn.

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Complete question:

Answer:

m = - 1

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (-2,0) (0, -2)

We see the y decrease by 2, and the x increase by 2, so the slope is

m = -2/2 = -1

So, the slope is -1

Answer:

m = - 1

Step-by-step explanation:

The ratio of water to lemon juice is 7:1. Thus, 7 cups of water are needed for 1 cup of lemon juice.

The table shows the proportional relationship between the amount of water and lemon juice needed to make lemonade in different quantities. The ratio of cups of water to cups of lemon juice remains constant for each quantity of lemonade. For example, to make 2 cups of lemonade, 1.5 cups of water are needed for every 1 cup of lemon juice. This means that if you want to make 4 cups of lemonade, you would need to double the amount of water and lemon juice required for 2 cups. This proportional relationship can be helpful in scaling the recipe up or down to make different quantities of lemonade.

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Complete question:

A drink recipe book has a table that shows the proportional relationship between cups of water and cups of lemon juice for different amounts of lemonade. If you need 6 cups of lemonade, the table shows you need 1 cup of lemon juice. Enter the number of cups of water needed for 1 cup of lemon juice.

Cups of Lemon Juice Cups of Water

1                                4

2                               8

3                               12

4                               16

a) The mean of the given probability distribution is 5.9.

b) The standard deviation of the given probability distribution is 4.64 (to 3 significant digits).

The mean and standard deviation of the discrete probability distribution with xi = 3, 5, 6, 7, 10 and p1 = 0.1, 0.3, 0.3, 0.2, 0.1 are as follows: Calculation of Mean The mean of the discrete probability distribution is calculated by multiplying each xi value by the probability pi, and then adding all the products together.μ = ∑ (xi . pi) = (3 × 0.1) + (5 × 0.3) + (6 × 0.3) + (7 × 0.2) + (10 × 0.1) = 5.9 Therefore, the mean of the given probability distribution is 5.9.Calculation of Standard Deviation The standard deviation of the discrete probability distribution is calculated using the formula below:σ = √[∑(xi - μ)² . pi]The calculations involved in finding the standard deviation are as follows:(3 - 5.9)² × 0.1 = 3.61(5 - 5.9)² × 0.3 = 0.49(6 - 5.9)² × 0.3 = 0.09(7 - 5.9)² × 0.2 = 0.49(10 - 5.9)² × 0.1 = 16.81σ² = 21.49Therefore, the variance is 21.49σ = √21.49 ≈ 4.639 ≈ 4.64 (to 3 significant digits)Hence, the standard deviation of the given probability distribution is 4.64 (to 3 significant digits).

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In order to solve for the measure of angle P, the equation x + y + z + w = 360° can be used.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles are measured in degrees or radians and are used to describe the direction of two intersecting lines in a plane. Angles are also used to measure the central angle of a circle and the angle between two curves.

This equation is known as the Angle Sum Theorem, which states that the sum of the measures of the angles of a triangle or a quadrilateral equals 360°. The measure of each angle of the quadrilateral can be used in the equation to solve for the measure of angle P, which is labeled as y. This equation can be written as x + y + z + w = 360° and then solved for the measure of angle P by subtracting x + z + w from both sides of the equation. This would result in y = 360° - (x + z + w). By substituting the measure of each angle into the equation, the measure of angle P can be found.

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The statement that is correct about the two angles that are said to be linear pair would be = <ABC and <CBD are adjacent angles. That is option A

A linear pair exists between angles that are on a straight line that are formed when two lines intersect eachother leading to the formation of the adjacent angles.

The linear angles are there said to be adjacent angles and the sum of these two angles are always = 180°.

Therefore from the given statements, the correct option about the two angles which are linear paired angles is that they are also adjacent to each other.

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The amount that is left over is: 65,500 - 59,499 = 6,001 pesos. A furniture dealer or business owner is referred to as a "mueblero" in Spanish.

The cost of the furniture was 2 x 7565 = 15,130 pesos in camas.

1 x 26,500 is equal to 26,500 pesos in a game of pool.

One times 17,869 equals 17,869 pesos in a rope.

Total expenditures were 15,130, 26,500, 17,869, and 59,499 pesos.

The amount that is left over is: 65,500 - 59,499 = 6,001 pesos.

A furniture dealer or business owner is referred to as a "mueblero" in Spanish. The question asks how much money the mueblero has left over after making the purchases since he had a specific amount of money to spend and acquired a number of items of furniture for his store.

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(A) The expected age μ of a super shopper 41.81

and, (B) the standard deviation σ for ages of super shoppers is 12.67

Given the data:

Age range, years 18-28 29-39 40-50 51-61 62 and over

Midpoint (x) 23 34 45 56 67

Percent of super shoppers 9% 46% 22% 11% 12%

Midpoint, x : 23 34 45 56 67

Frequency, f : 0.09_ 0.46 _ 0.22 __0.11 __ 0.12

The mean (m)= Σfx / Σf

= [(23 × 0.09) + (34 × 0.46) + (45 × 0.22) + (56 × 0.11) + (67 × 0.12)] ÷

                     (0.09 + 0.46 + 0.22 + 0.11 + 0.12)

= 41.81 / 1

Therefore, Mean = 41.81

Standard Deviation:

The standard deviation (or σ) is a measure of the distribution of data from the mean. A low standard deviation means the data is clustered around the mean, and a high standard deviation means the data is more scattered.

Standard deviation = Sqrt[(Σ(X² * f) / Σf) - m²)]

= ((23²× 0.09) + (34²× 0.46) + (45²× 0.22) + (56²× 0.11) + (67²× 0.12)) / 1

1908.51 - 41.81^2

= √(160.4339)

= 12.666250

= 12.67

Complete  Question:

Age range, years 18-28 29-39 40-50 51-61 62 and

over Midpoint x 23 34 45 56 67

Percent of super shoppers 9% 46% 22% 11% 12%

For the 62-and-over group, use the midpoint 67 years.

(a) Compute the expected age μ of a super shopper. (Round your answer to two decimal places.)

μ = yr

(b) Compute the standard deviation σ for ages of super shoppers. (Round your answer to two decimal places.)

σ = yr

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The graph that might be made by Johanna is graph (3).

Johanna has two variables: height and petal length. She plotted these variables on a graph to determine the relationship between them.

However, Johanna also found that there is one outlier in her data.

Each point on the graph represents the height and petal length of a single flower in Johanna's garden. The x-axis represents the height of the flower, and the y-axis represents the petal length.

Since there is a weak positive linear association between the two variables, the points on the scatter plot will be generally moving upwards from left to right.

In conclusion, Johanna's graph is most likely a scatter plot that shows the weak positive linear association between the height and petal length of the flowers in her garden, with one outlier that stands out from the rest of the data.

Hence the correct graph is (3).

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Complete Question:

Johanna measured the height and petal length of all the flowers in her garden. She plotted her results and found that the relationship between the variables suggests a weak positive linear association with 1 outlier.

Which of the following might be the graph Johanna made?

The trader bought 3 512 tables and 6(3 512) = 21 072 chairs.A table costs five times as much as a chair.

The cost of a chair is given as $1033. So, c = 1033Substituting c = 1033 in 5t + 1033 = 18 594,5t = 18 594 - 1033 5t = 17 561 t = 17 561/5 t = 3512.2Let c be the number of chairs and t be the number of tables.As the table costs 5 times as much as the chair, the total cost of the tables is 5t. The total cost of the chairs is c. The total cost of the tables and chairs is 5t + c = $18 594.Therefore, 5t + c = 18 594.The cost of a chair is given as $1033. So, c = 1033Substituting c = 1033 in 5t + 1033 = 18 594,

5t = 18 594 - 1033 5

t = 17 561

t = 17 561/5

t = 3512.2Therefore, the trader bought 3 512 tables and 6(3 512) = 21 072 chairs.

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The value of angle X in the given right triangle HXV is 59.5 ⁰.

The value of angle X in the given right triangle HXV is calculated by applying SOH CAH TOA identity as shown below.

SOH ⇒ sin θ = opposite side / hypothenuse side

CAH ⇒ cos θ = adjacent side / hypothenuse side

TOA ⇒ tan θ = opposite side / adjacent side

For the given triangle HXV, the value of angle X is calculated as follows;

cos X = 33 / 65

cos X = 0.5077

X = arc cos ( 0.5077 )

X = 59.5 ⁰

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