Use a system of equations to find the cubic function f(x)=ax3+bx2+cx+d that satisfies the equations. Solve the system using matrices. f(−2)=−7; f(−1)=2; f(1)=−4; f(2)=−7

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:

Domain of [tex]f^{-1}[/tex]: R - {-3}   or  (-∞, -3) ∪ (-3, ∞)

Range of [tex]f^{-1}[/tex]: R - {10}     or  (-∞, 10) ∪ (10, ∞)

The domain of a function is the set of all possible input values (also known as independent variables) for which the function is defined. The range of a function is the set of all possible output values (also known as dependent variables) that the function can produce.

Given the function f, state the domain and range of both f and [tex]f^{-1}[/tex], where

[tex]f(x) =\frac{3x+4}{10-x}[/tex]

Domain and range using inequalities,

Domain of f: R - {10}  or  (-∞, 10) ∪ (10, ∞)

Range of f: R - {-3}     or  (-∞, -3) ∪ (-3, ∞)

The inverse does not exist.

[tex]f^{-1} (x) =\frac{10x-4}{x+3}[/tex]

Domain of [tex]f^{-1}[/tex]: R - {-3}   or  (-∞, -3) ∪ (-3, ∞)

Range of [tex]f^{-1}[/tex]: R - {10}     or  (-∞, 10) ∪ (10, ∞)

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Answer:

x = 2, y = -2

Step-by-step explanation:

To solve by substitution, you first need an isolated variable in one equation. Luckily, y is isolated in both equations.

Because y = y, we can set the other sides of the equations equal to each other.

x - 4 = 4x - 10 [substitute]

The next step is to isolate and solve for x

x = 4x - 10 + 4

x - 4x = -6

-3x = -6

x = 2

Next, you substitute x into both equations.

y = (2) - 4

y = -2

y = 4(2) - 10

y = 8 - 10

y = -2

Because both equations work out to the same value, you have the correct answer.

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:

The residual is the difference between the observed etching rate and the predicted etching rate

The residual of a room temperature of 25 degrees Celsius is[tex]=\frac{-2um}{min}[/tex]

The least squares regression equation for predicting the etching rate from the room temperature is given as:

[tex]y=2+\frac{1}{5}x[/tex]

When the room temperature is 25 degrees Celsius, the regression equation becomes

[tex]y=2+\frac{1}{5}*25\\\\y=7[/tex]

The residual is calculated as:

Residual = Observed - Predicted

From the question, the observed etching rate is,

[tex]=\frac{-2um}{min}[/tex]

So, the residual equation becomes-

[tex]r=5\frac{um}{min}-7\frac{um}{min}[/tex]

Evaluate the difference

[tex]r=-2\frac{um}{min}[/tex]

The residual of a room temperature of 25 degrees Celsius is[tex]=\frac{-2um}{min}[/tex]

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Answer: So get your rump in that chair and study your pp off

Step-by-step explanation:

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:

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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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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The probability that they will all be non fiction is 0.0667. The solution has been obtained by using hyper-geometric distribution.

What is hyper-geometric distribution?

When sampling from a small population without replacement, the hyper-geometric distribution is a discrete probability distribution that determines the likelihood that an event occurs k times in n trials.

The formula is

P (X = x) = h (x, N, n, k) = [tex]\frac{C_{k,x} * C_{N-k, n-x} }{C_{N,n} }[/tex]

We are given

x = 4

N = 10 + 12 = 22

n = 4

k = 12

Substituting this in the formula, we get

⇒P (X = 4) = h (4, 22, 4, 12) = [tex]\frac{C_{12,4} * C_{22-12, 4-4} }{C_{22,4} }[/tex]

⇒P (X = 4) = h (4, 22, 4, 12) = [tex]\frac{C_{12,4} * C_{10, 0} }{C_{22,4} }[/tex]

⇒P (X = 4) = h (4, 22, 4, 12) = 0.0667

Hence, the probability that they will all be non fiction is 0.0667.

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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:

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 total area of the deck once will be 575.5 ft²

Mathematically, the area of a rectangular deck can be calculated by using this mathematical expression:

Area of a rectangular deck, A = LW

Therefore, the area of the additional dimension can be calculated as follows;

Area of an additional dimension, A = 23.25 x 14

Area of an additional dimension, A = 325.5 ft².

Now, we can calculate the total area of this deck as ;

Total area = original area + new area

Total area = 250 ft² + 325.5 ft²

Total area = 575.5 ft²

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Based on the description, this study is most prone to differential misclassification of exposure status. The correct answer is A.

The description of the study suggests that the nurses who collected the data were poorly trained in the use of the male pattern baldness scale. This means that they may have misclassified some men as having male pattern baldness when they did not actually have it, and vice versa.

This misclassification of exposure status (i.e., male pattern baldness) is more likely to be differential because the nurses were unaware of the purpose of the study and did not know whether the men were cases or controls. This means that their misclassification of exposure status is likely to be influenced by the outcome (i.e., MI).

For example, if the nurses believed that male pattern baldness was a risk factor for MI, they may have been more likely to classify cases as having male pattern baldness and controls as not having it, even if this was not accurate. This would result in differential misclassification of exposure status, which can bias the study results. The correct answer is A.

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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

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]

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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Kylie changed the ratio of blue to yellow in her paint mixture from 5:3 to 3:4, making the colour more yellowy. She could have started with either 3.5 litres of blue and 2.1 litres of yellow, or 7 litres of blue and 4.2 litres of yellow. She could have added either 0.7 litres of blue and 3.5 litres of yellow, or 1.4 litres of blue and 7 litres of yellow to achieve the new ratio.

The new colour is more yellowy than the first colour because the ratio of blue to yellow has changed. Initially, the ratio was 5:3, or 5 parts blue to 3 parts yellow. After Kylie added more blue and 5 times as much yellow than blue, the ratio changed to 3:4, or 3 parts blue to 4 parts yellow. This means yellow is now the majority colour, which makes the final colour more yellowy than the first.

To calculate the amount of blue and yellow in the new mixture, we can use the equation:

Blue : Yellow = 3 : 4

Therefore, the amount of blue needed is 3/7 of the total, and the amount of yellow is 4/7 of the total.

2a) How many litres of each colour could Kylie have started with?

Possibility 1: Kylie could have started with 3.5 litres of blue and 2.1 litres of yellow (3.5 : 2.1 = 5 : 3).

Possibility 2: Kylie could have started with 7 litres of blue and 4.2 litres of yellow (7 : 4.2 = 5 : 3).

2b) How many litres of each colour could Kylie have added?

Possibility 1: Kylie could have added 0.7 litres of blue and 3.5 litres of yellow (0.7 : 3.5 = 3 : 4).

Possibility 2: Kylie could have added 1.4 litres of blue and 7 litres of yellow (1.4 : 7 = 3 : 4).

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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)

According the question given above The value οf x is 42

The pοlygοnal shape has three sides and three angles are called as a triangle. A triangle's internal angles are always added up tο 180 degrees.

In right triangles, the trigοnοmetric ratiοs οf sine, cοsine and tangent can be used tο find unknοwn angles and the lengths οf unknοwn sides. The sides οf the triangle are knοwn as fοllοws:

Given diagram the three angles οf a triangle is given,

sο the sum οf all three angles is equal tο  180 degrees.

Therefοre, (3x - 20) + (x - 1) + (x - 9) = 180°

By simplificatiοn,

5x - 30 =  180°

5x = 180 + 30

5x = 210

x = 42

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The factorized expression au maximum is:

(3x+6)(84x³ - 189x² + 20x + 69)

To factorize the given expression au maximum, (3x+6)(4x−9)+(3x+6)(7x−3)(3x+6)(4x−9)+(3x+6)(7x−3), follow these steps:

Look for common factors in the terms. Notice that (3x+6) is a common factor in all terms.

Factor out the common factor, (3x+6), from each term:

(3x+6)[(4x−9) + (7x−3)(3x+6)(4x−9) + (7x−3

Now simplify the expression inside the brackets:

(3x+6)[(4x−9) + (21x² - 39x - 18x + 27)(4x−9) + (7x−3)]

Distribute the terms inside the brackets:

(3x+6)[(4x−9) + (84x³ - 153x² - 36x² + 63x - 108x + 81) + (7x−3)]

Combine like terms:

(3x+6)[(4x - 9) + (84x³ - 189x² + 9x + 81) + (7x - 3)]

Add the terms inside the brackets:

(3x+6)[84x³ - 189x² + 20x + 69]

So, the factorised expression au maximum is:

(3x+6)(84x³ - 189x² + 20x + 69)

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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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Answer:

Step-by-step explanation:

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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The probability that a pigeon chosen at random will receive an incorrect test outcome is 103/10,000 = 0.0103, or roughly 1.03%.

Let's assume that there are 10,000 pigeons in the population. Then, 1.5% of them, which is 150 pigeons, are infected with the virus.

Out of these 150 infected pigeons, the test will correctly identify 97% of them, which is 145.5 pigeons. The remaining 4.5 infected pigeons will be incorrectly identified as not having the virus.

Out of the 9,850 uninfected pigeons, the test will correctly identify 99% of them, which is 9,751.5 pigeons. The remaining 98.5 pigeons will be incorrectly identified as having the virus.

Therefore, the total number of pigeons that get an incorrect test result is 4.5 + 98.5 = 103.

So, the probability that a randomly selected pigeon gets an incorrect test result is 103/10,000 = 0.0103 or approximately 1.03%

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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 Solution of the matrix for (x, y) is (-1, 5) that is:  [tex]\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}-1\\5\end{array}\right][/tex]

A matrix is described by its elements, which are the numbers or symbols that make up the matrix, and its dimensions, which indicate how many rows and columns there are in the matrix. A matrix's inverse is a matrix that yields the identity matrix when multiplied by the original matrix. A matrix's inverse is denoted by and only applies to square matrices (matrices with an equal number of rows and columns).

[tex]\left[\begin{array}{ccc}4&2\\-4&2\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}6\\14\end{array}\right][/tex]

find the inverse matrix for the matrix

[tex]\left[\begin{array}{ccc}4&2\\-4&2\end{array}\right][/tex]

Find the determinant,

determinant = 4 × 2 (-4) × 2 = 16

Inverse matrix is

[tex]1/16 \left[\begin{array}{ccc}4&2\\-4&2\end{array}\right]^T = 1/16 \left[\begin{array}{ccc}2&-2\\4&4\end{array}\right][/tex]

So, the solution of the equation is

[tex]\left[\begin{array}{ccc}x\\y\end{array}\right] = 1/16 \left[\begin{array}{ccc}2&-2\\4&4\end{array}\right] \left[\begin{array}{ccc}6\\14\end{array}\right][/tex]

On solving,

Therefor, The Solution for (x, y) is (-1, 5).

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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 number 4: Because there are four cards with the number four in a regular deck of 52 cards (4 suits each containing a four), the chance of getting a four is 4/52, which may be reduced to 1/13 or about 0.077.

• The number 7 or a Jack: A regular deck of cards has four sevens and four jacks, for a total of eight cards that are either a seven or a jack. Picking a 7 or a Jack has a chance of 8/52, which may be reduced to 2/13 or roughly 0.154. • A red card or a Queen: A normal deck has 26 red cards (13 diamonds and 13 hearts) and 4 queens. to avoid counting them twice, we must remove the two red queens. As a result, the total number of red or queen cards is 26 + 4 - 2 = 28. Picking a red card or a queen has a chance of 28/52, which may be reduced to 7/13, or roughly 0.538. • A Spade or an Ace: A regular deck of cards has 13 spades and 4 aces, but we must deduct the ace of spades to avoid counting it twice. Therefore there are 13 + 4 - 1 = 16 cards that are either a spade or an ace. As a result, the chance of selecting a spade or an ace is 16/52, which may be reduced to 4/13 or roughly.

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Answer:

Below

Step-by-step explanation:

the last equation shows frequency of 5 for  greater than this mass

  the equation before it covers 20 to 30 kg   frequency 11

      so it could be ZERO   or it could be ELEVEN are above 26 kg ....you just cannot tell ....so the MINIMUM frequency would be  5 + ZERO = 5

              and the MAXIMUM would be 5 + ELEVEN = 16