use true diagram below and the given information to choose the conclusion that is true.

the last 2 options are: m m m

Answer:

[tex]a,b\ \mathrm{and}\ d\ \mathrm{are\ correct\ statements\ because\ corresponding\ sides\ of\ similar}\\\mathrm{quadrilaterals\ are\ proportional\ to\ each\ other.}[/tex]

Considering all the relationships within the diagram, we can conclude that the statement "O[tex]m\angle1 > m\angle2[/tex]" must be true. This is because it is the only statement that follows the hierarchy established in the diagram.

Based on the given diagram, we can deduce that the numbers are arranged in a hierarchical structure. The numbers "12" and "10" are positioned at the top, indicating that they are the highest values in the hierarchy.

Next, we have "O[tex]m\angle4 > m\angle2[/tex]" and "O[tex]m\angle1 > m\angle3[/tex]" branching out from "12." This suggests that "12" is greater than both "O[tex]m\angle 4 > m\angle2[/tex]" and "O[tex]m\angle1 > m\angle3[/tex]."

Further down the hierarchy, we have "O[tex]m\angle1 > m\angle2[/tex]" branching out from "O[tex]m\angle4 > m\angle2[/tex]." This implies that "O[tex]m\angle4 > m\angle2[/tex]" is greater than "O[tex]m\angle1 > m\angle2[/tex]."

Lastly, we have "O[tex]m\angle1 > m\angle2[/tex]" branching out from "O[tex]m\angle1 > m\angle3[/tex]." This suggests that "O[tex]m\angle1 > m\angle3[/tex]" is greater than "O[tex]m\angle1 > m\angle2[/tex]."

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Lamar will have approximately $4782.47 in the account after 6 years, assuming no withdrawals are made.

To calculate the amount Lamar will have in the account after 6 years with a 3% interest rate compounded semiannually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the annual interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the number of years

In this case, Lamar deposited $4000, the interest rate is 3% (or 0.03), the interest is compounded semiannually (n = 2), and the period is 6 years (t = 6).

Plugging these values into the formula, we have:

A = 4000(1 + 0.03/2)^(2*6)

Calculating inside the parentheses first:

A = 4000(1 + 0.015)^(12)

Simplifying further:

A = 4000(1.015)^(12)

Now we can use a calculator or software to evaluate (1.015)^(12):

A ≈ 4000(1.195618)

A ≈ $4782.47

Lamar will have approximately $4782.47 in the account after 6 years, assuming no withdrawals are made.

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Answer:

Therefore, the area of the real object represented by the scale drawing is 54 square cm.

Step-by-step explanation:

To determine the area of the real object represented by a scale drawing, we need to consider the scale factor. In this case, the scale factor is 1:3, meaning that every unit on the scale drawing represents three units in the real object.

The area of the scale drawing is given as 6 square cm. To find the area of the real object, we need to scale up the area by the square of the scale factor. Since the scale factor is 1:3, the scaling factor is 3.

To find the area of the real object, we multiply the area of the scale drawing by the scaling factor squared:

Area of real object = Area of scale drawing × (Scaling factor)^2

Substituting the values, we have:

Area of real object = 6 square cm × (3)^2

Area of real object = 6 square cm × 9

Area of real object = 54 square cm

Therefore, the area of the real object represented by the scale drawing is 54 square cm.

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Answer:

) The number of men who attended the sessions can be obtained by summing up the number of males in each session:

Total number of men = 12 + 18 + 17 = 47

Therefore, 47 men attended the sessions.

b) The number of people who attended Session 3 can be obtained by summing up the number of males and females in Session 3:

Total number of people in Session 3 = 17 (males) + 5 (females) = 22

Therefore, 22 people attended Session 3.

c) The sample size refers to the total number of attendees across all sessions. We can calculate it by summing up the number of males and females in each session:

Sample size = (12 + 8) + (18 + 9) + (17 + 5) = 69

Therefore, the sample size is 69.

d) To calculate the probability that a randomly selected person is male, we need to divide the number of males by the sample size:

Probability of selecting a male = Number of males / Sample size = 47 / 69 ≈ 0.6812

Therefore, the probability that a randomly selected person is male is approximately 0.6812 (rounded to four decimal places).

e) To calculate the probability that a randomly selected person attended Session 3, we need to divide the number of people who attended Session 3 by the sample size:

Probability of attending Session 3 = Number of people in Session 3 / Sample size = 22 / 69 ≈ 0.3188

Therefore, the probability that a randomly selected person attended Session 3 is approximately 0.3188 (rounded to four decimal places).

f) To calculate the probability that a randomly selected person is male and attended Session 3, we need to divide the number of males in Session 3 by the sample size:

Probability of being male and attending Session 3 = Number of males in Session 3 / Sample size = 17 / 69 ≈ 0.2464

Therefore, the probability that a randomly selected person is male and attended Session 3 is approximately 0.2464 (rounded to four decimal places).

Answer:

Step-by-step explanation:

From the given figure,

a and b are the co- interior angles.

Co- interior angles on parallel sides are supplementary [add upto 180°]

[tex] \sf a + b = 180\degree[/tex]

[tex] \sf m\angle a + m\angle b = 180\degree[/tex]

Now simply the value of a and b here,

[tex] \sf 10x + 80 = 180 [/tex]

Subtract 80 from both sides,

[tex] \sf 10x + 80 - 80 = 180 - 80[/tex]

[tex] \sf 10x = 100[/tex]

Divide both sides by 10,

[tex] \sf \dfrac{10x}{10} = \dfrac{100}{10} [/tex]

[tex]\pmb {x = 10}[/tex]

So the value of x is 10.

Answer:

oaw2 232 acre is 468688$

Step-by-step explanation:

O MEASUREMENT Unit conversions involving acres and hectares After she retired, a corporate executive moved to wine country and bought a 326.7 acre (ac) vineyard. Use the facts to find the area of the vineyard in square feet (ft²). OA² X Conversion facts for area 1 acre (ac) = 43,560 square feet (t²) 1 square mile (mi²) = 640 acres (ac) 1 hectare (ha) 2.5 acres (ac) Note that means "is For this problem, treat as if it were =. approximately equal to".​

Answer:

If f(-5) = 7, then the point P(-5, 7) will be on the graph of f

where -5 is the x-coordinate and 7 is the y-coordinate

Step-by-step explanation:

Answer:

3 pages in 5 seconds.

Step-by-step explanation:

Answer:

First pair: Angle-Angle-Side

Second pair: Leg-Leg or Side-Angle-Side

The specified lengths and angles of the triangles indicates that the congruence theorem that guarantees the triangles are congruent are;

2) ΔBAC ≅ ΔEDC by the SAA congruence theorem

The right triangles are congruent by the LH congruence theorem

Congruent triangles are triangles that have the same shape and size.

2) The measure of the angles and sides in the triangles ΔBAC and ΔEDC indicates that we get;

m∠BAC = m∠EDC = 63°

∠ACB ≅ ∠DCE by the vertical angles theorem, therefore;

m∠ACB = m∠DCE (Definition of congruent angles)

The angle sum property indicates that we get; m∠CBA = m∠CED = 72°, therefore;

∠CBA ≅ ∠CED

[tex]\overline{AC}[/tex] is congruent to [tex]\overline{DC}[/tex], therefore;

Therefore, ΔBAC is congruent to ΔEDC by the Side-Angle-Angle , SAA, congruence theorem

Second figure;

The lengths of the legs of the right triangles are 2 units and 6 units, the length of the hypotenuse sides of the triangles, based on the Pythagorean theorem are therefore the same, the right triangles are therefore congruent by the Leg Hypotenuse, LH congruence theorem

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The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Answer:

x = 27 , ∠ EAF = 27°

Step-by-step explanation:

∠ GAF = 90° , then

∠ GAC + ∠ CAF = ∠ GAF , that is

x + 63 = 90 ( subtract 63 from both sides )

x = 27

∠ DAE = 90°

since CD is a straight angle of 180° , then

∠ CAE = 90° , so

∠ CAF + ∠ EAF = ∠ CAE , that is

63° + ∠ EAF = 90° ( subtract 63° from both sides )

∠ EAF = 27°

The total number of legs of the animals on the farm is 10010.Let's break down the information given and calculate the total number of legs of the animals.

Given:The farmer has 65 cows.The number of goats she has is thirty times the number of cows, which means she has 30 * 65 = 1950 goats.

The number of goats is two times the number of chickens. Let's denote the number of chickens as C. Therefore, we have 2C = 1950.

From the equation above, we can solve for C: C = 1950 / 2 = 975 chickens.

Now, let's calculate the total number of legs:

The number of cow legs is 65 * 4 = 260 legs.

The number of goat legs is 1950 * 4 = 7800 legs.

The number of chicken legs is 975 * 2 = 1950 legs.

Adding up all the legs, we have:

260 + 7800 + 1950 = 10010 legs.

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Answer:

A = 344 cm²

Step-by-step explanation:

we can calculate the area of the complete rectangle (outer) with sides  26 cm and 17 cm

then subtract the area of the inner white rectangle with sides 14 cm and 7 cm from the outer area to be left with the purple shaded area, that is

A = (26 × 17) - (14 × 7) = 442 - 98 = 344 cm²

The range and IQR values of the Boxplot given are 12 and 5 respectively.

Range = 56 - 44 = 12

IQR = 53 - 48 = 5

Therefore, the range and IQR values are 12 and 5 respectively.

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The expression representing the amount of canned food collected by the three friends is 5xy + 5x^2 + 9. The expression representing the number of cans the friends still need to collect to meet their goal is 3x^2 - 9xy - 1.

Part A: To represent the amount of canned food collected by the three friends, we need to add up the number of cans collected by each friend. Given:

Jessa: 5xy + 17

Tyree: x^2

Ben: 4x^2 - 8

The expression representing the total amount of canned food collected so far by the three friends can be obtained by adding these individual expressions:

Total collected = Jessa + Tyree + Ben

Total collected = (5xy + 17) + (x^2) + (4x^2 - 8)

Total collected = 5xy + x^2 + 4x^2 + 17 - 8

Total collected = 5xy + 5x^2 + 9

Part B: To represent the number of cans the friends still need to collect to meet their goal, we subtract the total amount collected so far from their goal. Given the goal expression:

Goal = 8x^2 - 4xy + 8

The expression representing the number of cans the friends still need to collect is:

Cans still needed = Goal - Total collected

Cans still needed = (8x^2 - 4xy + 8) - (5xy + 5x^2 + 9)

Cans still needed = 8x^2 - 4xy + 8 - 5xy - 5x^2 - 9

Cans still needed = 3x^2 - 4xy - 5xy - 1

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Answer:

Step-by-step explanation:

Part A: An expression that represents the amount of canned food collected so far by the three friends is 4x4 + 5xy + 9.

My work for Part A:

Step 1: Write each equation of each friend into one with addition signs in the spaces:

5xy + 17 + x2 + 4x2 – 8.

Step 2: Rewrite the expression to have like terms next to each other: 5xy + 17 – 8 + x2 + 4x2.

Step 3: Combine like terms: 17 – 8 = 9, x2 + 4x2 = 4x4, which will make the new equation,

5xy + 9 + 4x4.

Step 4: Rewrite the expression in standard form: 4x4 + 5xy + 9.

Part B: An expression that represents the number of cans the friends still need to collect is

– 4x4 + 8x2 – 9xy – 1.

My work for Part B:

Step 1: Write an expression that represents their canned food collection goal subtracted by their amount of canned food collected so far: 8x2 – 4xy + 8 – 4x4 – 5xy – 9.

Step 2: Rewrite the expression to have like terms next to each other: 8x2 – 4x4 – 4xy – 5xy – 9 + 8.

Step 3: Combine like terms: - 4xy – 5xy = -9xy, -9 + 8 = -1, which will make the new equation,

8x2 – 4x4 – 9xy – 1.

Step 4: Rewrite the expression in standard form: – 4x4 + 8x2 – 9xy – 1.

Hope this helps!

Answer:

Coordinates of City Center: (0, 0)

Coordinates of mall: (2, 5)

Coordinates of park: (-5, -5)

Distance from mall to park:

[tex] \sqrt{ {(2 - ( - 5))}^{2} + {(5 - ( - 5))}^{2} } [/tex]

[tex] \sqrt{ {7}^{2} +{10}^{2} } = \sqrt{49 + 100} = \sqrt{149} = 12.2[/tex]

The distance from the mall to the park is about 12.2 miles.

A description that is representative of the data presented in the graph include the following: B. The amount of rainfall increases as an exponential function of time.

In Mathematics and Geometry, an exponential function can be represented or modeled by using the following mathematical equation:

[tex]f(x)=a(b)^x[/tex]

Where:

Also, the growth factor or common ratio can be determined by using this formula;

Common ratio, b = a₂/a₁ = a₃/a₂ = a₄/a₃ = a₅/a₄ = a₆/a₅

In conclusion, we can logically deduce that this graph represents an exponential function because it has a growth factor or common ratio that remains constant over time.

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Answer:

(a) The average rate of change from 0 to 2 is 6

(b) The average rate of change from 3 to 5 is 24

(c) The average rate of change from -3 to 0 is -9

Step-by-step explanation:

The formula for the average rate of change (AROC) is given by:

[tex]AROC=\frac{f(b)-f(a)}{b-a}[/tex]

(a):

Finding the AROC from 0 to 2

To find the average rate of change from 0 to 2, we use f(2) and f(0), while we plug in 2 for b and 0 for a:

[tex]\frac{f(2)-f(0)}{(2-0)}\\ \\\frac{((3(2)^2+4)-(3(0)^2+4))}{(2-0)} \\\\\frac{(16-4)}{(2)}\\ \\\frac{12}{2}\\ \\6[/tex]

Thus, the average rate of change from 0 to 2 is 6.

(b):

Finding the AROC from 3 to 5:

To find the average rate of change from 3 to 5, we use f(5) and f(3), while we plug in 5 for b and 3 for a:

[tex]\frac{f(5)-f(3)}{(5-3)}\\ \\\frac{((3(5)^2+4)-(3(3)^2+4))}{(2-0)} \\\\\frac{(79-31)}{(2)}\\ \\\frac{48}{2}\\ \\24[/tex]

Thus, the average rate of change from 5 to 3 is 24.

(c):

To find the average rate of change from -3 to 0, we use f(0) and f(-3), while we plug in 0 for b and -3 for a:

[tex]\frac{f(0)-f(-3)}{(0-(-3))}\\ \\\frac{((3(0)^2+4)-(3(-3)^2+4))}{(0+3)} \\\\\frac{(4-31)}{(3)}\\ \\\frac{-27}{3}\\ \\-9[/tex]

Thus, the average rate of change from -3 to 0 is -9.

Step-by-step explanation:

when you have a set of data , you can plot those data points on a x vs. y graph, and estimate all the missing points in between, by studying the trend that your data follows (eg., your variables x and y seem to have a linear association, or a logarithmic one, or an exponential one, etc)

hope i made myself clear!

The rational function that is graphed above include the following: A. [tex]F(x)=\frac{1}{(x-1)(x-5)}[/tex].

In Mathematics and Geometry, a rational function simply refers to a type of function which is expressed as a fraction.

In order to graph any rational function, you should determine the values for which it is undefined. This ultimately implies that, a function is considered as undefined when the value of the denominator is equal to zero, which represents vertical asymptote lines.

When x = 1, the rational function becomes undefined;

F(x) = 1/(x - 1)(x - 5)

F(x) = 1/(1 - 1)(1 - 5)

F(x) = 1/(0)(-4)

F(x) = undefined.

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Answer:

The value of q is 0.35.

The value of p is 0.16.

The value of r is 0.27.

The value of P(A given NOT B) is approximately 0.4211.

To calculate the values of p, q, and r, we can use the information provided in the Venn diagram and the probabilities of events A and B.

Given:

P(A) = 0.43

P(B) = 0.62

P(A∩B) = 0.27

Calculating the value of p:

The value of p represents the probability of event A occurring without event B. In the Venn diagram, p corresponds to the region inside A but outside B.

We can calculate p by subtracting the probability of the intersection of A and B from the probability of A:

p = P(A) - P(A∩B)

= 0.43 - 0.27

= 0.16

Therefore, the value of p is 0.16.

Calculating the value of q:

The value of q represents the probability of event B occurring without event A. In the Venn diagram, q corresponds to the region inside B but outside A.

We can calculate q by subtracting the probability of the intersection of A and B from the probability of B:

q = P(B) - P(A∩B)

= 0.62 - 0.27

= 0.35

Therefore, the value of q is 0.35.

Calculating the value of r:

The value of r represents the probability of both event A and event B occurring. In the Venn diagram, r corresponds to the intersection of A and B.

We are given that P(A∩B) = 0.27, so the value of r is 0.27.

Therefore, the value of r is 0.27.

Finding the value of P(A given NOT B):

P(A given NOT B) represents the probability of event A occurring given that event B does not occur. In other words, it represents the probability of A happening when B is not happening.

To calculate this, we need to find the probability of A without B and divide it by the probability of NOT B.

P(A given NOT B) = P(A∩(NOT B)) / P(NOT B)

We can calculate the value of P(A given NOT B) using the provided probabilities:

P(A given NOT B) = P(A) - P(A∩B) / (1 - P(B))

= 0.43 - 0.27 / (1 - 0.62)

= 0.16 / 0.38

≈ 0.4211

Therefore, the value of P(A given NOT B) is approximately 0.4211.

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Step-by-step explanation:

First one

say the dimensions are   x * h

for the shaded pentagon   x * h = 4590

  for the unshaded one   d * x   *   d *h  =   510    ( 'd' is the dilation factor)

                                          d^2 *  x * h  = 510

                  but you know x * h = 4590           (underlined above)  

                                      so   d^2 * 4590 = 510    <=====solve for 'd'

                                               d^2 = 510/4590

                                                 d^2 = 1/9

                                                    d = 1/3

So each dimension is scaled by 1/3  

  21 m in the first pentagon is scaled by 1/3 to x in the second pentagon

     1/3 * 21 = x = 7 m

Think you can do the triangle one now?  (It's a little different)

   area =  1/2  x * y   = 16  

    new area =    1/2  d * x   *   d * y = d^2  * 1/2   x*y

               d^2  16   =   71  

                d = 2.1065

   so multiply the dimensions of triangle 1 by 2.1065to get the new larger triangle      2.1065 * x = 9.5    shows x = 4.5 in

Answer:

x = [tex]\sqrt{7}[/tex] is a solution

Step-by-step explanation:

(x² - 7)² + 2x² - 14 = 0 ← factor out 2 from last 2 terms

(x² - 7)² + 2(x² - 7) = 0 ← factor out (x² - 7) from each term

(x² - 7)(x² - 7 + 2) = 0

(x² - 7)(x² - 5) = 0

equate each factor to zero and solve for x

x² - 7 = 0 ( add 7 to both sides )

x² = 7 ( take square root of both sides )

x = ± [tex]\sqrt{7}[/tex]

x² - 5 = 0 ( add 5 to both sides )

x² = 5 ( take square root of both sides )

x = ± [tex]\sqrt{5}[/tex]

solutions are x = - [tex]\sqrt{7}[/tex] , [tex]\sqrt{7}[/tex] , - [tex]\sqrt{5}[/tex] , [tex]\sqrt{5}[/tex]

The sum of the areas in the density histogram is indeed one.

To form a frequency histogram, count the number of observations falling within each bin range. Here's the frequency histogram for the given Test Scores vector, with each bin representing a 15-point range starting at 45 and going to 105:

Bin Range | Frequency

45 - 59 | 3

60 - 74 | 6

75 - 89 | 8

90 - 104 | 4

To form a density histogram, calculate the density (frequency divided by the total count) for each bin range. Here's the density histogram for the Test Scores vector with breaks at (45, 50, 70, 85, 100):

Bin Range | Density

45 - 49 | 0.1304

50 - 69 | 0.1739

70 - 84 | 0.3043

85 - 99 | 0.2609

100 - 114 | 0.1304

To find the sum of the areas in the histogram, sum up the densities for all the bins. In this case, the sum of the areas should be equal to 1:

Sum of densities = 0.1304 + 0.1739 + 0.3043 + 0.2609 + 0.1304 = 1

So, the sum of the areas in the density histogram is indeed one.

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Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) [tex]\times[/tex] (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) [tex]\times[/tex](x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) [tex]\times[/tex](x + 1/2)

(y - 6) = -1/4 [tex]\times[/tex](x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

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False. The statement is incorrect. The given probability P(X > 0.59) does not provide sufficient information to calculate the probability P(4 < X < 5.9) accurately.

Given that P(X > 0.59) = 0.33, we know that the probability of X being greater than 0.59 is 0.33.

This implies that the area under the normal distribution curve to the right of 0.59 is 0.33.

Now, we want to find P(4 < X < 5.9), which represents the probability of X being between 4 and 5.9.

Since the normal distribution is symmetric, we can infer that P(4 < X < 5.9) is equivalent to finding the area under the curve between -0.59 and 0, and then multiplying it by 2.

Since P(X > 0.59) = 0.33, the area to the right of 0.59 is 0.33. Therefore, the area to the left of 0.59 is 1 - 0.33 = 0.67.

Since the normal distribution is symmetric, the area between -0.59 and 0 is the same as the area between 0 and 0.59.

Therefore, the area between -0.59 and 0 is also 0.67.

So, the area between -0.59 and 0 is 0.67, and when multiplied by 2, it gives us 1.34.

Hence, P(4 < X < 5.9) = 1.34, which is not equal to 0.17. Therefore, the statement is false.

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