2. What is the value of x? Show your work.


can someone explain this to me? how would I find X? Thank you in advance!​

The probability that a truck drives between 150 and 156 miles in a day is 0.0247. Using the standard normal distribution table, the required probability is calculated.

The formula for calculating the probability distribution for a random variable X, Z-score is calculated. I.e.,

Z = (X - μ)/σ

Where X - random variable; μ - mean; σ - standard deviation;

Then the probability is calculated by P(Z < x), using the values from the distribution table.

The given data has the mean μ = 120 and the standard deviation σ = 18

Z- score for X =150:

Z = (150 - 120)/18

   = 1.67

Z - score for X = 156:

Z = (156 - 120)/18

  = 2

So, the probability distribution over these scores is

P(150 < X < 156) = P(1.67 < Z < 2)

⇒ P(Z < 2) - P(Z < 1.67)

From the standard distribution table,

P(Z < 2) = 0.97725 and P(Z < 1.67) = 0.95254

On substituting,

P(150 < X < 156) = 0.97725 - 0.95254 = 0.02471

Rounding off to four decimal places,

P(150 < X < 156) = 0.0247

Thus, the required probability is 0.0247.

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1. Solving linear equations:

(a) x = 4.

(b) r = 2/3.

2. Proportion:

(a) When x = 40, y = 100.

(b) When x = 40, y = 4.

3. System of equations:

(a) r = 8, s = 3.

(b) p = 5, q = -2.

4. Graphing lines:

(a) The slope of the line through (3, 4) and (-1, 3) is 1/4.

(b) The slope of the line 3x - 4y = 7 is 3/4.

(c) The slope-intercept form of the line through (5, -2) and (-1, 6) is y = (-4/3)x + 14/3.

5. Introductory quadratics:

(a) The solutions to the equation 4x² = 81 are -9/2, and 9/2.

(b) The solutions to the equation x² + 8x + 12 are -6, and -2.

(c) The solutions to the equation x² - 3x - 88 are -8, and 11.

6. The weight of an orange is 1 unit, the weight of an apple is 5 units, and the weight of a banana is 2 units.

7. x = 3.

1. Solving linear equations:

(a) 3x - 7 = 9 - x,

or, 3x + x = 9 + 7,

or, 4x = 16,

or, x = 16/4 = 4.

Thus, x = 4.

(b) (7 - 2r)/3 = 4r,

or, 7 - 2r = 3*4r = 12r,

or, -2r - 12r = -7,

or, -14r = -7,

or, r = -7/-14 = 1/2.

Thus, r = 1/2.

2. Proportion:

(a) x and y directly proportion, means x/y = constant.

When x = 8, y = 20.

Thus, x/y = constant, or, 8/20 = constant, or, constant = 0.4.

When x = 40,

x/y = 0.4,

or, y = x/0.4 = 40/0.4 = 100.

Thus, when x = 40, y = 100.

(b) x and y indirectly proportion, means xy = constant.

When x = 8, y = 20.

Thus, xy = constant, or, 8*20 = constant, or, constant = 160.

When x = 40,

xy = 160,

or, 40y = 160,

or, y = 160/40 = 4.

Thus, when x = 40, y = 4.

3. System of equations:

(a) r - s = 5 ...(i)

3r - 5s = 9 ... (ii)

3*(i) - (ii) gives:

3r - 3s = 15

3r - 5s = 9

(-) (+)    (-)

_________

2s = 6,

or, s = 3.

Substituting in (i), we get

r - s = 5,

or, r - 3 = 5,

or, r = 8.

Thus, r = 8, s = 3.

(b) 3p + 7q = 1 ...(i).

5p = 14q + 53,

or, 5p - 14q = 53 ...(ii).

2*(i) + (ii) gives:

6p + 14q = 2

5p - 14q = 53

____________

11p = 55,

or, p = 5.

Substituting in (i), we get:

3p + 7q = 1,

or, 3*5 + 7q = 1,

or, 7q = 1 - 15 = -14,

or, q = -14/7 = -2.

Thus, p = 5, q = -2.

4. Graphing lines:

(a) Slope of the line through (3, 4) and (-1, 3) is,

m = (4 - 3)/(3 - (-1)),

or, m = 1/4.

Thus, the slope of the line through (3, 4) and (-1, 3) is 1/4.

(b) The graph given: 3x - 4y = 7.

Representing in the slope-intercept form, y = mx + b, gives:

3x - 4y = 7,

or, 4y = 3x - 7,

or, y = (3/4)x + (-7/4).

Thus, the slope of the line 3x - 4y = 7 is 3/4.

(c) Slope of the line through (5, -2) and (-1, 6) is,

m = (6 - (-2))/(-1 - 5),

or, m = 8/(-6) = -4/3.

Substituting m = -4/3 in the slope-intercept form, y = mx + b, gives:

y = (-4/3)x + b.

Substituting y = 6, and x = -1 gives:

6 = (-4/3)(-1) + b,

or, b = 6 - 4/3 = 14/3.

Thus, the slope-intercept form of the line through (5, -2) and (-1, 6) is y = (-4/3)x + 14/3.

5. Introductory quadratics:

(a) 4x² = 81,

or, 4x² - 81 = 0,

or (2x)² - 9² = 0,

or, (2x + 9)(2x - 9) = 0.

Either, 2x + 9 = 0 ⇒ x = -9/2,

or, 2x - 9 = 0 ⇒ x = 9/2.

Thus, the solutions to the equation 4x² = 81 are -9/2, and 9/2.

(b) x² + 8x + 12 = 0,

or, x² + 2x + 6x + 12 = 0,

or, x(x + 2) + 6(x + 2) = 0,

or, (x + 6)(x + 2) = 0.

Either, x + 6 = 0 ⇒ x = -6,

or, x + 2 = 0 ⇒ x = -2.

Thus, the solutions to the equation x² + 8x + 12 are -6, and -2.

(c) x² - 3x - 88 = 0,

or, x² - 11x + 8x - 88 = 0,

or, x(x - 11) + 8(x - 11) = 0,

or, (x + 8)(x - 11) = 0.

Either, x + 8 = 0 ⇒ x = -8,

or, x - 11 = 0 ⇒ x = 11.

Thus, the solutions to the equation x² - 3x - 88 are -8, and 11.

6. We assume the weight of one orange, one apple, and one banana to be x, y, and z units respectively.

Thus, we have:

3x + 2y + z = 15 ... (i)

5x + 7y + 2z = 44 ... (ii)

x + 3y + 5z = 26 ... (iii)

2(i) - (ii) gives:

6x + 4y + 2z = 30

5x + 7y + 2z = 44

(-)  (-)  (-)        (-)

______________

x - 3y = -14 ... (iv)

5(i) - (iii) gives:

15x + 10y + 5z = 75

x + 3y + 5z = 26

(-) (-) (-)          (-)

________________

14x + 7y = 49 ... (v)

14(iv) - (v) gives:

14x - 42y = -196

14x + 7y = 49

(-)    (-)     (-)

_____________

-49y = -245,

or, y = 5.

Substituting in (v), we get:

14x + 7y = 49,

or, 14x + 35 = 49,

or, x = 14/14 = 1.

Substituting x = 1 and y = 5 in (i), we get:

3x + 2y + z = 15,

or, 3 + 10 + z = 15,

or, z = 2.

Thus, the weight of an orange is 1 unit, the weight of an apple is 5 units, and the weight of a banana is 2 units.

7. 3/(1 - (2/x)) = 3x,

or, 3/((x - 2)/x) = 3x,

or, 3x/(x - 2) = 3x,

or, 3x = 3x(x - 2),

or, 3x = 3x² - 6x,

or, 3x² - 9x = 0,

or, 3x(x - 3) = 0.

Either, 3x = 0 ⇒ x = 0,

or, x - 3 = 0 ⇒ x = 3.

Since we had a term 2/x, x cannot be 0.

Thus, x = 3.

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The dividends per share on each class of stock for each of the four years for Seventy-Two Inc. are as follows:

                                            Year 1       Year 2        Year 3           Year 4

Distributed Dividends    $32,000    $40,000    $36,000        $36,000

Outstanding shares          60,000      60,000      60,000           60,000

Dividend per share           $0.53       $0.67          $0.60             $0.60

                                          Year 1       Year 2        Year 3           Year 4

Distributed Dividends    $0              $32,000     $44,000       $64,000

Outstanding shares        400,000    400,000     400,000       400,000

Dividend per share        $0              $0.08            $0.11              $0.16

                              3% Cumulative Preferred       Common Stock

Outstanding shares          60,000                        400,000

Par Value                            $20                              $25

Total value                       $1,200,000              $10,000,000

Annual dividend            $36,000 ($1,200,000 x 3%)

                                            Year 1       Year 2        Year 3           Year 4

Distributed Dividends    $32,000    $72,000    $80,000       $100,000

Cumulative Preferred      $32,000    $40,000    $36,000        $36,000

Common Stock                $0              $32,000    $44,000        $64,000

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Answer:

equation 1 has no solution

Step-by-step explanation:

when you compare each of the equations, all the equations gives a correct answer with the exception of equation 1

Esto significa que debemos tener 58 páginas de plástico para contener las 517 tarjetas.´

Sabemos que cada página puede almacenar hasta 9 cartas.

Entonces queremos ver cuantos grupos de 9 cartas hay en el conjunto de 517, para ver esto tomamos el cociente entre 517 y 9.

N = 517/9  = 57.44

Y no podemos tener un numero racional, así que debemos redondear al proximo número entero, que es 58.

Esto significa que debemos tener 58 páginas de plástico para contener las 517 tarjetas.

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The possible values of y are 9n where n is an integer greater than 0 equal to 0

The statement is given as;

y is a multiple of 9

The above means that

The number y can be divided by 9 without remainder

The numbers in this category are:

Numbers = 9, 18, 27, 36, 45......

This can be rewritten as:

Numbers = 9n where n is an integer greater than 0 equal to 0

Hence, the possible values of y are 9n where n is an integer greater than 0 equal to 0

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Answer:

1/7

Step-by-step explanation:

Lets start with the probability of flipping tails, 1/2.

Then the probability of the day starting with the letter s, 2/7.

Calculate the final probability by multiplying the two together.

[tex]\frac{1}{2}*\frac{2}{7}=\frac{2}{14}[/tex]

You can simplify 2/14 down to 1/7

Answer: y = 5.4

Step-by-step explanation: This is a proportional statement. So we can set up a system of proportions.

So we know when x is 5, y is 3. Thus, we can set up a proportion [tex]\frac{x}{y}[/tex] such that substituting will give [tex]\frac{5}{3}[/tex].

Now, we know when x is 9, y is some unknown number. So we can set up the second proportion as [tex]\frac{9}{y}[/tex].

Since 5/3 and 9/y are directly proportional, these 2 expressions are therefore equal. So we have [tex]\frac{5}3}[/tex] [tex]= \frac{9}{y}[/tex].

Cross multiplying, we get [tex]5y = 27[/tex].

Dividing by 5, we get [tex]y = 5.4[/tex]

Hope this helped!

There are 120 ways to color the 4 rectangles

The given parameters are:

Paints, n = 5

Rectangles, = 4

The number of ways to color the rectangles is

[tex]Ways = ^nP_r[/tex]

This gives

[tex]Ways = ^5P_4[/tex]

Apply the permutation formula

[tex]Ways = \frac{5!}{1!}[/tex]

Evaluate the expression

Ways = 120

Hence, there are 120 ways to color the 4 rectangles

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The equation of the ellipse in standard form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)

By analytical geometry we know that foci are along the major axis of ellipses and beside the statement we find that such axis is parallel to the x-axis of Cartesian plane. Then, the standard form of the equation of the ellipse is of the following form:

(x - h)² / a² + (y - k)² / b² = 1, where a > b     (1)

Where:

Now, we proceed to find the vertex and the lengths of the semiaxes:

a = 10 units.

b = 8 units.

Vertex

V(x, y) = 0.5 · F₁(x, y) + 0.5 · F₂(x, y)

V(x, y) = 0.5 · (3, 2) + 0.5 · (- 9, 2)

V(x, y) = (1.5, 1) + (- 4.5, 1)

V(x, y) = (- 3, 2)

The equation of the ellipse in standard form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)

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The conclusion that can be made based on the hypothesis is:

1. It's a valid conclusion.

2. It is a valid conclusion.

3. It is a valid conclusion.

According to the law of detachment, when the conditional and the hypothesis are true, the conclusion will be true.

Therefore, if 6x < 42, the value of x will also be less than 6. This is valid.

When an angle is more than 90°, it's an obtuse angle and since A is 103°, it's valid.

Also, the statement about the violin being a string instrument is logically valid.

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The given operation is not a vector space because it fails axiom 8 ("distributivity of scalar multiplication with respect to field addition").

A vector space can be defined as a space (set) which comprises vectors, whose elements can be added under the associative and commutative operation, and can be multiplied by scalars under the associative and distributive operation.

This ultimately implies that, a vector space must be comprised of at least one element, which is generally regarded as its zero vector and the smallest possible vector space.

For every element {u, v and w} in vector (V), and element {a and b} in vector (F), this 8th axiom must be satisfied in order to have a vector space:

(k + m)u = ku + mu

Note: The above axiom (k + m)u = ku + mu is generally referred to as the "distributivity of scalar multiplication with respect to field addition."

Given the following vector:

k(x, y, z) = {k²x, k²y, k²z}

If x₁ · x₂ ≥ 0, then, (kx₁) · (kx₁) = k²x₁y₁ ≥ 0 [Closed in scalar multiplication].

If x₁ · x₂ ≥ 0, x₂ · y₂ ≥ 0, then (x₁ + x₂) · (y₁ + y₂):

x₁y₁ + x₂y₂ + x₁y₂ + x₂y₁ < 0

x₁y₁ + x₂y₂ < -(x₁y₂ + x₂y₁) [Not closed in vector addition].

In conclusion, we can infer and logically deduce that the given operation is not a vector space because it fails axiom 8 ("distributivity of scalar multiplication with respect to field addition").

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Complete Question:

Determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail.

The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = {k²x, k²y, k²z}.

Answer:

11/12

Step-by-step explanation:

no of sample space=12

number of 7 to occur is 1/12

number of not 7:

since the total probability is 1

so 1-1/12=11/12

The rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)

The function is given as:

f(x) = 3x^3 + 2x^2 + 3x + 6

For a function P(x) such that

P(x) = ax^n +...... + b

The rational roots of the function p(x) are

Rational roots = ± Possible factors of b/Possible factors of a

In the function f(x), we have:

a = 3

b = 6

The factors of 3 and 6 are

a = 1 and 3

b = 1, 2, 3 and 6

So, we have:

Rational roots = ±(1, 2, 3, 6)/(1, 3)

Split the expression

Rational roots = ±(1, 2, 3, 6)/1 and ±(1, 2, 3, 6)/3

Evaluate the quotient

Rational roots = ±(1, 2, 3, 6, 1/3, 2/3, 1, 2)

Remove the repetition

Rational roots = ±(1, 2, 3, 6, 1/3, 2/3)

Hence, the rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)

The complete parameters are:

The function is given as:

f(x) = 3x^3 + 2x^2 + 3x + 6

The rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)

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Hi

6% increase is multiply by 1,06

done 40 times

so : 250* 1,06^40 = 2571 ,

Answer:

I believe it should be d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

About 1/4 scored higher and 3/4 scored lower

Step-by-step explanation:

84 is on the right side line

Each line represents 25 % of the score

It is 75 percent ( 3 lines) of the way

She scored higher than 75% of the students and lower than 25% of the students

About 1/4 scored higher and 3/4 scored lower

Answer:

f(x) = g(x) + 9 because it is shifted 9 to the right

The relationship between all pairs of special angles 1, 2, 3, and 4 created by transversal line b and parallel lines d and e include:

These are usually formed when two straight lines meet at a common endpoint or vertex.

Angles 3 and 4 are equal due to them being alternative interior angles and other relationships are mentioned above.

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Answer:

84,08964 [gr.].

Step-by-step explanation:

for more details see in the attachment.

The value of the median, lower and upper quartile

The minimum value = 10

The maximum value = 38

The median is the value that is found in the center of the data when it is ordered from lowest to highest. In the event that there is no value that precisely corresponds to the center, the value will be determined by taking the average of the values that are located on each side of the middle.

10  11  12  15  19  24  27  29  33  38

Median = 21.5

The intermediate value of the data that is located to the left of the median is known as the lower quartile.

10  11  12  15  19

lower quartile = 12

The intermediate value of the data that is located to the right of the median is known as the upper quartile.

24  27  29  33  38

upper quartile = 29

In conclusion, the 5 number summary is 10, 12, 21.5, 29, 38 → A

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Answer: minimum 10 first quartile 11.5 median 12.5 third quartile 16 maximum 20

Step-by-step explanation:

Answer: $3.2a

Step-by-step explanation: We need to decrease $8a by 60 percent because $8a is the price after a 60% increase. 8 x 6/10 is 48/10 which as a mixed number is 4 8/10 or 4.8. Now, we subtract 4.8 from 8 which yields our answer of 3.2.

Answer:

1.873

Step-by-step explanation:

Use the exponent rule for roots

[tex]\sqrt[4]{3^{7} } = 3^{\frac{4}{7} }=3^{0.5714} = 1.873[/tex]

Good luck!

Answer:

$15666.83 (2dp)

Step-by-step explanation:

Mean = Total of all values / Number of Values

= [tex]\frac{17484+14978+13521+14500+18540+14978}{6}[/tex]

=[tex]\frac{94001}{6}[/tex]

= $15666.83 (2dp)

Answer: [tex]x \leq 3[/tex]

Step-by-step explanation:

[tex]9-3x \geq 2(x-3)\\\\9-3x \geq 2x-6\\\\15-3x \geq 2x\\\\15 \geq 5x\\\\3 \geq x\\\\x \leq 3[/tex]

The time at Sydney when Dan rings his friend is 1 : 30 am (option B).

The first step is determine the time difference between London and Sydney.

Time difference = time at Sydney - time at London

( 12 + 10pm) - 12pm

22pm - 12pm = 10 hours

The second step is to add the time difference to the time it was when Dan rang.

15 : 30 pm + 10pm = 25 : 30

We know that there are only 24 hours in day, so subtract 24 hours from 25 : 30

25 : 30 - 24 = 1 : 30 am

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Answer:

Equation of a line has a form as below:

y=ax+b

Given:

b ( the y intercept)= -5

a ( the slope)= -3

so, y= -3x -5 is the equation of the line.

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