Point O is the center of this circle. What is mzBCA?
A. 56
B. 62
C. 72
D.76

The probability that a compact car's randomly chosen mpg would be higher than 30 is 0.797.

Given data;

A certain compact car's mpg (miles per gallon) has a mean of 31 and a standard deviation of 1.2 and is regularly distributed.

We need to get the probability that the mpg for a randomly selected compact car would be more than 30.

Therefore;

Mean = μ = 31

Standard deviation = σ = 1.2

Let;

P(X > 30) = P(X - 31/1.2 > 30 - 31/1.2)

               = P(Z > -0.833)

               = 0.797

Hence, the probability that the mpg for a randomly selected compact car would be more than 30 is 0.797.

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The simplified form of the given expression; negative 1 and 2 over 3 minus 9 and 2 over 5 as required is; -166/15 (negative 166 over 15).

It follows from the task content that the simplified form of the given expression is to be determined.

Since the given expression is; -1 ⅔ - 9 ⅖.

First, the mixed numbers as in the task content must be converted to fractions so that we have;

- 1 ⅔ = -5/3 and

9 ⅖ = 47/5

Therefore, the required evaluation is; -5/3 - 47/5

= -25/15 - 141/15

= (-25 - 141) / 15

= -166/15

Therefore, the required simplified form of the expression is; negative 166 over 15.

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The correct equation is f(x) = 4x³ + 6x² − x .  A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

The value of the function is f(x). The slope of the line is m. b is either the function's value at x=0 or the position at which the line in the coordinate plane crosses the y-axis. x is the x-value. This form is called the slope-intercept form.

The slope of a linear function is calculated by rearranging the equation to its general form, f(x) = mx + c; where m is the slope.

in question f(-2) = - 6

so x= -2

In function f(x) = 4x³ + 6x² - x

F(-2) = 4(-2)³ + 6 (-2)² - (-2) = - 6

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Answer: the slope is unidentified

Step-by-step explanation:

The graph of the linear function f(x) = 3x + 4 is plotted.

For the given question, the function is given as;

f(x) = 3x + 4

Put x = 0, f(x ) = 4 ;(0, 4)

Put f(x) = 0, x = -1.33 ;(-1.33, 0)

Plot the points of the coordinate axis as shown in the graph.

Thus, the graph of the linear function f(x) = 3x + 4 is plotted.

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The function has a maximum value of 30 at x = 3.

Given Function:

f(x) = -3[tex]x^{2}[/tex]+18x+3

here a = -3 , b = 18 , c = 3

a is negative so it has maximum value

x = -b/2a

= -18/2*(-3)

= -18/-6

= 18/6

= 3

f(x) = -3*[tex]3^2[/tex] + 18*3 + 3

= -3*9+54+3

= -27+54+3

= 27+3

= 30

Therefore the function has a maximum value of 30 at x = 3.

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The equation of the function graphed for 0 ≤ x ≤ 360 is

Transformation is a term used in mathematics to refer to the movements made by objects.

Transformation that took place in the graph is of two types namely

The translation involves moving the graph downward by 1 unit. This movement shifts the graph from running across the x axis to making x axis the crest

The vertical stretch is by a factor of 2. A complete cycle would have been rom 0 to 180. however two cycles are now covered within this period.

The graph is of showing cos x (blue) and y = -1 + cos 2x (red) is attached

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Answer:  would be y=9x+10

Step-by-step explanation: Use the point slope form

The value of x by setting up equation is 16.

Given in question,

∠VZW = (2x + 32)°

∠RZY = (3x + 16)°

∠VZW = ∠RZY

2x + 32 = 3x + 16

2x - 3x = 16 - 32

        -x = -16

         x = 16

Hence, x = 16.

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Answer:

x = - 7 , x = 10

Step-by-step explanation:

(x - 10)(x + 7) = 0

equate each factor to zero and solve for x

x - 10 = 0 ⇒ x = 10

x + 7 = 0 ⇒ x = - 7

Answer:

f(5) = -5

Step-by-step explanation:

To find the value of f(5), find the value of y when x = 5.

To find the value of y from a given value of x, find the position of x on the x-axis, then trace vertically until you meet the line.

Once you meet the line, trace horizontally to the y-axis to find the corresponding value of y.

Therefore, the value of f(5) is -5.

See attachment.

Answer:

Step-by-step explanation:

Given the graph of the function f(x).

In order to find the value of f for any value of x on the graph, find the point x on the x-axis, then add a vertical line from this point to the graph. The y-coordinate of the intersection is the value of the function at given x-coordinate.

We are asked to find the value of f(5).

This is f(5) = - 5 as per above explanation.

See the attached for better understanding.

The solution of given system of linear equations is x = 3.6 and y = 2.5.

A "system" of equations is a collection of equations that you answer all at once. Ax + By + C = 0, where A and B are the coefficients and C is the constant, can be used to describe a linear equation. Non-linear equations are more difficult to comprehend than linear equations.

Solving the equations,

5x +4y = 8

10x − 4y = 46

Adding the above equations, we get

5x + 10x + 4y - 4y = 8 + 46

15x=54

Dividing by 15,

x = 3.6

Now, putting the value of x in second equation,

10(3.6) - 4y = 46

36 - 4y = 46

4y = -10

Dividing by 4, we get

y = -2.5

Therefore, the solution of given system of linear equations is x = 3.6 and y = 2.5.

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For a unimodal distribution which is symmetrical with a mean price of $2.11 and standard deviation of $0.56, a local grocer’s price of $3.50 in standard units would be 2.282 and it is unusually expensive.

A unimodal distribution refers to a distribution with one clear peak as the values increase to a single highest point after which they. It can be symmetrical or non-symmetrical. A symmetrical distribution refers to a distribution whose mean, mode, and median are all equal.

The standard score (z) is given by:

z = (x - µ)/σ where µ is the mean and σ is the standard deviation.

To determine the value of z for $3.50 price:

z = (3.5 – 2.11)/0.56 = 2.482

From the z-table, the probability of z ≥ 2.282

P (z ≥ 2.282) = 1 – P (z < 2.282) = 1 – 0.98876 = 0.0112 or 1.12%

Hence, the price of $ 3.50 is unusually high.

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Answer:

D

Step-by-step explanation:

there are no restrictions on the domain and

- ∞ < x < ∞

That is the domain is all real numbers

The total number of times the dice will land on 1 or on 5 is 153.

What is probability?

All of the probabilities will add up to 1. This gives us the equation.

P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1

P(1) + 0.17 + 0.08 + 0.16 + 0.14 + 0.1 = 1

P(1) + 0.65 = 1

P(1) = 1 - 0.66

P(1) = 0.35

We now need to find the probability of 1 or 5.

P( 1 or 5) = P(1) + P(5)

= 0.35 + 0.16

= 0.51

We now use the predicting outcomes formula

Expected = P( 1 or 5) * No. of times

= 0.51 * 300

= 153

Hence, the total number of times the dice will land on 1 or on 5 is 153.

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The values of x and y are 3 and 4.

Given:

shows an equilateral triangle with the lengths of its sides given in terms of x and y.

A 4x cm B 3y cm C (x + y + 5) cm

In equilateral triangle all sides are equal:

4x = 3y = x+y+5

4x = 3y

4x - 3y = 0.                            ---------eq(1)

4x = x + y + 5

3x - y = 5.                              ----------eq(2)

solving eq 1  -  eq 2*3 we get,

4x - 3y - 9x + 3y = 0 - 15

-5x = -15

x = 3

4x - 3y = 0

4*3 - 3y = 0

12 = 3y

y = 12/3

y = 4

Therefore The values of x and y are 3 and 4.

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The summation of 10 yards line and 15 yard is 25 yards and the ball represents zero situation when the ball is in net and goals.

Given,

The team receives the ball on their own yards = 10 yards.

that is,

initial position of the ball = 10 yards.

Using summation, (the summation is to add or subtract any two numbers or more terms by doing operation, to get answer).

They make a gain of 15 yards in the first play.

Their final position in 10 yards plus 15 yards

= 10 + 15

=25 yards.

Therefore, the yard line is 25 yards.

The zero situation of the game is when the ball is in net and the player make a goal.

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Answer:

parallel- same slope so the slope is 5, the slope will also be 5

perpendicular- reciprocal slope (if a whole # like 5, it goes to -1/5)

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The Probability that someone holds b.s. degree if it is known that he or she earns more than $100,000 is 0.75.

Considering the values given in the question,

P(earns more than $100000 without college education) = 0.2

P(earns more than $100000 with a B.S. or higher degree) = 0.6

P(Has a B.S. degree) = 0.5

P(earns more than $100000) = P(earns more than $100000 | without college education) × P(without college education) + P(earns more than $100000 | with a B.S. or higher degree) × P(has a B.S. degree)

= 0.2 × (1 - 0.5) + 0.6 × 0.5

= 0.4

P(at least a B.S. degree | earns more than $100,000) = P(earns more than $100000 | with a B.S. or higher degree) × P(has a B.S. degree) / P(earns more than $100000)

= 0.6 × 0.5 / 0.4

= 0.75

Therefore, If a person's income above $100,000 is known, there is a 0.75  probability that they have at least a b.s. degree.

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The scientific notation representation is 2.6 x [tex]10^{-2}[/tex].

Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We therefore employ scientific notations.

Given:

(0. 00032) (5.2 x [tex]10^6[/tex])/ 6.4 x [tex]10^5[/tex]

Now, solving the above expression

= 0.001664 x 10² / 6.4

= 0.00026  x 10²

= 2.6 x [tex]10^{-2}[/tex]

Hence, the scientific notation representation is 2.6 x [tex]10^{-2}[/tex].

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The equation that are equivalent to the equation 1/4 (8x + 56) = 20 are 56 + 8x = 80 and 2x = 6

The equation is

1/4 (8x + 56) = 20

Solve the equation

8x + 56 = 80

8x = 80 - 56

8x = 24

x = 24/8

x = 3

The first equation is

56 + 8x = 80

8x = 80 - 56

8x = 24

x = 24/8

x = 3

The second equation is

14 = 20 - 8x

8x = 20 - 14

8x = 6

x = 6/8

x = 3/4

The third equation is

2x + 14 = 5

2x = 5 - 14

2x = -9

x = -9/2

The fourth equation is

2x = 6

x = 6/2

x = 3

Hence, the equation that are equivalent to the equation 1/4 (8x + 56) = 20 are 56 + 8x = 80 and 2x = 6

The complete question is:

Which equations are equal to this equation? Select all that apply.

1/4 (8x + 56) = 20

a. 56 + 8x = 80

b. 14 = 20 - 8x

c. 2x + 14 = 5

d. 2x = 6

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Answer:

2/5

Step-by-step explanation:

flip 5/6 to become 6/5 then cross reduce then cross multiply

The total length of the sari Divya make is 6 yards, so option A is correct.

Four sides, four corners, and four right angles (90°) make up the enclosed 2-D shape known as a rectangle. A rectangle has opposite sides that are parallel and equal. A rectangle has length and width because it is a two-dimensional form. The length of a rectangle is its longer side; its breadth is its shorter side.

Given:

The length of saris Divya can make = 6 yards,

As the graph is showing,  to make a sari Divya required 6 yards of fabric,

Therefore, the total length of the sari Divya make is 6 yards.

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Answer:

1 ; -5 ; 2x

Step-by-step explanation:

1. We must have 0x equal to a number that is not 0

example = 1

5x - 5x = 5 + 1

0 = 6 (false)

2 we must have 0 = 0

-5

5x - 5x = 5 - 5

0 = 0

3 the x must stay

example = 2x

5x - 5 = 5x + 2x

2x = -5

2/2 x = -5/2

x = -5/2

Answer:

  no

Step-by-step explanation:

You want to know if side lengths 26 in, 36 in, 46 in form a right triangle.

The integer side lengths will form a right triangle if they are a Pythagorean triple, or a multiple of one.

We notice that these side lengths have a common difference of 10 in. That makes them an arithmetic sequence. The only Pythagorean triples that are an arithmetic sequence are {3, 4, 5} and its multiples. The shortest side is 3 times the common difference.

The lengths {26, 36, 46} cannot form a right triangle. The attachment shows the triangle is an obtuse triangle.

No, the triangle is not a right triangle.

__

Additional comment

The side lengths will form a right triangle if and only if they satisfy the relation a² +b² = c², where a, b are the two short sides.

  26² +36² = 1972 ≠ 2116 = 46²

The slope of the line perpendicular to the line 2x - 12y = 120 will be -6.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have the following equation -

2x - 12y = - 120

Rearranging the equation, we get -

2x - 12y = 120

12y = 2x - 120

6y = x - 60

y = (1/6)x - 10

The slope of the line perpendicular to the line 2x - 12y = 120 will be -

m[2] = -1 / (1/6) = - 6

m[2] = - 6

Therefore, the slope of the line perpendicular to the line 2x - 12y = 120 will be -6.

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