Calculate the length of the diagonal of the state of Wyoming.

The expression (a²b¹c)² × (6a³b) × (2c³)³ × (4ab¹) × (2c³) is equivalent to the expression 384a⁸b⁴c¹⁴.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

⇒ (a²b¹c)² × (6a³b) × (2c³)³ × (4ab¹) × (2c³)

By simplifying, we have

⇒ a⁴b²c² × 6a³b × 8c⁹ × 4ab¹ × 2c³

⇒ 384a⁸b⁴c¹⁴

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Answer:

3 gallons

Step-by-step explanation:

For every value of green ( 'x') ....white is 3 times as much

  for 1 gallon green     ====> 3 gallons white

Answer:

16.19

Step-by-step explanation:

Use the cosine rule:

[tex]\sqrt{a^{2} +b^{2} -2abcosy} \\\\\sqrt{16^{2} +20^{2} -(2)(16)(20)cos(52)} \\\\\\= 16.19cm[/tex]

Answer:

9

Step-by-step explanation:

The Pythagorean Theorem is a² + b² = c². c² is the hypotenuse while a² and b² are the legs.

So plugging it into the equation,

a² + 12² = 15²

a² + 144 = 225

a² = 81

a = 9

steps:

1. square the values

2. isolate the missing value

3. take the square root of both sides

Answer:

Step-by-step explanation:

hello :

Answer:

[tex]\fbox {2,400 pounds}[/tex]

Step-by-step explanation:

Information we have :

What we need to find :

Solving :

The value of x for a height 1 foot below the starting point will be the negative 2.76.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

A water ride with heights above and below the starting point can be modeled by the function is given below.

y = 3 sin⁡ (π / 2 (x + 3) − 2), Within the interval 0 < x < 5

We know that π / 2 = 90°

Then the value of x for a height 1 foot below the starting point will be

           1 = 3 sin⁡ (90 (x + 3) − 2)

        1/3 = sin⁡ (90 (x + 3) − 2)

   19.47 = 90 (x + 3) − 2

   21.47 = 90 (x + 3)

0.2385 = x + 3

          x = -2.76

Then the value of x will be the negative 2.76.

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Answer:

The first, third and last sequences

Answer:

1.a.  skew

1.b.  parallel

1.c.  none of the above

1.d.  perpendicular

1.e.  parallel

1.f.  skew

2.a.  never

2.b.  always

2.c.  always

2.d.  sometimes, sometimes, sometimes

Step-by-step explanation:

For these questions, it is critical to know the definitions of each of the terms.

Problem Breakdown

1.a.  skew  [tex]\overset{\longleftrightarrow}{AB} \text{ and } \overset{\longleftrightarrow}{EF}[/tex]

Point E is not on line AB.  Any three non-linear points form a unique plane (left face), so A, B, and E are coplanar.  Point F is not in plane ABE.  Since line EF and line AB do not intersect and are not coplanar, they are skew.

1.b.  parallel [tex]\overset{\longleftrightarrow}{CD} \text{ and } \overset{\longleftrightarrow}{EH}[/tex]

Line CD is parallel to line AB, and line AB is parallel to line EH.  Parallel lines have a sort of "transitive property of parallelism," so any pair of those three lines is coplanar and parallel to each other.

1.c.  none of the above  [tex]\overset{\longleftrightarrow}{AC} \text{ and } \overset{\longleftrightarrow}{GA}[/tex]

Line AC and line GA share point A, necessarily intersecting at A.  Therefore, line AC and line GA cannot be parallel or skew.

Any three points form a unique plane, so these two lines are coplanar, however, do they form a right angle?  If the figure is cube-shaped, as depicted, then no.

Note that each line segment AC, AG, and CG are all the diagonal of a cube face.  A cube has equal edge lengths, so each of those diagonals would be equal.  Thus, triangle ACG is an equilateral triangle.

All equilateral triangles are equiangluar, and by the triangle sum theorem, the measures of the angles of a planar triangle must sum to 180°, forcing each angle to have a measure of 60° (not a right angle).  So, lines AC and GA are not perpendicular.  (If the shape were a rectangular prism, these lines still aren't perpendicular, but the proof isn't as neat, there is a lot to discuss, and a character limit)

"none of the above"

1.d.  perpendicular  [tex]\overset{\longleftrightarrow}{DG} \text{ and } \overset{\longleftrightarrow}{HG}[/tex]

Line DG and line HG share point G, so they intersect.  Both lines are the edges of a face, so they intersect at a right angle.  Perpendicular

1.e.  parallel  [tex]\overset{\longleftrightarrow}{AC} \text{ and } \overset{\longleftrightarrow}{FH}[/tex]

Line AC is a diagonal across the top face, and line FH is a diagonal across the bottom face.  They are coplanar in a plane that cuts straight through the cube from top to bottom, but diagonally through those faces.

1.f.  skew  [tex]\overset{\longleftrightarrow}{CD} \text{ and } \overset{\longleftrightarrow}{AG}[/tex]

Point A is not on line CD, and any three non-linear points form a unique plane (the top face), so C, D, and A are coplanar.  Point G is not in plane ACD. Since line CD does not intersect and is not coplanar with line AG, by definition, the lines are skew.

2.a.  Two lines on the top of a cube face are never skew

Two lines are on a top face are necessarily coplanar since they are both in the plane of the top face.  By definition, skew lines are not coplanar.  Therefore, these can never be skew.

2.b.  Two parallel lines are always coplanar.

If two lines are parallel, by definition of parallel lines, they are coplanar.

2.c.  Two perpendicular lines are always coplanar

If two lines AB and CD are perpendicular, they form a right angle.  To form a right angle, they must intersect at the right angle's vertex (point P).

Note that A and B are unique points, so either A or B (or both) isn't P; similarly, at least one of C or D isn't P.  Using P, and one point from each line that isn't P, those three points form a unique plane, necessarily containing both lines.  Therefore, they must always be coplanar.

2.d.  A line on the top face of a cube and a line on the right side face of the same cube are sometimes parallel, sometimes skew, and sometimes perpendicular

Consider each of the following cases:

These 4 cases prove it is possible for a pair of top face/right face lines to be parallel, perpendicular, skew, or none of the above.  So, those two lines are neither "always", nor "never", one of those choices.  Therefore, they are each "sometimes" one of them.

Answer:

G. 0.45

Step-by-step explanation:

To find expected value, you simply multiply the value of each outcome (the numbers in the left column) by its probability

(the numbers in the right column) and then add them all together.

0(0.7) + 1(0.2) + 2(0.05) + 3(0.05)

0 + 0.2 + 0.1 + 0.15 = 0.3 + 0.15 = 0.45

The expected value is 0.45. Thus, the correct option is G.

In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

The expected value is calculated as,

E(x) = 0 x 0.70 + 1 x 0.20 + 2 x 0.05 + 3 x 0.05

E(x) = 0 + 0.20 + 0.10 + 0.15

E(x) = 0.45

Thus, the correct option is G.

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A. all real numbers

the doman are the x values and in this equation they are infinite making the domain all real numbers

Answer:

x=50

Step-by-step explanation:

3x-5=145(vertically opposite angle)

3x=145+5

3x=150

x=150/3

x=50

DON'T FORGET TO WRITE DEGREE

Answer:

x = 50

Step-by-step explanation:

Vertically opposite angles are of equal measure.

3x - 5 = 145

3x = 145 + 5

3x = 150

x = 50

That's all i know, Hope it helps!

Y=x+8

Table

[tex]\boxed{\begin{array}{c|c}\bf x&\bf y\\ \rm 2&\rm 10\\ \rm 0&\rm 8\\ \rm 4&\rm 12\end{array}}[/tex]

How?

x=2

x=0

x=4

Answer:

[tex]\large\begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 2 & 10 \\\cline{1-2} 0 & 8 \\\cline{1-2} 4 & 12 \\\cline{1-2}\end{array}[/tex]

Step-by-step explanation:

Given rule:

[tex]y=x+8[/tex]

The rule tells us that to the corresponding y-values, simply substitute the given value of x into the given rule:

[tex]x=2 \implies y=2+8=10[/tex]

[tex]x=0 \implies y=0+8=8[/tex]

[tex]x=4 \implies y=4+8=12[/tex]

Therefore, the completed table is:

[tex]\large\begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 2 & 10 \\\cline{1-2} 0 & 8 \\\cline{1-2} 4 & 12 \\\cline{1-2}\end{array}[/tex]

Using the normal distribution, it is found that 0.2119 = 21.19% of rainy days have rainfall with pH below 5.0.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 5.43, \sigma = 0.54[/tex]

The proportion of rainy days have rainfall with pH below 5.0 is the p-value of Z when X = 5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{5 - 5.43}{0.54}[/tex]

Z = -0.8

Z = -0.8 has a p-value of 0.2119.

0.2119 = 21.19% of rainy days have rainfall with pH below 5.0.

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The way to write this expression in mathematics is A'∩B

In order to get the right way to write this expression we have to break it down in two parts.

First we are told that some of the elements are not in A.

This is represented as A'.

Then we are told that they are in the set B. Hence we have it written as B.

Then the expression  not in set A but are in set B would be written as

A'∩B.

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Step-by-step explanation:

I'm going to assume you mean

[tex]log(5^{125})[/tex] which can be rewritten as [tex]125 log(5)[/tex] since if you start with [tex]log(a) = x = > 10^x=a\\(10^x)^c=a^c\\c *log(a^c)[/tex]since when you do (10^x)^c you're just multiplying the exponent which is represented by the x but is equal to the log you just multiply the log which is why you can bring it in front.

You can then approximate the value of log(5) using a calculator and multiply by 125 to get around 87.371

Answer:

Step-by-step explanation:

1 ft/s = 0.681818 mph

355.7 * 0.681818 = 242.5226626

355.7 ft/s = 242.5226626 mph

The probability that a class attendee is a non-member of the gym and is attending a barre class or is a member of the gym and is attending a boot camp class is 0.009.

Probability refers to a possibility that deals with the occurrence of random events.

The marketing team has gathered data from a random month, in which there were 2039 class attendees.

The probability that a class attendee is a non-member of the gym and is attending a barre class

= 185/2039

= 0.09

The probability that a class attendee is a member of the gym and is attending a boot camp class

= 204/2039

= 0.10004

The probability for both the event would be

= 0.09 x 0.10004

= 0.009

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Answer:

First Graph:  -2x - 1 = 3(^-x)

Last Graph: 2^(-x) + 2 = 5^-x + 3

Step-by-step explanation:

For a system of equations to have a solution set, the graphs that depict them must intersect at one point.

Both graphs #1 and #5 do not intersect, hence graphs #1 and #5 are the only graphs that do not have solutions while the other graphs do.

Answer:

[tex]\text{length of \textit{CA}} \ = \ 12.0 \ \ \ (\text{nearest tenth})[/tex]

Step-by-step explanation:

Radian measure is the ratio of the length of a circular arc to its radius.

A radian is the measurement of the central angle which subtends an arc whose length is equal to the length of the radius of the circle.

In the case of the unit circle, as shown in the figure below, one radian is the angle of the sector with a radius of 1 and circular arclength of 1.

Following this definition, the magnitude, in radians, of one complete revolution of a unit circle is the circumference of the unit circle divided by its radius, [tex]\displaystyle\frac{2\pi}{1}[/tex] or [tex]2\pi[/tex]. Thus, [tex]2\pi[/tex] radians is equal to [tex]360^{\circ}[/tex] degrees. Alternatively, one radian is equal to [tex]\displaystyle\frac{180^{\circ}}{\pi} \ \approx \ 57.296^{\circ} \ \ \ (3 \ d.p.)[/tex].

Since radian measure is defined as the ratio of the arc length of a sector to its radius, hence

                                                        [tex]\displaystyle\frac{s}{r} \ = \ \theta \\\\ s \ = \ r\theta[/tex]

where [tex]s[/tex] is the arclength, [tex]r[/tex] is the radius, and [tex]\theta[/tex] is the central angle, in radians.

Therefore, the length of CA is

                                           [tex]\displaystyle\frac{s}{\theta} \ = \ r \\ \\ r \ = \ \displaystyle\frac{26}{124^{\circ} \ \times \ \displaystyle\frac{\pi}{180^{\circ}} \ \text{rad}} \\ \\ r = \displaystyle\frac{26 \ \times \ 45}{31 \ \times \ 3.14} \\ \\ r\ = \ 12.0 \ \ \ \ \left(\text{nearest tenth}\right)[/tex]

1) The definitely true for the statement is b) P(-5) = 3.

2) The three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.

If there is a polynomial p(x), and a constant number 'a', then

[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]

where g(x) is a factor of p(x)

Given;

1) When the polynomial P(x) is divided by x+5, the remainder is 3.

If a polynomial P(x) is divided by (x-a), then the remainder is P(a).

If the polynomial P(x) is divided by (x+5), then the remainder will be P(-5).

So, P(-5) = 3

Therefore, the definitely true for the statement is b) P(-5) = 3.

2) P is a 3 degree polynomial with real coefficients and three zeros. Two of the zeros are 5 and 3+4i.

The complex roots always exist in conjugate pairs so,

3 + 4i and 3 - 4i

Thus, the three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.

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Answer:

you got that

Step-by-step explanation:

wet wet wet

Answer:

{ x : x > 2 }

Step-by-step explanation:

4x - 3 + 6x > 5x + 7 , that is

10x - 3 > 5x + 7 ( subtract 5x from both sides )

5x - 3 > 7 ( add 3 to both sides )

5x > 10 ( divide both sides by 5 )

x > 2

Answer:

Anita= 25 years old

Sumbo= 10 years old

Step-by-step explanation:

Start by forming 2 equations that represent the given information.

Let Anu's and Sumbo's ages be A and S respectively.

A= S +15 -----(1)

A² +S²= 725 -----(2)

Now, solve for A and S by substitution.

Substitute (1) into (2):

(S +15)² +S²= 725

Expand:

S² +2(S)(15) +15² +S²= 725

2S² +30S +225= 725

-725 on both sides:

2S² +30S -500= 0

Divide both sides by 2:

S² +15S -250= 0

Factorise:

(S +25)(S -10)= 0

S +25= 0             or            S -10= 0

S= -25 (reject)     or            S= 10

Sumbo's age cannot be a negative value hence -25 is rejected.

Substitute S= 10 into (1):

A= S +15

A= 10 +15

A= 25

The rate of the gas left in the tank will be -6 and the equation will be given as y = -6x + 20.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

The rate of gas will be calculated as:-

Suppose the hours are represented by x and the gallons are represented by y.

The rate of the gas will be the slope so the slope will be calculated as:-

[tex]m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m = \dfrac{2-20}{3-0}[/tex]

[tex]m =\dfrac{-18}{3}[/tex]

m = -6

The equation will be given as:-

y = mx + c

y  = -6x + 20

Therefore the rate of the gas left in the tank will be -6 and the equation will be given as y = -6x + 20.

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Step-by-step explanation:

as the velocity is not constant over time, we actually have to integrate v(t) over the interval 0<=t<=5 to get the distance.

v(t) = 60×ln(t + 1)

V(t) = 60 × integral(ln(t + 1)) between 0 and 5.

integral(ln(t + 1)) = (t + 1)ln(t + 1) - t + C

V(t) = 60 × ((t + 1)ln(t + 1) - t + C)

the distance traveled between t = 0 and t = 5 is then

60 × ((5 + 1)ln(5 + 1) - 5 + C) - 60 × ((0 + 1)ln(0 + 1) - 0 + C) =

= 60×(6ln(6) - 5 + C) - 60×(1ln(1) + C) =

= 60×(5.750556815... + C) - 60×C =

= 60×5.750556815... = 345.0334089... ≈ 345 km

Answer:

1/2 - 1/3,

1 - 1/2,

1/4 + 1/2

Step-by-step explanation:

1/4 + 1/2 = 1/4 + 2/4 = 3/4

1/2 - 1/3 = 3/6 - 2/6 = 1/6

1 - 1/2 = 2/2 - 1/2 = 1/2

Hence, the desired order is

1/2 - 1/3,

1 - 1/2,

1/4 + 1/2

James receives a pay increase of 100% per month and has a starting salary of $500.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let b represent the rate of pay increase and a represent the initial pay.

Let us assume that he had received 128000 after the 8 months. hence:

128000 = ab⁸   (1)

Also in the 10th month, he had received 512000, hence:

512000 = ab¹⁰    (2)

From the both equations:

a = 500, b = 2

rate of increase = 200% - 100% = 100%

James receives a pay increase of 100% per month and has a starting salary of $500.

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Using the concepts of domain and range of a function, the correct statement regarding the graph of the function f(x) = -(x + 3)(x - 1) is given by:

The domain is all real numbers, and the range is all real numbers less than or equal to 4.

In a graph:

The graph of f(x) = -(x + 3)(x - 1) is given at the end of the answer, hence:

Hence the correct statement is:

The domain is all real numbers, and the range is all real numbers less than or equal to 4.

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