Evaluate the expression

The solution is : the percentage of cars that are driving less than 45 mi/hr is 2.3%

Here, we have,

Since the speeds of cars are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = speeds of cars

µ = mean speed

σ = standard deviation

From the information given,

µ = 55 mi/hr

σ = 5 mi/hr

The probability that a car is driving less than 45 mi/hr is expressed as

P(x < 45)

For x = 45

z = (45 - 55)/5 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.023

Therefore, the percentage of cars that are driving less than 45 mi/hr is

0.023 × 100 = 2.3%

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4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.

5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.

In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;

RU ║ ST

Slope of side RU = Slope of side ST

Slope of RU = (y₂ - y₁)/(x₂ - x₁)

Slope of RU = (1 + 3)/(5 + 3)

Slope of RU = 4/8

Slope of RU = 0.5.

Slope of RS = (y₂ - y₁)/(x₂ - x₁)

Slope of RS = (-9 + 3)/(-4 + 3)

Slope of RS = -6/-1

Slope of RS = 6.

Slope of ST = (y₂ - y₁)/(x₂ - x₁)

Slope of ST = (-2 - 1)/(10 - 5)

Slope of ST = -3/5

Slope of ST = -0.6.

Slope of UT = (y₂ - y₁)/(x₂ - x₁)

Slope of UT = (-2 + 9)/(10 + 4)

Slope of UT = 7/14

Slope of UT = 0.5.

Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.

Question 5.

In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance RT = √[(-2 + 3)² + (10 + 3)²]

Distance RT = √170 units.

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance US = √[(5 + 4)² + (1 + 9)²]

Distance US = √181 units.

Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.

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Correct option is A, the iS point-slope form of the line is y+ 8 = -4(x-2). A straight line's equation can be written as both a point slope form and a slope intercept form.

A line equation written using a single line point and the slope of the line is the simplest definition of the term "point-slope form." The slope is expressed in point form as the ratio of the change in y values to the change in x values, also known as the rise over run (x, y).

The point slope form is useful when there is a slope and one or more points are present. Standard form is often easier to employ while doing algebraic computations. Depending on our needs or our level of expertise, we can alter the form of an equation. Both the point slope form and the slope intercept form can be used to express the equation for a straight line. The point slope form highlights any point on the line as well as the slope. The slope and y-intercept of a line are only shown in slope intercept form.

Given,

the slope of line = - 4 and point = (2,-8)

The equation of line = y - yo = m (x - xo)

where m = slope and x,y are coordinates

y + 8 = - 4 (x - 2)

y + 8 = - 4x + 8

y = - 4x

Therefore, the correct answer is option A, y+ 8 = -4(x-2)

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Answer:

Step-by-step explanation:

That means that its complement is 90 - 40 = 50 degrees. This also means that its supplement is 180 - 40 = 140 degrees. Therefore, a half of its supplement is 70 degrees and when added to the 50 degree complement the total is 120 degrees, just as the problem said it should be.

==========================================================

Explanation:

Let x be the unknown angle

Its supplement is 180-x, since it must add to x to get 180

The angle x is half of the supplement 180-x, meaning,

x = half of supplement of x

x = half of (180-x)

x = (1/2)*(180-x)

x = 0.5*(180-x)

x = 90 - 0.5x

x+0.5x = 90

1.5x = 90

x = 90/1.5

x = 60

The unknown angle is 60 degrees. It's supplement is 120 because 60+120 = 180, and we can see that 60 is half of 120. So that confirms we have the correct x value.

The last step is to find the complement of angle x. We subtract from 90 like so

90-x = 90 - 60 = 30 which is the final answer

As a check, we can see that 60+30 = 90 to show that we have complementary angles.

------------

Extra info:

It might be easy to mix up the terms "supplementary" and "complementary". What helps me remember is that "supplementary" and "straight angle" both start with S. This could be one way to remember that supplementary angles always add to 180.

Also, both "complementary" and "corner" both start with C, which may be one way to remember that complementary angles always add to 90.

Answer:

  745

Step-by-step explanation:

You want the original number of books in the library if adding 298 children's books increased the fraction of children's books from 2/5 to 4/7.

We often like to work problems like this in terms of "ratio units." Here, we'll let x represent the number of books in a ratio unit. This means the number of children's books is originally 2x, and the total number of books is originally 5x. Then we have ...

  (2x +298)/(5x +298) = 4//7

Cross multiplying gives ...

  7(2x +298) = 4(5x +298)

  3(298) = 6x . . . . . . . . . . . . . subtract (14x+4(298))

  149 = x

  745 = 5x . . . . . . the original number of books in the library

There were 745 books in the library at first.

__

Additional comment

If we let x represent the original number of library books, then the arithmetic involves more fractions. You would have an equation like ...

  2/5x +298 = 4/7(x +298)

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The value of df, when x = π/4 and dx = 1/24, is (-5π - 5√2)/(96√2).

To find the derivative of the function f(x) = -5cos(x) + xtan(x), we'll use the sum and product rules of differentiation. Let's start by finding df/dx.

Apply the product rule:

Let u(x) = -5cos(x) and v(x) = xtan(x).

Then, the product rule states that (uv)' = u'v + uv'.

Derivative of u(x):

u'(x) = d/dx[-5cos(x)] = -5 * d/dx[cos(x)] = 5sin(x) [Using the chain rule]

Derivative of v(x):

v'(x) = d/dx[xtan(x)] = x * d/dx[tan(x)] + tan(x) * d/dx[x] [Using the product rule]

= x * sec^2(x) + tan(x) [Using the derivative of tan(x) = sec^2(x)]

Applying the product rule:

(uv)' = (5sin(x))(xtan(x)) + (-5cos(x))(x * sec^2(x) + tan(x))

= 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Simplify the expression:

df/dx = 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Now, we need to evaluate df/dx at x = π/4 and dx = 1/24.

Substitute x = π/4 into the derivative expression:

df/dx = 5(π/4)sin(π/4)tan(π/4) - 5(π/4)cos(π/4)sec^2(π/4) - 5cos(π/4)tan(π/4)

Simplify the trigonometric values:

sin(π/4) = cos(π/4) = 1/√2

tan(π/4) = 1

sec(π/4) = √2

Substituting these values:

df/dx = 5(π/4)(1/√2)(1)(1) - 5(π/4)(1/√2)(√2)^2 - 5(1/√2)(1)

Simplifying further:

df/dx = 5(π/4)(1/√2) - 5(π/4)(1/√2)(2) - 5(1/√2)

= (5π/4√2) - (10π/4√2) - (5/√2)

= (5π - 10π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

Now, to evaluate df/dx when dx = 1/24, we'll multiply the derivative by the given value:

df = (-5π - 5√2)/(4√2) * (1/24)

= (-5π - 5√2)/(96√2)

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12121211.ooooooooooo

Answer:

The proportion of all correctly classified violins that are old is equal to the proportion of all new violins that are incorrectly classified.

Step-by-step explanation:

According to the table, we have that the correct option is:

5.)The proportion of all correctly classified violins that are old is equal to the proportion of all new violins that are incorrectly classified.

Statement 1:

15 of 33 new are correctly classified, thus, the proportion is:

\(p_N = \frac{15}{33} = 0.4545\)

18 out of 31 old, thus:

\(p_O = \frac{18}{31} = 0.58\)

Proportions are different, thus, statement 1 is false.

Statement 2:

13 out of 31 old are incorrectly classified, thus:

\(p = \frac{13}{31} = 0.4194\)

Different than 0.4545, thus, statement 2 is false.

Statement 3:

Out of 31 incorrectly classified, 13 are old.

Out of 33 correctly classified, 15 are new.

Different proportions, thus, statement 3 is false.

Statement 4:

Out of the 33 new, 15 are correctly classified and 18 incorrectly, different proportions, thus, statement 4 is false.

Statement 5:

18 out of 33 correctly classified are old.

18 out of 33 new violins are incorrectly classified.

Same proportion, thus, statement 5 is true.

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Answer: 3000

Step-by-step explanation: (6)(500)

3000

Answer:

2.83333333333

Step-by-step explanation:

(3 2/5) / (1 1/5) = 2.83333333333

Answer:

85/30 or 2.833333333

Step-by-step explanation:

When dividing fractions, you must find the reciprocal of the second number and multiply it as usual.

It is also much easier to solve after you convert these numbers to improper fractions.

In this case,

3 2/5 = 17/5

1 1/5 = 6/5

17/5 ÷ 6/5

17/5 x 5/6

85/30 (17/6 reduced)

or

2.83333333333333333333

Answer:

$2,880

Step-by-step explanation:

18 x 40 = 720 earned per week

720 x 4 (weeks) = 2880 earned in 4 weeks

Answer:

6

Step-by-step explanation:

mulyiplying is for finding out the area

The probability that the student chosen at random was male OR got an "A" is 31/58.

To find the probability that the student was male OR got an "A," we need to calculate the probability of each event separately and then add them together.

Let's calculate the probability of the student being male:

Total number of males = 11

Total number of students = 58

Probability of the student being male = Number of males / Total number of students = 11/58

Now, let's calculate the probability of the student getting an "A":

Total number of students who got an "A" = 20

Probability of the student getting an "A" = Number of students who got an "A" / Total number of students = 20/58

To find the probability of the student being male OR getting an "A," we add the two probabilities together:

Probability (Male OR A) = Probability (Male) + Probability (A) = 11/58 + 20/58 = 31/58

Therefore, the probability that the student chosen at random was male OR got an "A" is 31/58.

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The speed when the object and dropped from a height of 350 feet and takes exactly 5 seconds is 70 feet per seconds.

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity

In this situation, when dropped from a height of 350 feet, it takes exactly 5 seconds for the stone to hit the ground.

The speed will be:

= Distance / Time

= 350 / 5

= 70 feet per seconds

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Complete question

A moving object travels 350 feet in 5 seconds assuming that the object travels at a constant speed , When dropped from a height of 350 feet , It takes exactly 5 seconds for the stone to hit the ground. Calculate the speed.

400+315m>19,930

315m>19,530

m>62

Answer:

$1.30

Step-by-step explanation:

What you do is add the original 65 cents to the additional 65 cents that were shown to get 130. Since it's more than 100 you make it into dollars, so the final answer is $1.30.

Answer:

$1.30

Step-by-step explanation:

You need to know how coins look like. The middle one is a quarter and the other four are dimes. We know that quarters are worth 25 cents and dimes are worth 10 cents. Because there are 4 dimes, you do 4x10 which is equal to 40. We know that there is only one quarter so we do 40+25 which is equal to 65. Therefore, the tip is 65 cents Then, you add 65 cents to 65 cents again because Faaz had already put 65 cents there. 65+65 is equal to 130. 130 is equal to 1 dollar and 30 cents. Therefore, the tip is $1.30

Answer:

157.1

Step-by-step explanation:

We plug in what v is.

12.3(6)=73.8

Then we plug in what w is

11.9(7)=83.3

Lastly, we add the two numbers together to get 157.1

Hope it helped :)

Economies of scale occur when average cost declines with an increase in output. This occurs up to output level Q1.

Diseconomies of scale occur when average cost increases with an increase in output. This begins at output level Q3.

The phenomenon known as economies of scale occurs when the size or magnitude of the production generated by a business increases while the average cost per unit of output decreases.

The Long Run Average Cost Curve demonstrates how a firm's average expenses change over time. The shift from point A to point B illustrates how the cost per unit decreases as the curve slopes down. Because of economies of scale, the average cost grows less proportionally to output over the downward sloping region of the curve.

Minimum efficient scale is the level of output where economies of scale have been fully exploited.

A competitive firm produces at the minimum point of ATC in the long run and thus achieves productive efficiency.

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\( \cos(90 - ø) \)

Step-by-step explanation:

The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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Answer:

33mph

Step-by-step explanation:

because if u divide 99 by 3 that is the answer

In system of equations the condition for the system to have For part a) no solution are -2a+b+c ≠ 0,  have one solution are -2a+b+c = 0 and 11y + 8z = 3a+b has a solution. For part b)  have no solution are -2(c-b+2a) ≠ 0 and have one solution are -2(c-b+2a) = 0 and 2y + 3z = b has a solution. For part c)  has a unique solution for any values of a and b, there are no conditions on a and b for the system to have a solution. For part d)  no solution are a = b = c = 0. To have one solution are a ≠ 0, b ≠ 0, and c ≠ 0. For part (e), the system has no solution when b ≠ 0, and infinitely many solutions when b = 0. For part (f),has no solution when a = 1, and a unique solution when a ≠ 1.

(a) use Gaussian elimination to find its row echelon form.

The augmented matrix for the system is:

[ 3  1 -1 | a ]

[-1  2  5 | b ]

[ 5  3 -4 | c ]

Performing Gaussian elimination, we get:

Now we have three cases:

If -2a+b+c ≠ 0, then the last row of the row echelon form corresponds to the equation 0x + 0y + 0z = -2a+b+c, which has no solution.

If -2a+b+c = 0 and 11y + 8z = 3a+b has a solution, then the system has one solution.

If -2a+b+c = 0 and 11y + 8z ≠ 3a+b, then the system has infinitely many solutions.

Similarly, use Gaussian elimination to find its row echelon form. The augmented matrix for the system is:

[ 2  1 -1 | a ]

[ 0  2  3 | b ]

[ 2  1 -3 | c ]

Performing Gaussian elimination, we get:

[ 2  1 -1 | a ]

[ 0  2  3 | b ]

[ 0  0 -2 | c-b+2a ]

Now we have three cases:

If -2(c-b+2a) ≠ 0, which has no solution.

If -2(c-b+2a) = 0 and 2y + 3z = b has a solution, then the system has one solution.

If -2(c-b+2a) = 0 and 2y + 3z ≠ b, then the system has infinitely many solutions.

Writing the system in matrix form and using Gaussian elimination, we get:

[-1  3  2 | -8 ]

[ 0  0  1 |  2b+3 ]

[ 1 -3 -2 |  a   ]

Performing Gaussian elimination, we get:

[ 1 -3 -2 |  a   ]

[ 0  1  0 |  2b+3 ]

[ 0  0  1 |  2b+3 ]

This row echelon form corresponds to the following system of equations:

x - 3y - 2z = a

y = 2b + 3

z = 2b + 3

Therefore, the solution to the system is:

x = a + 6b + 9

y = 2b + 3

z = 2b + 3

Since the system has a unique solution for any values of a and b, there are no conditions on a and b for the system to have a solution.

Writing the system in matrix form and using Gaussian elimination, we get:

[ 1  a  0 | 0 ]

[ 0  b  1 | 0 ]

[ 0  0  c | 0 ]

Performing Gaussian elimination, we get:

[ 1  a  0 | 0 ]

[ 0  b  1 | 0 ]

[ 0  0  c | 0 ]

This row echelon form corresponds to the following system of equations:

x + ay = 0

y + bz = 0

z + cx = 0

The system has a unique solution (x = y = z = 0) if and only if a, b, and c are all nonzero.

(e) Writing the system in matrix form and using Gaussian elimination, we get:

[ 3 -1  2 | 0 ]

[ 3  1 -1 | 0 ]

[ 2 -2  3 | b ]

Performing Gaussian elimination, we get:

[ 3 -1  2 | 0 ]

[ 0  2 -3 | 0 ]

[ 0  0  0 | b ]

Now we have two cases:

If b ≠ 0, then the last row of the row echelon form corresponds to the equation 0x + 0y + 0z = b, which has no solution.

If b = 0, then the system corresponds to the equations 3x - y + 2z = 0 and 3x + y - z = 0, which can be rewritten as 6x = 0 and 2z = 0. This implies that x = 0 and z = 0. Substituting these values into the first equation, we get:

3(0) - y + 2(0) = 0

-y = 0

y = 0

Therefore, the solution to the system is (x, y, z) = (0, 0, 0). Since the system has a unique solution when b ≠ 0, the condition for the system to have no solution is b ≠ 0, and the condition for the system to have infinitely many solutions is b = 0.

(f) Writing the system in matrix form and using Gaussian elimination, we get:

[ 1  a -1 | 1 ]

[-1  a-2 1 | -1]

[ 1 -2 a-2 | 1 ]

Performing Gaussian elimination, we get:

[ 1  a -1 | 1 ]

[ 0  a-2 0 | 0 ]

[ 0  0 a-1 | 1 ]

Now we have two cases:

If a = 1, becomes 0 = 1, which has no solution.

If a ≠ 1, then the system has a unique solution. In this case, the system corresponds to the equations x + ay - z = 1, -x + (a - 2)y + z = -1, and x - 2y + (a - 2)z = 1/(a - 1). Solving for x, y, and z, we get:

x = (2 - a)/(a - 1)

y = -1/(a - 2)

z = (-a + 3)/(a - 1)

Therefore, the condition for the system to have no solution is a = 1, and the condition for the system to have a unique solution is a ≠ 1.

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Answer:

I just solved this as well and I got 102m as well.

Step-by-step explanation:

56 and -56 cancek eachother out. 57m + 45m can be added since they have the same variable. 57 + 45 is 102. So the answer is 102m.

Answer:

102

Step-by-step explanation:

Answer:      5x2-2x-7

Step-by-step explanation:

(4x2 + 3x - 1) + (x2 - 5x - 6)

=4x2+3x-1+x2-5x-6

=5x2-2x-7

Answer:

y= x+15

Step-by-step explanation:

I think that will be your equation

Answer:

It a polynomial

It is a monomial

3rd degree

Step-by-step explanation:

\(-a^3\) is a polynomial

It is a 3rd degree monomial.

Hope this helps!

Answer:

um so this is kinda hard not going to lie but here i think its like whatever is n than add and then subtracts it so yes

Step-by-step explanation: