2. Answer the following questions:
a. Determine the exact value of the expression: tan (cos-¹ (-16/19)). Make sure your answer is in simplified
radical form.
b. Explain why sin-¹ (tan 2π/3) does not have an answer.
Answer:

Based on the definition of a right angle, the value of x is: B. 40.

A right angle is an angle that measures exactly 90 degrees, or one quarter of a full circle. The symbol used to represent a right angle is a small square placed in the corner where the two lines or rays meet

Therefore, if two parts of a right angle measures 10 degrees and 2x respectively, we would have:

2x + 10 = 90

Subtract 10 from both sides:

2x = 90 - 10

2x = 80

2x/2 = 80/2

x = 40

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The Average rate of change is defined as

r{average} = Δy/Δx = (y₂ - y₁/x₂ - x₁).

The rate at which one quantity changes per unit change with the other quantity is called unit rate.

Given is the average rate of change.

Average rate of change is defined as the change in the value of a quantity over the interval change in the other quantity.

Mathematically -

r{average} = Δy/Δx = (y₂ - y₁/x₂ - x₁)

Therefore, the Average rate of change is defined as

r{average} = Δy/Δx = (y₂ - y₁/x₂ - x₁).

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Answer:

what basic business principle does the author of your reading material state that automakers igno red in recent years leading to the need for an industry bailout

The probability that a random sample of 150 bowlers will have an average score greater than 165 is 0

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is used to measure the likelihood or chance of an event occurring, ranging from impossible (0 probability) to certain (1 probability).

The basic concept of probability involves determining the ratio of the number of favorable outcomes to the total number of possible outcomes. This ratio is expressed as a fraction, decimal, or percentage.

For example, if you toss a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads is 1/2 or 0.5 or 50%, and the probability of getting tails is also 1/2 or 0.5 or 50%.

To give the probability that a random sample of 150 bowlers will have an average score greater than 165

P( [tex]\bar X[/tex]> 165) = P(z > (165 - 157)/(12/√(150)))

= P(z > 8.16)

= 0 [since from z table]

= 0

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Answer:

The efficiency of the transmission and drive mechanism is 57.5%, rounded to two decimal places.

Step-by-step explanation:

We can use the following formula to calculate the efficiency of the transmission and drive mechanism:

Efficiency = (Power output / Power input) x 100%

where "Power output" refers to the amount of power delivered to the driving wheels, and "Power input" refers to the amount of power produced by the engine.

Determine the power input: The problem states that the automobile engine produces 120 horsepower, so this is our power input.

Power input = 120 hp

Determine the power output: The problem states that only 69 horsepower is delivered to the driving wheels of the car, so this is our power output.

Power output = 69 hp

Calculate the efficiency using the formula:

Efficiency = (Power output / Power input) x 100%

Substituting the values we found in steps 1 and 2, we get:

Efficiency = (69 / 120) x 100%

Simplifying this expression, we get:

Efficiency = 0.575 x 100%

Efficiency = 57.5%

Therefore, the efficiency of the transmission and drive mechanism is 57.5%, rounded to two decimal places.

Answer:

r≈0.56m

Step-by-step explanation:

C=2πr

r=C

2π=3.5

2·π≈0.55704m

Answer:2.2%

Step-by-step explanation: I took the test

The cumulative frequency graph indicates that the percentage of the vehicles that go over the 30 mph speed limit is about 62.6% which more than the allowable 20%, therefore, a speed camera will have to be installed.

The cumulative frequency is the sum of the frequency up to an interval. The cumulative frequency indicates the total number of observations located above or below a value.

The cumulative frequency graph indicates the value of the sum of the number of vehicles travelling at a particular speed, therefore;

The cumulative frequency of cars traveling at 20 mph = 13

Cumulative frequency of cars traveling at 10 mph = 8

The cumulative frequency if the cars travelling at 30 mph = 50

Cumulative frequency of the cars travelling at 40 mph = 59

The cumulative frequency of the cars traveling at 50 mph = 60

Number of cars that go over the 30 mph speed limit = 59 + 60 = 119

Percentage of the cars that go over the 30 mph is therefore;

The percentage of cars that go over the 30 mph speed limit is 62.6% which is more than the 20%, therefore;

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The evaluation of the limits of the piecewise function at the specified intervals are as follows;

[tex]\lim\limits_{x\to2^+}\frac{f(x) -1}{f(x + 4)} = -2[/tex]

[tex]\lim \limits_{x\to 1^-}f(f(x) + 1) = 11[/tex]

[tex]\lim\limits_{h\to 0}\frac{f(6+h) - f(6)}{h} = 2[/tex]

A piecewise function is a function with rules or definition of the function based on the interval of the function.

The equation representing the piece wise function at x → 2⁺, can be found as follows;

Points on the graph of the function are; (3, 2), and (4, 1)

Slope of the graph of the function = (1 - 2)/(4 - 3) = -1

Equation of the function is; y - 2 = -1·(x - 3) = 3 - x

y = 3 - x + 2 = 5 - x

y = 5 - x

y = f(x) = 5 - x

f(x) - 1 = 5 - x - 1 = 4 - x

f(x) - 1 = 4 - x

f(x + 4) = 5 - (x + 4) = 5 - x - 4 = 1 - x

f(x - 4) = 1 - x

[tex]\frac{f(x) - 1}{f(x + 4)} = \frac{4 - x}{1 - x}[/tex]

The coordinate points on the piecewise function at x → 1⁻ are; (0, 3), and (1, 4)

The slope of the graph is; (4 - 3)/(1 - 0) = 1

The equation is; y - 3 = x

y = f(x) = x + 3

f(f(x) + 1) = f((x + 3) + 1) = f((x + 3) + 3 + 1) = f(x + 7)

f(x + 7)  = (x + 7 + 3) = x + 10

The points on the piecewise function at x = 6 are; (5, 2), and (7, 6)

The slope is; (6 - 2)/(7 - 5) = 2

The equation is; y - 2 = 2·(x - 5) = 2·x - 10

y = 2·x - 10 + 2 = 2·x - 8

y = f(x) = 2·x - 8

f(6 + h) = 2·(6 + h) - 8 = 12 + 2·h - 8 = 4 + 2·h

f(6) = 2 × 6 - 8 = 4

f(6 + h) - f(6) = 4 + 2·h - 4 = 2·h

[tex]\frac{f(6 + h) - f(6)}{h} = \frac{2\cdot h}{h}= 2[/tex]

The limits of the function is therefore;

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The solution to the system of equation 2x - 3y = 4 and -2x + 6y = -10 is (-1,-2).

Given the system of equation in the question;

2x - 3y = 4

-2x + 6y = -10

First, solve for y in equation one.

2x - 3y = 4

2x - 4 = 3y

3y = 2x - 4

Divide each term by 3

y = (2/3)x - 4/3

Now, solve the system of equation, plug y = (2/3) - 4/3 into equation two and solve for x.

-2x + 6y =-10

Plug in y = (2/3) - 4/3

-2x + 6( (2/3)x - 4/3 ) = -10

Simplify

-2x + 4x - 8  = -10

2x - 8 = - 10

2x = -10 + 8

2x = -2

x = -2/2

x = -1

Now, plug x = -1 into equation two and solve for y.

-2x + 6y = -10

Plug in x = -1

-2( -1 ) + 6y = -10

2 + 6y = -10

6y = -10 - 2

6y = -12

y = -12/6

y = -2

Therefore, the value of x is -1 and y is -2.

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Step-by-step explanation:

The difference between 1 and 7/8  is  0.125

The difference between 1 and 1(1/5) is 0.2

The number closer in value to 1 is the one with a lesser difference therefore, the correct answer is 7/8

Step-by-step explanation:

[tex]1 - \frac{7}{8} = 0.125[/tex]

while:

[tex] 1 \times \frac{1}{5} - 1 = 0.2[/tex]

then: 0.125<0.2

Answer:

First choice

Step-by-step explanation:

Answer:

Th answer is the FIRST CHOICE(A).

Have a GOOD DAY!

x - intercept of line A = (1 , 0)

x - intercept of line B = (-4, 0)

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.

A line with no curve is called straight line.

Given,

Equation of line A

y = 6x - 6

for x - intercept y = 0

0 = 6x - 6

6x = 6

x = 6/6

x = 1

x - intercept = (1 , 0)

Given table of values on line B

x   y

-4  0

-2  -1

0   -2

By the table, when y = 0, x = -4

x- intercept of line B = (-4 , 0)

Hence, (1, 0) is x - intercept of line A.

(-4 , 0) is x - intercept of line B.

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no

it doesn't start at (0,0)

x^2 + 4x + 4 is a perfect square trinomial that can be factored as (x + 2)^2.

Explanation:
To complete the expression x^2 + 4x + __ as a perfect square trinomial, we can take half of the coefficient of x (which is 4), square it, and then add it to the expression.

Half of 4 is 2, and 2 squared is 4, so we can add 4 to the expression to get:

x^2 + 4x + 4

This expression is a perfect square trinomial and can be factored as:

(x + 2)^2

Answer:

Step-by-step explanation:

If the generation time of bacteria is 30 minutes, it means that in every 30 minutes, the number of cells will double. Let No = 100 be the initial number of cells, and n be the number of generations at that point.

Using the given formula N1 = N x 2^n, we can find the number of cells at any given time t, in minutes.

For t = 30 minutes:

The number of generations in 30 minutes is 1 (since generation time is also 30 minutes)

N1 = 100 x 2^1 = 200 cells

For t = 60 minutes:

The number of generations in 60 minutes is 2 (since generation time is 30 minutes)

N1 = 100 x 2^2 = 400 cells

For t = 90 minutes:

The number of generations in 90 minutes is 3 (since generation time is 30 minutes)

N1 = 100 x 2^3 = 800 cells

For t = 120 minutes:

The number of generations in 120 minutes is 4 (since generation time is 30 minutes)

N1 = 100 x 2^4 = 1600 cells

Therefore, after 30 minutes, the number of cells will be 200, after 60 minutes it will be 400, after 90 minutes it will be 800, and after 120 minutes it will be 1600.

Answer:

See Screenshot

Step-by-step explanation:

Answer:

2.8

Step-by-step explanation:

To calculate the GPA of the student, we first need to calculate the total number of grade points earned by the student. We can do this by multiplying the number of credits for each course by the corresponding grade point value and then adding up the results:

A in a 3-credit course: 4 x 3 = 12 grade points

B in each of three 4-credit courses: 3 x 4 = 12 grade points each, for a total of 3 x 12 = 36 grade points

C in a 2-credit course: 2 x 2 = 4 grade points

D in a 3-credit course: 1 x 3 = 3 grade points

Total grade points earned = 12 + 36 + 4 + 3 = 55

Next, we need to calculate the total number of credits earned by the student:

A in a 3-credit course = 3 credits

B in each of three 4-credit courses = 3 x 4 = 12 credits

C in a 2-credit course = 2 credits

D in a 3-credit course = 3 credits

Total credits earned = 3 + 12 + 2 + 3 = 20

To find the GPA, we divide the total grade points earned by the total credits earned:

GPA = Total grade points earned / Total credits earned

GPA = 55 / 20

GPA = 2.75

Therefore, the GPA of the student is 2.75.

To calculate the GPA, convert each grade into points, multiply each point value by the number of credits for that course, and add the total. Then divide the total by the total credits. Using this calculation, the student's GPA is 2.75.

The grade point average (GPA) is calculated on the basis of the grades earned in each course and the course's credit value. First, each grade is converted into points. Then, each point value is multiplied by the number of credits for that course. Finally, the total points are added together, and the sum is divided by total credits to yield GPA.

The total credits are 3 (for A) + 12 (for Bs) + 2 (for C) + 3 (for D) = 20. The total points are 12 (for A) + 36 (for Bs) + 4 (for C) + 3 (for D) = 55. Hence, the GPA is 55 total points ÷ 20 total credits = 2.75.

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Answer:

Step-by-step explanation:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of a line is a measure of how steep the line is, and it is defined as the change in y divided by the change in x between any two points on the line. In other words, if we choose two points (x1, y1) and (x2, y2) on the line, then the slope of the line is:

m = (y2 - y1) / (x2 - x1)

The y-intercept of a line is the point where the line crosses the y-axis. In other words, it is the value of y when x = 0. To find the y-intercept of a line given in slope-intercept form, we simply look at the constant term (the term with no x) in the equation.

In the given equation, y = -6x - 7, we can see that the coefficient of x is -6, which means that the slope of the line is -6. This tells us that as we move along the line from left to right, the y-value will decrease by 6 units for every 1 unit that the x-value increases. In other words, the line is sloping downwards from left to right.

To find the y-intercept of the line, we look at the constant term, which is -7. This tells us that when x = 0, y is equal to -7. So the y-intercept is the point (0, -7), which means that the line crosses the y-axis at the point (0, -7).

To summarize, the slope of the line y = -6x - 7 is -6, which means that the line is sloping downwards from left to right. The y-intercept of the line is (0, -7), which means that the line crosses the y-axis at the point (0, -7).

It cost to build a fence around a square field which is 240 feet on each side $2040.

What is a square?

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can also be explained as a rectangle with two adjacent sides that are of equal length.

Given that fencing is sold in 8-foot sections at $15 per section and the fence posts cost $4 each.

The length of each side is 240 feet.

The perimeter of the square field is 4×240 = 960 feet.

The number of sections that need to fence the field is 960/8 = 120.

The number of posts that need to fence the field is 120.

The cost of 120 Fencing sections is 120×$15 = $1800.

The cost of 120 posts is 120 × 4 = $240.

The total cost of the  fence around a square field  is  $1800 + $240 = $2040

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The data collected at the beginning of the process, after a problem has been identified, are known as baseline data.

Baseline data is used as a reference point for measuring the performance of a process before any changes or improvements are made. This allows for a comparison to be made between the initial performance and the performance after changes have been implemented, in order to assess the effectiveness of the changes.

In summary, baseline data is important for evaluating the success of a process improvement initiative and for making informed decisions about further changes.

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a)The value of acceleration will be 4.8 m/s²

b)The total distance travelled is 505 m.

a) As all the movement happens along a straight line, we need to define an axis only, which we call x-axis, being the positive direction the one followed by the car.

We can choose to place our origin at the location where the motorcycle was stopped at the side of the road (assuming that it is the same point  for the car when it passes him), so our initial position is 0.

We can also choose our time origin to be the same as the instant that the motorcycle starts from rest, so t₀ = 0.

With these assumptions, and assuming also that the acceleration is constant, we can write two equations, one for the car (at constant speed) and the another one for the motorcycle, as follows:

xc = vx*t

xm= 1/2*a*t²

When the motorcycle passes the car, both distances traveled from the origin will be equal each other, i.e., xc = xm :

⇒ vx*t = 1/2*a*t²

We have as givens vx=35 m/s and t = 14.5 sec when both equations are equal each other.

⇒ 35 m/s* 14.5 s = 1/2*a*(14.5)²(s)²

Solving for a:

a = (2* 35 m/s) / 14.5 s = 4.8 m/s²

b) Replacing the value of a in the equation for xm, we have:

xm = 1/2*4.8 m/s²* (14.5)²s² = 505 m.

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Answer:

B. 5

Step-by-step explanation:

The expression "4 to the power of 5" can be written as 4^5. Here, 4 is the base, and 5 is the exponent. So the exponent in the expression 4 to the power of 5 is option B, 5.

Answer:

-195

Step-by-step explanation:

1+1+1+1-200+1

1+1+1+1-4x50+1

-195

Hopes this helps!!

I don't know if you have this answer!!

Answer: X would equal 134

Step-by-step explanation: You add 25 and 21 together and then subtract that from 180 then that number would be your answer.

The amount of cards in each row is a factor of 60 in each scenario, ensuring that Vildia will utilize all 60 cards and that there will be an equal number of cards in each row.

In mathematics, a combination is a way of selecting a subset of items from a larger set, where the order of the selected items does not matter. A combination is different from a permutation, which is a way of selecting a subset of items from a larger set, where the order of the selected items does matter.

Here,

If Vildia wants to set up a card game using 60 cards and wants to make an array with the same number of cards in each row, she could arrange the cards in the following ways:

1 x 60: In this case, Vildia would arrange all 60 cards in a single row.

2 x 30: In this case, Vildia would arrange the cards in two rows, each containing 30 cards.

3 x 20: In this case, Vildia would arrange the cards in three rows, each containing 20 cards.

4 x 15: In this case, Vildia would arrange the cards in four rows, each containing 15 cards.

5 x 12: In this case, Vildia would arrange the cards in five rows, each containing 12 cards.

6 x 10: In this case, Vildia would arrange the cards in six rows, each containing 10 cards.

10 x 6: In this case, Vildia would arrange the cards in ten rows, each containing 6 cards.

12 x 5: In this case, Vildia would arrange the cards in twelve rows, each containing 5 cards.

15 x 4: In this case, Vildia would arrange the cards in fifteen rows, each containing 4 cards.

20 x 3: In this case, Vildia would arrange the cards in twenty rows, each containing 3 cards.

30 x 2: In this case, Vildia would arrange the cards in thirty rows, each containing 2 cards.

60 x 1: In this case, Vildia would arrange all 60 cards in a single column.

Note that in each case, the number of cards in each row is a factor of 60, which ensures that Vildia will use all 60 cards and that there will be an equal number of cards in each row.

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Answer: one

Step-by-step explanation:

The volume of the sand pit is V = 694.6 feet²

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

Let the volume of the rectangle be represented as V

Now , the length of the sand pit = 30.2 feet

The width of the sand pit = 9.2 feet

The depth of the sand pit = 30 inches = 2.5 feet

Now , the volume of the rectangular pit = L x W x H

On simplifying the equation , we get

The volume of the rectangular pit V = 30.2 x 9.2 x 2.5

The volume of the rectangular pit V = 694.6 feet²

Hence , the volume of the rectangular sand pit is 694.6 feet²

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Step-by-step explanation:

1/2 cup per 1/4 bag goes to the less than

all the other ones should be in the greater than category

Answer:

y= -3

Step-by-step explanation:

Because the only line that does through 4,-3 is y =-3

To find the scale factor of the dilation, we can compare the corresponding dimensions of the original and the enlarged card.

The original card has a length of 3 1/2 inches and is being enlarged to a length of 5 1/4 inches. So the scale factor for the length is:

5 1/4 inches / 3 1/2 inches = 3/2

Similarly, the original card has a width of 2 inches and is being enlarged to a width of 3 inches. So the scale factor for the width is:

3 inches / 2 inches = 3/2

Therefore, the scale factor of the dilation is 3/2 or 1.5.