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The trigonometric ratio sine compares the lengths of the right triangle's two sides. Sin, though commonly abbreviated to sin, is actually pronounced sine.

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Answer:

5.00

Step-by-step explanation:

Using the Pythagorean theorem, we know that the string needed to go from D to C is 3 inches and from E to D is 2.7 inches.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

So, according to the given information:

We know that:
CE = 1.1 in

EC = 2.7 in

Then,

The string needed to go from E to D is 2.7 in (Given).

String needed to go from D to C:

Using the Pythagorean theorem: c = √a² + b²

Now, calculate DC as follows:

DC = √a² + b²

DC = √1.1² + 2.7²

DC = 2.91548

Rounding off DC: 3 in

Therefore, using the Pythagorean theorem, we know that the string needed to go from D to C is 3 inches and from E to D is 2.7 inches.

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The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

Answer:

It is clear from the graph,

Thus, x=-6 is the zero of g.

Step-by-step explanation:

A zero of the linear function 'g' on the graph of a linear function can be observed where the 'y-value' is zero.

In other words,

It is clear from the graph,

Thus, x=-6 is the zero of g.

Answer:

B) 68 cm²

Step-by-step explanation:

Answer:

Female: 93/328

Adult: 103/328

Baby: 61/328

Step-by-step explanation:

71 + 93 + 103 + 61 = 328

Male: 71/328

Female: 93/328

Adult: 103/328

Baby: 61/328

Answer:

1/2

Step-by-step explanation:

because 5 times 1/2 and you get 2 1/2

The probability that the randomly choosen sample contains less than 2 guppies is:

P  = 0.234

The probability will be equal to the sum between the probability of selecting 0 guppies and 1 guppi.

35% of the fish in the tank are guppies, then the probability of not selecting one of them is:

p = (0.65)^7  = 0.049

And the probability of selecting one is:

q = (0.65)^6*(0.35)*7 = 0.185

Then the probability that the sample contains less than 2 guppies is:

P = p + q = 0.049 + 0.185 = 0.234

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Given any real number x, the ceiling of x, denoted as ⌈x⌉, is the smallest integer n such that n is greater than or equal to x.

In other words, ⌈x⌉ is the unique integer n that satisfies the following two conditions:

n is greater than or equal to x

n is the smallest integer that satisfies condition 1

For example, if x = 2.4, then ⌈x⌉ = 3 because 3 is the smallest integer that is greater than or equal to 2.4. Similarly, if x = -1.9, then ⌈x⌉ = -1 because -1 is the smallest integer that is greater than or equal to -1.9.

The ceiling function is useful in various mathematical and computational contexts, such as in rounding up numbers, calculating the smallest integer greater than or equal to a given value, and approximating functions.

It is a fundamental concept in discrete mathematics and is used in many applications, including computer science, optimization, and operations research.

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Answer:

1.45%

Step-by-step explanation:

\( \frac{8.12}{560} (100) = .0145(100) = 1.45\%\)

The sets are equivalent to (1, 2) is none of above (option d)

In this case, we are given the set (1, 2) and asked to determine which of the provided sets are equivalent to it: (1) (1, 20), (2) N1 U N2, (3) (1, 1), or (4) none of the above. Let's analyze each option in detail to find the correct answer.

(1, 20):

This set includes all numbers between 1 and 20, excluding the endpoints. The elements in this set are 2, 3, 4, ..., 19. Therefore, this set is not equivalent to (1, 2) since it does not contain only the numbers 1 and 2. Therefore, option (a) is not correct.

N1 U N2:

The notation N1 and N2 is not universally defined, so we can't make any assumptions about the elements in these sets without further clarification. However, it is important to note that the set (1, 2) contains the elements 1 and 2. Therefore, for option (b) to be correct, both N1 and N2 must contain 1 and 2 as well. If that is the case, then the union of N1 and N2 will indeed be equivalent to (1, 2). Without more information about the nature of N1 and N2, we cannot definitively say whether option (b) is correct.

To summarize, option (a), (b) and option (c) are not equivalent to (1, 2).

Hence the correct option is (d).

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The total surface area of the trapezoidal prism is S = 3,296 inches²

Given data ,

Let the total surface area of the trapezoidal prism is S

Now , the measures of the sides of the prism are

Side a = 10 inches

Side b = 32 inches

Side c = 10 inches

Side d = 20 inches

Length l = 40 inches

Height h = 8 inches

Lateral area of prism L = l ( a + b + c + d )

L = 40 ( 10 + 32 + 10 + 20 )

L = 2,880 inches²

Surface area S = h ( b + d ) + L

On simplifying the equation , we get

S = 2,880 inches² + 8 ( 52 )

S = 3,296 inches²

Hence , the surface area of prism is S = 3,296 inches²

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The diameter of the ball is approximately 16.67 meters.

To find the diameter of the ball, we can use the relationship between the distance traveled and the number of revolutions.

The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter.

Given that the ball rolls a distance of 3.5 meters and makes 15.0 revolutions, we can calculate the circumference of the path it travels:

C = 3.5 m * 15.0 = 52.5 m

Since each revolution covers the circumference of the ball, we have C = πd. Plugging in the known value for C, we can solve for the diameter (d):

52.5 m = πd

Dividing both sides of the equation by π, we get:

d = 52.5 m / π

Using a calculator, we can evaluate this expression:

d ≈ 16.67 meters

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The statement that is false is: Correlation is used to define the variables of only non-linearly related data sets.

Correlation is a measure of the relationship between two variables of a data set and can be positive, negative, or 0. It is used to measure the degree to which the two variables of a data set resemble each other, regardless of whether the data set is linear or non-linear. The correlation between any two variables can be easily measured and compared, allowing for more detailed analysis of the data set.

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Answer:

I believe it's c.

Step-by-step explanation:

Starts and includes 2, goes until and includes 5.

Answer:

C

Step-by-step explanation:

Domain represents the possible x-values and the line on the graph only runs through x-values between 2 and 5.

Answer:

A. The equation of the line is y=−2.5x+10.

C. The y-intercept is k.

F. The value of k is 10.

Step-by-step explanation:

A line passes through points (0, k) and (4,0) and has a slope of –2.5. Which statements are true regarding the graph of the line?

A. The equation of the line is y=−2.5x+10.

B. The equation of the line is y=−2.5x.

C. The y-intercept is k.

D. The y-intercept is 4.

E. The value of k is 4.

F. The value of k is 10.

Solution:

The slope of a line is the ratio of the vertical change to the horizontal change. The slope (m) of a line passing through \((x_1,y_1)\ and\ (x_2,y_2)\) is:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Given that the line passes through (0, k) and (4,0)

\(m=\frac{y_2-y_1}{x_2-x_1}\)

\(-2.5=\frac{0-k}{4-0}\\\\-2.5=\frac{-k}{4}\\\\k=10\)

The equation of the line is given as:

\(y-y_1=m(x-x_1)\\\\y-10=-2.5(x-0)\\\\y = -2.5x+10\)

The y intercept is the value of y when x = 0, hence intercept = k

Given the line that passes through points (0, k) and (4,0) and has a slope of –2.5, we need to get the value of "k

The formula for calculating the slope of a line is expressed as:

\(m=\frac{y_2-y_1}{x_2-x_1}\\-2.5 = \frac{0-k}{4-0}\\-2.5=\frac{-k}{4} \\Cross \ multiply\\-2.5 \times 4 = -k\\-10 = -k\\k = 10\)

Hence the value of k is 10.

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From the coordinate given (0, 10) and (4, 0), we can see that the y intercept and x intercept of the graph is 10 and 4 respectively

To determine the set of reflections that would carry hexagon ABCDEF onto itself, we need to identify the lines of reflection that preserve the hexagon's symmetry.

A hexagon has six sides and six vertices. The lines of reflection that can carry the hexagon onto itself are those passing through the midpoints of opposite sides or through the midpoints of opposite vertices.

In this case, there are three possible lines of reflection that would preserve the hexagon's symmetry:

1. The line passing through the midpoints of AB and CD.

2. The line passing through the midpoints of BC and DE.

3. The line passing through the midpoints of CD and EF.

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Answer:

198

Step-by-step explanation:

rectangular side (9,3)

9x3=27

27x2= 54 (because there's rectangular sides)

Square end(6,3)

6x3=18

18x2=36(two square sides)

top&bottom sides

6x9=54

54xsquared2=108(two sides)

add all together

54+36+108=198cm(squared)

2√3

To simplify the given radical expression √363 - 3√27, follow these steps:

Step 1: Find the prime factorization of the numbers inside the radicals.
- 363 = 3 × 121
- 27 = 3 × 3 × 3

Step 2: Simplify the square roots.
- √363 = √(3 × 121) = √(3 × 11²) = 11√3
- 3√27 = 3 × √(3 × 3 × 3) = 3 × 3√3 = 9√3

Step 3: Combine the terms with the same radicals.
- 11√3 - 9√3

Step 4: Simplify by combining the coefficients.
- (11 - 9)√3 = 2√3

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Using rounding concepts, the rounding of $13.59582 to cents is of $13.60.

To round a number to the nearest cent, we have to look at the third decimal digit.

In this problem, the third digit is of 5, which means that one should be added to the second digit, since the sum results in 0 we add to the first digit, hence the rounding of $13.59582 to cents is of $13.60.

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A relationship might exist in a sample even though it does not exist in the population, because of b) Sampling error

In statistical analysis, a relationship might appear in a sample even though it does not exist in the population due to sampling error. This occurs when the sample is not fully representative of the population, leading to discrepancies between the sample statistics and the true population parameters.

Sampling error can cause random fluctuations that mistakenly suggest a relationship, which may not be present in the larger population. It is important to consider the limitations and potential sources of error when generalizing findings from a sample to the broader population. So b option is correct.

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A. P(on time & under budget) and it is a joint probability statement.

B. P(polluted & within 10 miles of city) and it is a joint probability statement.

C. P(intense hurricanes | climate change) and it is a conditional probability statement.

D.  P(beam fails | weld defect) and it is a conditional probability statement.

E.  P(strong & ductile beams) and it is a joint probability statement.

A.  Joint probability refers to the probability of two events occurring at the same time. In this case, the probability of a project being on time and under budget is given.

B. Joint probability refers to the probability of two events occurring at the same time. In this case, the probability of a river being polluted and within 10 miles of the city is given.

C. Conditional probability refers to the probability of one event occurring, given that another event has occurred. In this case, the probability of hurricanes becoming more intense, given climate change, is given.

D.Conditional probability refers to the probability of one event occurring, given that another event has occurred. In this case, the probability of a beam failing, given a weld defect, is given.

E. Joint probability refers to the probability of two events occurring at the same time. In this case, the probability of a beam being both strong and ductile is given.

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Answer:

x and y can be any two numbers greater than zero such that y is also greater than x

D.no more than 45

C.50 miles per hour

Step-by-step explanation:

Let the two numbers be such that x< y because we have been given y/x>1 and x/y< 1 .

Suppose we take y= 9 and x= 3 then

9/3 > 1

3>1

Also

3/9 < 1

1/3 < 1

x and y can be any two numbers greater than zero such that y is also greater than x

2. Total weight that can be carried is 3000 pounds.

The big machine is 300 pounds. The weight that the truck can carry beside the big machine is 3000-300= 2700 pounds.

The smaller machines weigh 60 pounds

The number of smaller machines that can be carried is 2700 ÷ 60= 45 other than the big machine.

3. Total distance = Speed * time

                           = 48 * (40/60) = 32 miles

New distance = 32+ 8= 40 miles

New time = 48 minutes

Speed = distance / time = 40/ 48/60=  50 miles per hour

Answer:

6*6*5/3=180/3=60

thus the answer is 60

There is reason for concern about the impact of automation on the job market, it is important to consider the potential benefits and opportunities that may arise from these changes.

The future of work will be shaped by a variety of factors, and it is up to individuals, businesses, and policymakers to navigate this changing landscape in a way that benefits everyone.

A Pew Research study conducted in 2017 found that about 75% of Americans believe that robots and computers may take over many of the jobs that people currently do. People are becoming increasingly aware of the potential for automation to impact their jobs and industries. This has sparked debate about the role of automation in the economy, and whether or not it will lead to job displacement.

However, it is important to note that not all jobs are equally at risk of automation, and many new jobs may be created as a result of technological advancements.

In conclusion, while there is reason for concern about the impact of automation on the job market, it is important to consider the potential benefits and opportunities that may arise from these changes.

The future of work will be shaped by a variety of factors, and it is up to individuals, businesses, and policymakers to navigate this changing landscape in a way that benefits everyone.

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Answer:

Bank A charges 10.4 a month. Bank B charges 27.00 a month

Step-by-step explanation:

Bank A step by step-

0.20 x 52 = 10.4

Bank B step by step=

52-25 = 27

27 x 1.00 = 27.00