The highway has a maximum speed limit of 55 mph. Which vehicles are safely
obeying this speed limit? Check all that apply.

An example of an optimistic explanatory style would be viewing a bad grade on a test as something that doesn't often happen, will probably not affect your final grade, and is probably because you did not get enough sleep the night before the test.

An optimistic explanatory style involves interpreting negative events or outcomes in a positive and constructive manner. It involves attributing the causes of negative events to external, temporary, or specific factors rather than internal, permanent, or global factors.

In the given example, option (a) demonstrates an optimistic explanatory style. It suggests that the bad grade on the test is not a common occurrence ("something that doesn't often happen"), indicating that it is viewed as an isolated incident. Furthermore, it minimizes the impact of the bad grade by stating that it will probably not affect the final grade. Instead of attributing the cause to personal incompetence or intelligence.

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The conclusion that is correct in a two-tailed test at α = .05 is There appears to be no difference in the mean occupancy rates.

From the given values:

Thus, the P-value = 0.1791

Interpret results. Since the P-value (0.1791) is greater than the significance level (0.05), we failed to reject the null hypothesis.

From the above test, we do not have sufficient evidence in favor of the claim that there is a difference in the mean occupancy rates.

Thus, option A is correct.

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Answer:

(2,3); (-6,5); (2,-3); (5,-7)

Step-by-step explanation:

The properties of eclipsing binary systems are detected by examining a light curve.

Eclipsing binary systems are a type of binary star system where the stars orbit each other in such a way that they periodically pass in front of each other from the perspective of an observer on Earth. This results in periodic variations in the total amount of light observed from the system, which is known as the light curve.

By studying the shape and timing of the light curve, astronomers can determine a number of properties of the binary system, such as the orbital period, the sizes and masses of the stars, and their distance from Earth.

For example, the duration and depth of the eclipses can be used to estimate the sizes of the stars, while the timing of the eclipses can reveal information about their orbital period and any changes in their orbit over time. By analyzing the light curve in detail, astronomers can gain valuable insights into the structure, behavior, and evolution of binary star systems.

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The average speed of the car while taking photos in m/s is 1.6 m/s

Total photos taken = 2

Time taken = 0.5 seconds

Distance = 0.8m

Thus, this can be noted as -

Distance = Marks on the road between the two photos = 0.8 meters

Time = Time between the two photos = 0.5 seconds

Speed is defined as the rate at which a distance travelled or a height reached changes. It has a time component. In the given case, the speed camera is taking photos and we are required to calculate the average speed of the car

Calculating the speed -

Average Speed = Distance ÷ Time

Substituting the values -

= 0.8 /0.5

= 1.6

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Given inequality equation is -2x - 3.7 < 6.3

The answer is x >-5

Add 3.5 to both sides

-2x - 3.7 < 6.3

-2x - 3.7+3.7 < 6.3+3.7

Simplify

-2x < 6.3+3.7

-2x < 10

Divide both sides by the same factor and flip the relation because the factor is negative

-2x < 10

\(\frac{-2x}{-2} < \frac{10}{-2}\)

Now, Simplify by cancelling the terms that are in both the numerator and denominator

= \(x > \frac{10}{-2}\)

Divide the numbers

= x > -5

Hence the answer is, the inequality of the equation -2x - 3.7 < 6.3 is

x > -5

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False. The best big-o bound that any algorithm that multiplies two n-bit numbers can achieve is O(n^2), not O(n+n) or O(2n).

An algorithm is a set of instructions or a procedure for solving a problem or performing a task. In computer science, an algorithm is typically a step-by-step process for solving a problem or performing a computation. Algorithms can be expressed in various forms, such as natural language, pseudocode, flowcharts, or programming languages. They are used in a wide range of applications, from simple arithmetic operations to complex data processing and artificial intelligence. The efficiency and correctness of an algorithm depend on various factors such as the input size, the data structure, and the computational complexity of individual operations.

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Because each of n bits of a number x must be multiplied by each of n bits of a number y, the best big-o bound that any algorithm that multiplies two n-bit numbers can achieve is O(n+n)-O(n^2

While it is true that each of n bits of a number x must be multiplied by each of n bits of a number y, it is possible to achieve a better big-o bound than O(n+n) or O(2n). The best-known algorithm for multiplying two n-bit numbers, the Karatsuba algorithm, achieves a big-o bound of O(n^log2(3)), which is faster than O(n^2).

Therefore, the statement that the best big-o bound that any algorithm that multiplies two n-bit numbers can achieve is O(n+n) or O(n^2) is false.
Main answer: b. false

The given statement implies that the best big-O bound for multiplying two n-bit numbers is O(n+n)-O(n^2), which simplifies to O(2n)-O(n^2) or simply O(n^2). However, this is not the best bound achievable for multiplying two n-bit numbers. The best known algorithm, the Karatsuba algorithm, has a time complexity of O(n^log2(3)), which is approximately O(n^1.585). This is faster than O(n^2) and thus, the statement is false.

The best big-O bound that any algorithm that multiplies two n-bit numbers can achieve is not O(n^2), but rather O(n^log2(3)), as demonstrated by the Karatsuba algorithm. Therefore, the given statement is false.

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Answer:

x=0

Step-by-step explanation:

-8-3x=-8(1-7x)

add 8 to both sides =( -3x=56x)

subtract 56x from both sides (-59x=0)

divide both sides by -59 = (x=0)

The domain and range are the set of x and values of the function are in the table.

the function as a table,

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

What is the domain and range?

The domain and range are fundamental concepts in mathematics that are used to describe the input and output values of a function or relation.

The domain of a function refers to the set of all possible input values, or x-values, for which the function is defined.

The range of a function refers to the set of all possible output values, or y-values.

To find the domain and range of functions and represent them in different formats.

To find the domain and range of a function:

The domain refers to the set of all possible input values (x-values) for the function.

The range refers to the set of all possible output values (y-values) for the function.

To represent the function as a table, you would list the input-output pairs. For example:

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

To represent the function as a mapping, you would indicate the correspondence between the input and output values.

For example:

-3     ->   -4

-1     ->     2

0     ->     0

-3    ->     5

2     ->     4

To represent the function as a graph, The x-values would be on the horizontal axis, and the y-values would be on the vertical axis.

The points (-3, -4), (-1, 2), (0, 0), (-3, 5), and (2, 4) would be plotted accordingly.

Hence, The domain and range are the set of x and values of the function are in the table.

the function as a table,

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

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Answer:

The value of f(9) is equal to 498.

Step-by-step explanation:

Given that,

f(x) = 6x²+12

We need to find the value of x(9).

Put x = 9 in the given function.

f(9) = 6(9)²+12

f(9) = 498

So, the value of f(9) is equal to 498.

Vertical angles are always congruent, which means that they are equal. Adjacent angles are angles that come out of the same vertex. Adjacent angles share a common ray and do not overlap. The size of the angle xzy in the picture above is the sum of the angles A and B.

M = A + |B| is the function's highest possible value. When sin or cos x equals 1, this maximum value is reached. m = A |B| is the function's lowest possible value. If either cos x or sin x is equal to 1, this minimum will be reached.

Example :

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Answer:

The number line has to be shown in a picture if you want more specific instructions from others.

Step-by-step explanation:

Show a picture

Answer:

8

Step-by-step explanation:

The 110 degree angle is oppoiste to the angle across it.

Using PLT-C the other angle on the bottom of it should be 70 degrees.

since the 70 degrees is on a straight angle the angle beside it should 110

14(8)-2 = 110

Answer:

D) (12x^2 - x - 1)/(6x^2)

Step-by-step explanation:

to find the quotient of the given rational expressions, and the correct answer:

(4x+1)/(6) ÷ (x)/(3x-1)

To divide the two rational expressions, we can multiply the first fraction by the reciprocal of the second fraction:

(4x+1)/(6) × (3x-1)/(x)

Now, we can multiply the numerators and denominators of the resulting expression:

[(4x+1)(3x-1)] / [6x]

Expanding the numerator using the distributive property, we get:

[12x^2 - 4x + 3x - 1] / [6x]

Simplifying the numerator, we get:

[12x^2 - x - 1] / [6x]

We can further simplify the numerator by factoring it:

[12x^2 - x - 1] = (4x+1)(3x-1)

Substituting this factored form into the previous expression, we get:

[(4x+1)(3x-1)] / [6x]

= (12x^2 - x - 1) / (6x)

Therefore, the correct answer is:

D) (12x^2 - x - 1)/(6x^2)

I hope that helps! Let me know if you have any further questions.

Answer:

19

Step-by-step explanation:

corresponding angles equal each other

9x-25=8x-6

x-25=-6

x=19

We can determine the quadrant by analyzing the range of u/2: Quadrant I: 0 < u/2 < π/2, Quadrant II: π/2 < u/2 < π, Quadrant III: π < u/2 < 3π/2, Quadrant IV: 3π/2 < u/2 < 2π

Since (3π/4) < u/2 < π, u/2 lies in Quadrant II.

To determine the quadrant in which u/2 lies, we need to first find the value of u/2.

We know that sec u = 11/2, and we can use the identity sec^2 u = 1 + tan^2 u to find the value of tan u:

sec^2 u = 1 + tan^2 u

(11/2)^2 = 1 + tan^2 u

121/4 = 1 + tan^2 u

tan^2 u = 117/4

tan u = ±√(117/4)

We know that 3/2 < u < 2, so we can conclude that u is in the second quadrant (where tan is negative). Therefore, we take the negative square root:

tan u = -√(117/4)

tan(u/2) = ±√[(1 - cos u) / (1 + cos u)]

tan(u/2) = ±√[(1 - √(1 - sin^2 u)) / (1 + √(1 - sin^2 u))]

tan(u/2) = -√[(1 - √(1 - (11/2)^2)) / (1 + √(1 - (11/2)^2))]

tan(u/2) ≈ -0.715

Since tan(u/2) is negative, we know that u/2 is in the third quadrant. Therefore, the answer is Quadrant III.

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Answer:

Step-by-step explanation:

Answer:

(c) negative

Step-by-step explanation:

hope this helps

Answer:

The percentage change each year is 2%

Step-by-step explanation:

Generally, we can have an exponential equation written as;

f(t) = I( 1 + r)^t

where f(t) is the value at a certain time

I is the initial value at t = 0

r is the growth rate

t is the time we are looking at

Thus, we have it that;

1.02 = 1 + r

r = 1.02 -1

r = 0.02

So, let us write 0.02 as a percentage

We have this as 2/100 which is the same as 2%

The percentage change each year is 2%

The difference in the account balances at the end of the loan terms is given as follows:

$1,686.87.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for the offer 2 are given as follows:

P = 75000, r = 0.035, n = 12, t = 62/12.

Hence the balance of the offer 2 is given as follows:

B = 75000 x (1 + 0.035/12)^(12 x 62/12)

B = $89,842.51.

The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:

91529.38 - 89842.51 = $1,686.87.

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Yes, frequency distributions can be made for both categorical and quantitative data.

A frequency distribution is a table that shows how often each value occurs in a data set. It is a way of summarizing data and can be used for both categorical and quantitative data.

Categorical data is data that can be divided into categories, such as gender or eye color. A frequency distribution for categorical data would show how many times each category appears in the data set.

Quantitative data is numerical data, such as height or weight. A frequency distribution for quantitative data would show how many times each numerical value appears in the data set.

In both cases, the frequency distribution helps to summarize and visualize the data in a clear and concise way.

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p = number of pages written before today

p+16 = number of pages written currently

p+16 > 50

p+16-16 > 50-16

p > 38

Carl had written more than 38 pages, but less than 50 pages, before today.

For example, he could have written p = 40 pages

p+16 = 40+16 = 56 which fits the description of "more than 50".

Something like p = 30 doesn't work since

p+16 = 30+16 = 46 which comes up short.

The inequality that represents the situation is x + 16 > 50 and the solution is x > 34.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other.

Given, Carl wrote 16 pages today,

bringing hi total number of page written to more than 50.

Let x be the number of pages he wrote before today.

And we have the inequality,

x + 16 > 50

To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Subtract 16 on both sides.

x > 34

Therefore, he wrote more than 34 pages before today.

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A mockingbird will beat its wings approximately 1,680 times in 2 minutes.

To find the number of times a mockingbird will beat its wings in 2 minutes, we need to determine the average number of wing beats per second and then multiply that by the total number of seconds in 2 minutes.

From the given data, we can see that the mockingbird's wing beats per second are as follows:

30 seconds -> 420 wing beats

90 seconds -> 1,260 wing beats

150 seconds -> 2,100 wing beats

To find the average number of wing beats per second, we can sum up the total number of wing beats and divide it by the total number of seconds:

Total wing beats = 420 + 1,260 + 2,100 = 3,780

Total seconds = 30 + 90 + 150 = 270

Average wing beats per second = Total wing beats / Total seconds = 3,780 / 270 = 14

Now that we know the average number of wing beats per second is 14, we can calculate the total number of wing beats in 2 minutes (120 seconds) by multiplying the average by the number of seconds:

Total wing beats in 2 minutes = Average wing beats per second * Total seconds = 14 * 120 = 1,680

Therefore, a mockingbird will beat its wings approximately 1,680 times in 2 minutes.

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The rectangle's area is decreasing at a rate of 40 square meters per day when the length is 10 meters and the width is 18 meters.

We have to find the rate of change of area of the rectangle, that is, dA/dt.

Let L be the length and W be the width of the rectangle.

So, the area of the rectangle, A = L * W

Now, when the length is 10m and width is 18m,

then A = L * W

= 10 * 18

= 180 sq. meters

Differentiating both sides of A = L * W with respect to time, t, we get:

dA/dt = d/dt (L * W)

On applying product rule of differentiation, we get:

dA/dt = (dL/dt) * W + L * (dW/dt)

We know that dL/dt = -5 (given: The length of a rectangle is decreasing at a rate of 5 meters per day)

and dW/dt = 5 (given: the width is increasing at a rate of 5 meters per day).

So, dA/dt = (-5) * 18 + 10 * 5

= -90 + 50

= -40 square meters per day.

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Answer:

square is the answer for this question

Answer:

Jillene will spend $345.60 in 6 months.

Step-by-step explanation:

To find the answer we will turn 24% into a decimal.  24% ÷ 100 = 0.24.  Now multiply 0.24 by $240 and we get $57.60.  Because we are trying to find how much Jillene will spend in 6 months, we will multiply $57.60 by 6, which is $345.60.  Therefore, $345.60 is our answer.

Answer: $1785.60

Step-by-step explanation:

240 x 6 = 1440

240 x 0.24 = 57.6

57.6 x 6 = 345.6

1440 + 345.6 = 1785.60

Final Answer: $1785.60

If \(\displaystyle g( x) =( x-5)^{3}( 2x-7m)^{4}\) and \(\displaystyle x=5\) is a root with multiplicity \(\displaystyle n\), we can determine the value of \(\displaystyle n\) by evaluating \(\displaystyle g( x) \) at \(\displaystyle x=5\).

Substituting \(\displaystyle x=5\) into \(\displaystyle g( x) \), we have:

\(\displaystyle g( 5) =( 5-5)^{3}( 2( 5)-7m)^{4}\)

Simplifying this expression, we get:

\(\displaystyle g( 5) =( 0)^{3}( 10-7m)^{4}\)

\(\displaystyle g( 5) =0\cdot ( 10-7m)^{4}\)

\(\displaystyle g( 5) =0\)

Since \(\displaystyle g( 5) =0\), it means that \(\displaystyle x=5\) is a root of \(\displaystyle g( x) \). However, we need to determine the multiplicity of this root, which refers to the number of times it appears.

In this case, the root \(\displaystyle x=5\) has a multiplicity of \(\displaystyle n\). Since the function \(\displaystyle g( x) \) evaluates to \(\displaystyle 0\) at \(\displaystyle x=5\), it implies that the root \(\displaystyle x=5\) appears \(\displaystyle n\) times in the factored form of \(\displaystyle g( x) \).

Therefore, the value of \(\displaystyle n\) is \(\displaystyle 3\) (the multiplicity of the root \(\displaystyle x=5\)).

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