a cyclist takes a trail there and back every day and likes to average 10 miles per hour. if on the way out the cycles gets to the midway point and noticed that he was only going 5 miles per hour, how fast does he have to go on the second half to average 10 miles per hour for the whole trip?

The statement that represents the share as a rhombus if and only if the angles are perpendicular and the sides are congruent is "150".

A rhombus is a parallelogram with sides that are congruent. In a rhombus, the diagonals bisect each other at right angles; that is, they divide each other into two equal parts. The opposite angles of a rhombus are congruent to each other. In a rhombus, the diagonals are perpendicular to each other. This is because the diagonals bisect each other, and the only way two lines can bisect each other is if they are perpendicular.

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In this case, the experimental probability is D. 0.860

First, note that Experimental probability, also known as Empirical probability, is founded on real experiments and adequate documentation of events.

In the table we can see that he rolled the cube 1000 times, and he recorded that 140 of those times he rolled a 5.

Then, the probability of rolling a 5 will be equal to:

P1 = 140/1000 = 0.14

Now, the probabilty of NOT rolling a 5, is equal to the rest of the probabilities, this is:

P2 = 1 - 0.14 = 0.86

then the correct option is D

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Jimmy rolls a number cube multiple times and records the data in the table above. At the end of the experiment, he counts that he had rolled 140 fives. Find the experimental probability of not rolling a five, based in Jimmy’s experiment. Round the answer to the nearest thousandth.

A. 0.140

B. 0.167

C. 0.667

D. 0.860

The limit of the given function is  π/2.

What is a limit?

A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals.

Here, we have

Given: \(\lim_{(x,y) \to \pi, \pi /2} y sin(x-y)\)

We have to find the limit of the given function.

=  \(\lim_{(x,y) \to \pi, \pi /2} y sin(x-y)\)

Now, we substitute the value of each variable.

x = π and y = π/2

= y sin(x-y)

= π/2sin(π-π/2)

= π/2sinπ/2

= π/2sin(90°)   (∴sin90° = 1)

= π/2×1

= π/2

Hence, the limit of the given function is  π/2.

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Answer:

4%

Step-by-step explanation:

commission rate = (amount earned on sales / total cost of items sold) x 100

\(\frac{378}{9000}\) × 100 = 4.2%

To convert to the nearest whole number, look at the first number after the decimal,

two is less than 5, thus we would add zero to 4.

4.2% becomes 4%

The names of 0 employees are written on 0 cards. the cards are placed in a​ bag, and three names are picked from the bag - here simple random sampling technique was used.

Basic irregular testing can provide you with an extremely precise image of how your motto performs with the typical individual, yet it won't give you nitty gritty data about unambiguous gatherings. Utilizing straightforward irregular testing permits scientists to make speculations about a particular populace and leave out any inclination. This can assist with deciding how to settle on future choices. It has been expressed that "the rationale behind straightforward arbitrary examining is that it eliminates predisposition from the choice method and ought to bring about delegate tests".

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The evaluated function is f(2) = 36

From the question, we have the following parameters that can be used in our computation:

f(x) = 6^x

Also, from the question, we have

x = 2

This means that we calculate f(2)

Substitute the known values in the above equation, so, we have the following representation

f(2) = 6^2

Evaluate

f(2) = 36

Hence, the solution is 36

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Complete question

Evaluate f(x) = 6^x when x = 2

If the graph of f(x) = x² is translated to form g(x) = (x – 5)² + 1, a graph which represent g(x) is: A. On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Translating the squared parent function f(x) = x² five (5) to the right and 1 unit up, we have the following:

f(x) = x²   →  g(x) = f(x - (5)) + 1

g(x) = (x – 5)² + 1

In this context, we can logically deduce that the squared parent function f(x) was translated five (5) to the right to create function g(x) as shown in the graph attached below.

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Answer:

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

The g(x) has a = 1 and vertex (h, k) = (5, 1). With a > 0, the graph opens up.

Only one of them include the parabola with vertex (5, 1):

We mentioned that it opens up and the vertex is correct.

Let's confirm the two points on the graph (2, 10) and (8, 10):

Answer:

Step-by-step explanation:

Fist you isolate the variable by subtracting 2 from both sides

To get -3 _<_x<1

This is the answer to number 6

By evaluating the above integral over this region, we can find the probability of ppy ě xq. This expression is useful for calculating conditional probabilities in multivariate distributions.

To find ppy ě xq, we can use the following expression:
∫∫ f(x,y) dy dx over the region where y ≥ p, y ≤ q, and x ≤ xq
This expression represents the integral of the joint density function f(x,y) over the desired region, where y is between p and q, and x is less than or equal to xq. The result of this integration will give us the probability that a random variable (x,y) falls within this region.
To visualize this, we can draw the region of the joint density function f(x,y) on a two-dimensional plane. The horizontal axis represents x, and the vertical axis represents y. Then, we can shade in the area where y is between p and q, and x is less than or equal to xq. This shaded region represents the desired area that we want to find the probability of.

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The initial amount invested is  $2.88.

The formula that can be used to determine the initial amount invested is:

P = FV ÷ (1 + r)^n

Where:

8500 ÷ (1 + 0.00274)^2920

= 8500 ÷ (1.00274^2920) = $2.88

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When given the sets a = {1, 2, 3, 4, 5} and b = {0, 3, 6}, the operations yield the following results: a) a∪b = {0, 1, 2, 3, 4, 5, 6}, b) a∩b = {3}, c) a−b = {1, 2, 4, 5}, and d) b−a = {0, 6}.

To explain further, the union of sets a and b (a∪b) includes all the elements from both sets without repetition. In this case, a∪b = {0, 1, 2, 3, 4, 5, 6} because it contains all the elements from sets a and b.

The intersection of sets a and b (a∩b) refers to the common elements present in both sets. In this case, a∩b = {3} since 3 is the only element that appears in both sets a and b.

The set difference a−b consists of elements that are in set a but not in set b. Here, a−b = {1, 2, 4, 5} because these elements are present in set a but not in set b.

Finally, the set difference b−a represents elements that are in set b but not in set a. In this case, b−a = {0, 6} because these elements are present in set b but not in set a.

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The idea that group work theories are appropriate for all clients all the time is a myth (Third option).

About Group Process:

The term "group process" describes how people collaborate within an organization to complete tasks. Typically, organizations invest a lot of time and effort into defining and achieving goals, but little thought is usually given to how those goals are affecting the most valuable resource of a group - its people.

Since different clients have different demands and priorities, group work might not be suitable for many, but not for all. Different types of clients require different types of collaboration, type of group or individuals, and working strategies that work for their goals the best.

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Based on the information provided, the researcher should choose option a, which is to fail to reject/retain the null hypothesis. This is because the absolute value of the obtained statistic (tobt) (-1.98) is less than the absolute value of the critical value (tcrit) for a two-tailed t test with an alpha level of .05 and with df=29 (which is +/-2.045).

To clarify some of the terms used, the researcher in this scenario is conducting a hypothesis test to compare the population of senior citizens' average hours of sleep to that of the general population. She collected a sample of 30 senior citizens to represent the population. The null hypothesis is the statement that there is no difference between the two populations in terms of average hours of sleep. The alternative hypothesis is the statement that the senior citizens sleep fewer hours than the general population. The obtained statistic (tobt) is a measure of how far the sample mean deviates from the null hypothesis. The critical value (tcrit) is the cutoff value used to determine whether the obtained statistic is significant enough to reject the null hypothesis.
c. Fail to Reject/Retain the null. absolute value of tobt < absolute value of tcrit

Explanation:
The researcher performed a two-tailed single-sample t-test to compare the sleep hours of a sample of 30 senior citizens with the general population. The obtained statistic (tobt) is -1.98, and the critical value (Tcrit) for this test with an alpha level of .05 and df=29 is +/-2.045.

To make a decision, we compare the absolute values of tobt and tcrit:

Absolute value of tobt: |-1.98| = 1.98
Absolute value of tcrit: 2.045

Since the absolute value of tobt (1.98) is less than the absolute value of tcrit (2.045), we fail to reject the null hypothesis. This means the researcher cannot conclude that there is a significant difference in sleep hours between senior citizens and the general population based on her sample.

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Answer:

The inverse function of f(x) is ... f⁻¹(x) = log (x/9.16)/log (1.0054)

Step-by-step explanation:

Starting equation... f(x) = 9.16(1.0054)ˣ

Visually rewritten... y = 9.16(1.0054)ˣ

Flipping x and y... x = 9.16(1.0054)ʸ

Isolating (1.0054)ʸ... x/9.16 = (1.0054)ʸ

Taking the log of both sides... log (x/9.16) = y log (1.0054)

Isolating y... log (x/9.16)/log (1.0054) = y

Solution... y = log (x/9.16)/log (1.0054)

Step-by-step explanation:

Answer:

5. p (6) = -6

6. f (-9) = -3

7. g (-4) = 15

8. h (5) = 19

9. u answered already

10. p (-9) = 9

11. f (-11) = -5

12. g (1) = 0

13. h(-4) = -8

14. k (10) = 181

15. p (11) = 11

16. f(-8) = -2

17. g (-10) = 99

18. h (3) = 13

19. k (6) = 49

20. p (99) = -99

21. f(0) = 6

22. g (2) = 3

23. h(0) = 4

24. k(3) = 7

25. p(-1/2) = 1/2

26. f (0.4) = 6.4

27. g (1/2) = -3/4

28. h (-1.2) = 0.4

29. k (1/2) = -1/2

30. p (\(\sqrt{6}\)) = -\(\sqrt{6}\)

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The required GCF is 8.

The greatest common factor is that greatest number from the factors which divides the number completely.

For example take numbers 12 and 16.

The factors of 12 are 2×2×3.

And the factors of 16 are 2×2×2×2.

We can clearly see that the common factors are 2×2 which gives 4. So, 4 is the greatest common factor which divides both 12 and 16.

Here it is given to find the greatest common factor of 16 and 40.

Factors of 16 = 2×2×2×2

Factors of 40 = 2×2×2×5

We can see clearly the common factors are 2×2×2 which gives 8.

So, 8 is the greatest common factor.

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Question 1-

To determine which two points would a line of fit go through to best fit the data on the scatter plot, we need to visually analyze the pattern of the data points and choose two points that the line would pass through to represent the overall trend.

Without the actual scatter plot provided, I am unable to directly analyze it. However, based on the given answer choices:

A. (1,9) and (9,5)

B. (1,9) and (5,7)

C. (2,7) and (4,3)

D. (2,7) and (6,5)

Since I don't have the scatter plot, I cannot accurately determine which points would best fit the data. I would recommend carefully reviewing the scatter plot and selecting the two points that seem to represent the general trend or pattern of the data. The two points that form a line that closely follows the general direction of the data points would be the best choices.

Question 2-

To determine the slope of the relationship between the number of hours Laila danced, x, and the money she raised, y, we need to examine the graph and calculate the slope using the formula:

Slope = (change in y) / (change in x)

However, since the graph is not provided, it is not possible to directly calculate the slope. However, we can still evaluate the given answer choices based on their explanations:

A. The slope is 1/4, which means that the amount the student raised increases by $0.75 each hour.

B. The slope is 4, which means that the amount the student raised increases by $4 each hour.

C. The slope is 12, which means that the student will finish raising money after 12 hours.

D. The slope is 20, which means that the student started with $20.

From the explanations provided, it seems that option B would be the most reasonable choice. A slope of 4 would indicate that for each additional hour Laila danced, she raised $4. However, without the actual graph, it is challenging to confirm the accuracy of the answer choice or its real-world interpretation.

The equation on the interval  [0,2pi)

Sin x/2=sq root 2- sin x/2 is 90° , 270°

Trigonometric function, in mathematics, one of six functions (sine [sin], cosine [cos], tangent [tan], cotangent [cot], secant [sec], and cosecant [csc]) that represent ratios of sides of right triangles.

\(Sin^2(\frac{\theta}{2} )\) = \(\frac{1}{2}(1-cos\theta)\)

\(= > sin(\theta/2)=\sqrt{\frac{1}{2} (1-cos\theta}\)

\(Sin(\frac{x}{2} )\) = \(\sqrt{2}-sin\frac{x}{2}\)

\(Sin(\frac{x}{2} )\) = \(\frac{\sqrt{2} }{2}\)

Substituting:

\(\sqrt{\frac{1}{2}(1-cosx) } =\frac{\sqrt{2} }{2}\)

Squaring on both sides:

\(\frac{1}{2}(1-cosx)=\frac{2}{4}\)

\(\frac{1}{2}-\frac{1}{2}cosx = \frac{1}{2}\)

cos x =0

x = arccos(cosx) = arccos(0) = 90° , 270°

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Answer:

line B is the best model of data

Step-by-step explanation:

Line be is the best model for this since it runs through the data acting as an average.

Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

The area of the given trapezoidal site is 250,000 sq. ft.

The area of the trapezoidal with the dimensions of both bases and the height is given by the formula,

Area = 1/2 × height × (base1 + base2)

Units: square units

The given trapezoidal site has a base of 150 feet, i.e., base1 = 150 ft; a height of 2000 ft, i.e., height = 2000 ft and a parallel base of 100 feet, i.e., base2 = 100 ft.

Then, the area of the trapezoidal is

= 1/2 × 2000 × (150 + 100)

= 1/2 × 2000 × 250

= 250,000 sq. ft

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The given expression ((y-b)²/(y-b+1)+(y-b)/(y-b+1) after being reduced to a polynomial, can be represented as y-b.

In order to reduce the given equation to a polynomial, we are required to simplify and combine like terms. First, we can simplify the expression in the numerator by expanding the square:

((y-b)²/(y-b+1) = (y-b)(y-b)/(y-b+1) = (y-b)²/(y-b+1)

Now, we can combine the two terms in the equation by finding a common denominator:

(y-b)²/(y-b+1) + (y-b)/(y-b+1) = [(y-b)² + (y-b)]/(y-b+1)

Next, we can combine the terms in the numerator by factoring out (y-b):

[(y-b)² + (y-b)]/(y-b+1) = (y-b)(y-b+1)/(y-b+1)

Finally, we can cancel out the common factor of (y-b+1) in the numerator and denominator to get the polynomial:

(y-b)(y-b+1)/(y-b+1) = y-b

Therefore, the equation ((y-b)²)/(y-b+1)+(y-b)/(y-b+1)  after being simplified, is equivalent to the polynomial y-b.

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The volume of the given solid is πa³/4 cubic units.

Given that the base of a solid is a quadrant of a circle of radius a and each cross-section perpendicular to one edge of the base is a semicircle whose diameter lies in the base.

To find the volume of the solid, we'll integrate the area of the cross-section over the height of the solid.

Let us consider a cross-section with thickness dx at a distance x from the vertex of the quadrant, as shown in the figure below.

Here, the diameter of the semicircle forming the cross-section is 2(x + a).

Therefore, the radius of the semicircle is (x + a).

Area of the cross-section = Area of the semicircle= π[(x + a)²]/2

Volume of the solid = ∫Area dx from 0 to a= ∫π[(x + a)²]/2 dx from 0 to a= π/2 ∫(x² + 2ax + a²) dx from 0 to a= π/2 [(a³/3 + 2a²/2 + a³/2) - (0)] = πa³/4 cubic units

Therefore, the volume of the given solid is πa³/4 cubic units.

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Answer:.

Step-by-step explanation:

Answer: t = 37.8 degree

Step-by-step explanation:

We know that a circle has 360 degrees, this is half a circle, so it total is 180 degrees.

We add 63.7 with 78.7 = 142.4 degree

Take 180 - 142.2 = 37.8 degree

The value of y is :

y = ln(2/(eˣ + 1))

Given equation is :

(e-2x+y +e-2x) dx - eydy = 0

To solve the separable equation, we need to separate the variables in the differential equation.

The given differential equation can be written as,

(e-2x+y +e-2x) dx - eydy = 0

Let's divide by ey and write it as,

(\(e^{-y}\) (e⁻²ˣ+y +e⁻²ˣ )) dx - dy = 0

(\(e^{-y}\) (e⁻²ˣ+y +e⁻²ˣ )) dx = dy

Taking the integral of both sides of the equation we get:

∫(\(e^{-y}\)  (e⁻²ˣ+y +e⁻²ˣ )) dx = ∫ dy

On the left side we can write,

\(e^{-y}\)  ∫(e⁻²ˣ+y +e⁻²ˣ ) dx= y + C

After solving this differential equation, the value of y is y = ln(2/(eˣ + 1)).

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El área superficial total de los veinte tarugos es mayor que el área superficial cubierta por el pegamento.

En esta pregunta debemos calcular el área superficial total de los tarugos (\(A_{s}\)), en milímetros cuadrados, y comparar el resultado con la cifra afirmada por Eduardo. El área superficial total es:

\(A_{s} = 20\cdot \pi\cdot (5\,mm)^{2}\cdot (80\,mm)\)

\(A_{s} \approx 125663.706\,mm^{2 }\)

En consecuencia, el área superficial total de los veinte tarugos es mayor que el área superficial cubierta por el pegamento. Francisca tiene la razón. \(\blacksquare\)

El enunciado omite las dimensiones geométricas de cada tarugo (5 milímetros de radio y 80 milímetros de longitud).

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Answer:

Step-by-step explanation:

equation of The line L : y = -(1/2)x + 6

A(8 , b) ∈ L  then b = -(1/2)(8) +6 then b = -4 + 6 = 2

Therefore ,

A(8 , 2)

AB = 2

CD = 6

BC = 8

…………………………………………

Area of the trapezoid ABCD

= (CB÷2)×(AB + CD)

= (8÷2)×(6+2)

= 32