What is the largest possible value
could take given that it must be an integer?
x<5

Answer:

C) 10839

Step-by-step explanation:

.For example, 21, 4, 0, and −2048 are integers, while 9.75, 512, and √2 are not.

In parallelogram lonm, om is 34.

What is parallelogram?

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.

A quadrilateral with the opposing sides parallel is called a parallelogram. A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.

First we have OQ =QM,

So 2x+3=3x-4,

x =7.

Hence OM =2(17)=34.

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Answer: D) 34

Step-by-step explanation:

edge 2023

The average speed is the ratio of the distance covered to the time taken.

The distance Hanna travels at 60 miles = 70 miles

The further distance she travels = 40 miles

The average speed of the entire journey = 46 mph

The correct response values is arrived at through the following steps

\(\displaystyle Average \ speed = \mathbf{\frac{Total \ distance }{Time}}\)

Therefore;

\(\displaystyle Time= \frac{Total \ distance }{Average \ speed}\)

The values of total distance and time are plugged into the above equation to find the time she takes to travel each part of the journey as follows;

The time she takes to travel 70 miles in hours is; \(\displaystyle Time= \frac{70}{60} = \frac{7}{6}\)

The time she takes to travel the total distance of 70 miles + 40 miles = 110 miles, is given as follows;

\(\displaystyle Time= \frac{70 + 40}{46} = \mathbf{\frac{55}{23}}\)

The time in hours she travels 40 miles is therefore,

\(\displaystyle t = \frac{55}{23} -\frac{7}{6} = \frac{169}{138}\)

\(\displaystyle Her \ average \ speed \ in \ the \ final \ 40 \ miles = \frac{40 \ miles }{\frac{169}{138} \ hours} \approx \underline{ 32.66 \ mph}\)

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The absolute maximum value of the function g(x) = |x|−3|x 1| on the closed interval [-2,2] is 5. This is because the absolute value of x has its maximum value of 2 on the interval and the absolute value of x-1 has its maximum value of 3 on the same interval. Therefore, the maximum value of g(x) is 5

The function g(x) = |x|−3|x 1| is defined as the absolute value of x minus the absolute value of x minus 1. This means that the value of g(x) will always be negative or zero, depending on the value of x. On the closed interval [-2,2], the absolute value of x can range from 0 to 2, while the absolute value of x minus 1 can range from 1 to 3. Thus, the maximum value of g(x) on the interval is the difference between these two values, which is 5. This is because the absolute value of x is at its maximum of 2 and the absolute value of x minus 1 is at its maximum of 3 on the interval, so the difference between them is 5.

The absolute maximum value of function g(x) = |x|−3|x 1| on the closed interval [-2,2] can be calculated as follows:

First, let x = 2, then g(2) = |2|−3|2-1| = |2|−3|1| = 2−3 = -1

Second, let x = -2, then g(-2) = |-2|−3|-2-1| = |-2|−3|-3| = 2−3 = -1

Finally, let x = 0, then g(0) = |0|−3|0-1| = |0|−3|-1| = 0−3 = -3

Therefore, the absolute maximum value of g(x) is 5, which is obtained when x = 0

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The ratio of the horizontal change to the vertical change of a line would not be used to describe a slope. Thus the correct option is option C.

The slope of a line is defined as the ratio of the vertical change (rise) to the horizontal change (run) of a line.

Slope=Vertical Change/Horizontal Change

This is also represented as the "ratio of rise to run of a line".

Slope=Rise/Run

In the given question, however, option C states that the "ratio of the horizontal change to the vertical change of a line".

Horizontal Change/ Vertical Change= 1/slope

This is an incorrect statement since the ratio of the horizontal change to the vertical change of a line is the reciprocal of the correct ratio.

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Ann factored the expression completely

Max did not factor completely

The trinomial: 4x^2 - 6x - 4

ax^2 + bx + c

Factors of 16 = 2 and 8

The sum of -8 and 2 gives -6, while the product gives -16 (a × c = 4× 4)

we factorise:

4x^2 -8x + 2x - 4

4x (x - 2) + 2(x -2)

(4x + 2) (x - 2)

factorising completely, 2 is common to the first expression in bracket

2(2x + 1)(x - 2) = 2(x - 2)(2x + 1)

Ann factored: 2(x - 2)(2x + 1)

Max factored: (x - 2)(4x + 2)

From our workings, we can see Ann factored the expression completely

Max did not factor completely

Reason: one of the factors of the expression could still be factorise

4x + 2 can be factorise as 2(2x + 1)

Answer:

Assuming the leak took 2 hours to fix, the original height of the pool is 5 feet.

Step-by-step explanation:

This is probably the most simple "high school" problem I've seen in a while. All you have to do is move the negative 0.25 to the other side to isolate x. That gives you 4.75 + 0.25, or 5 feet.

The 50th percentile is NOT a measure of dispersion. What is a measure of dispersion? A measure of dispersion is a statistical term used to describe the variability of a set of data values. A measure of dispersion gives a precise and accurate representation of how the data values are distributed and how they differ from the average. A measure of central tendency, such as the mean or median, gives information about the center of the data; however, it does not give a complete description of the distribution of the data. A measure of dispersion is used to provide this additional information.

Measures of dispersion include the range, interquartile range, variance, and standard deviation. The 50th percentile, on the other hand, is a measure of central tendency that represents the value below which 50% of the data falls. It does not provide information about how the data values are spread out. Therefore, the 50th percentile is not a measure of dispersion.

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The following are the statements which are true to the following:

a. simple graph does not have parallel edges or self-loops.

b.  in a connected, directed graph, every node is reachable from all other nodes.

c.  there cannot be any cycle in a tree.

d.  if a graph g is a forest, then there is no cycle in g.

We have the following:

a. a simple graph devoid of self-loops or parallel edges. consequently valid.

A simple graph is one that doesn't contain self-loops or parallel edges.

b. In a directed, connected graph, every node may be reached from every other node. consequently valid.

When all of the directed edges in a directed graph are replaced with undirected edges, the resulting undirected underlying graph is a connected graph, which indicates that the directed graph is weakly connected (or just connected).

c. A tree cannot contain a cycle. consequently valid

The aforementioned claim is accurate. Cycles cannot be contained in a tree since it is a non-linear data structure. Cycles are a possible feature of a graph.

d. If a graph g is a forest, then g does not include a cycle. consequently valid

The acyclic graph of a forest (i.e., a graph without any graph cycles). Therefore, forests are made up only of (potentially unconnected) trees, therefore the name "forest." All trees, empty graphs, and the singleton graph are a few examples of forests.

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Answer:

the correct graph is the one that shows a horizontal segment, followed by a positive slope segment, followed by a flat segment, and then a negative slope segment that is option B.

What is graph?

In mathematics, a graph is a visual representation of a set of objects and the connections between them. The objects, which are often called vertices or nodes, are typically represented by points or circles on the graph. The connections between the objects, which are often called edges or arcs, are typically represented by lines or curves connecting the points or circles.

Here,

To represent Marie's situation in a graph, we need to plot her golf cart's distance from the first hole over time. Let's analyze the given information to determine what the graph should look like.

For the first 30 minutes, Marie stayed at the first hole, so her distance from the first hole would be 0 during that time.

For the next 2 hours, Marie drove away from the first hole. Her distance from the first hole would increase during this time.

After 2 hours of driving, Marie stopped for lunch. Her distance from the first hole would remain constant during this time.

After lunch, Marie took 2 more hours to drive back to the first hole. Her distance from the first hole would decrease during this time.

The x-axis represents time in hours, and the y-axis represents distance from the first hole in miles. The graph starts at the origin, where the golf cart stays for the first 30 minutes, and then goes up with a positive slope for 2 hours as the golf cart moves away from the first hole. Then, the graph remains flat for 1 hour during lunch, before going down with a negative slope for 2 hours as the golf cart returns to the first hole.

As a result, the right graph is option B, which displays a horizontal section followed by a positive slope segment, a flat segment, and then a negative slope segment.

Step-by-step explanation:

No, u + v is not in V and there is no scalar c such that cu is in V.

a. No, u + v is not in V. Since x < 0 and y > 0 for u and v, the sum of u and v will have a positive x-coordinate, which violates the condition that x < 0 for vectors in V.

b. Let u = [-1, 1]. To show that cu is not in V for any scalar c, we can assume that cu is in V and derive a contradiction.

If cu is in V, then its x-coordinate must be negative, i.e., cu = [-c, y] for some positive y.

But this means that u = [-1, y/c] is also in V, which contradicts the fact that x < 0 for vectors in V.

Therefore, there is no scalar c such that cu is in V.

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Answer:

x=1 is the correct answer

Therefore, when Savannah is 42 feet above the ferris wheel's horizontal diameter, her angle of rotation is approximately 68.6 degrees.

Given by the question.

Let's first draw a diagram to visualize the situation.

      *

    *    *

  *        * <-- Ferris wheel at 3 o'clock position

 *          *

*            * <-- Highest point

*______________*______

      62 ft

The Ferris wheel is a circle with radius 62 feet, and Savannah is sitting in a bucket that moves along the circle. When she is at the highest point, she is 62 feet away from the center of the circle, and when she is on the horizontal diameter, she is 62 feet - 42 feet = 20 feet away from the center of the circle.

To find Savannah's angle of rotation, we can use the cosine function.

cos(theta) = adjacent / hypotenuse

In this case, the adjacent side is 20 feet, and the hypotenuse is 62 feet.

cos(theta) = 20/62

To solve for theta, we need to take the inverse cosine of both sides.

theta = cos^-1(20/62)

Using a calculator, we get:

theta = 68.6 degrees

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Answer:

Choice A) 0 < x < 18

Step-by-step explanation:

10x = 6x + 20

subtract

4x = 20

solve for x

x = 5

Based on the given data, we can calculate the control limits using 3-sigma for the diameter of the auto pistons.

a) The value of x is 155.56 mm (rounded to two decimal places).

b) The value of R is 4.44 mm (rounded to two decimal places).

c) Using 3-sigma, the Upper Control Limit (UCL) for the diameter is calculated as:

UCL = x + 3R = 155.56 + 34.44 = 156.93 mm (rounded to two decimal places)

The Lower Control Limit (LCL) for the diameter is calculated as:

LCL = x - 3R = 155.56 - 34.44 = 154.19 mm (rounded to two decimal places)

d) Using 3-sigma, the Upper Control Limit for the Range (UCLR) is calculated as:

UCLR = D4 * R = 2.115 * 4.44 = 7.89 mm (rounded to two decimal places)

The Lower Control Limit for the Range (LCLR) is always 0 in this case since negative ranges are not possible.

e) If the true diameter mean should be 155 mm, the new centerline (nominal line) would be 155 mm. In this case, the UCL and LCL would be calculated using 3-sigma as follows:

UCL = Nominal + 3R = 155 + 34.44 = 156.37 mm (rounded to two decimal places)

LCL = Nominal - 3R = 155 - 34.44 = 153.63 mm (rounded to two decimal places)

Please note that the control limits calculated using 3-sigma assume a normal distribution and the data follows the same pattern in the future.

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The complete question is:

What is the value of x? = x= 155.56 mm (round your response to two decimal places). b) What is the value of R? R= 4.44 mm (round your response to two decimal places). c) What are the UCL, and LCL; using 3-sigma? Upper Control Limit (UCL) = 156.93 mm (round your response to two decimal places). Lower Control Limit (LCL) = 154.19 mm (round your response to two decimal places). d) What are the UCLR and LCLR using 3-sigma? Upper Control Limit (UCLR)= 7.89 mm (round your response to two decimal places). Lower Control Limit (LCLR)= 0.99 mm (round your response to two decimal places). e) If the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are the new UCL and LCL? Upper Control Limit (UCL)= 156.37 mm (round your response to two decimal places). Lower Control Limit (LCL;)= 153.63 mm (round your response to two decimal places). Refer to Table 56.1-Factors for Computing Control Chart Limits (3 sigma) for this problem Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: Day 1 2 3 4 5 Mean x (mm) 150.9 153.2 153.6 153.5 154.6 Range R (mm) 4.0 4.8 4.1 4.8 4.5

Answer:

10.7a−8.1b

I hope I helped you!

To find the average value of the function f(x, y) = 8x + 5y over the given triangle, we need to calculate the double integral of f(x, y) over the region and then divide it by the area of the triangle.

The vertices of the triangle are (0, 0), (2, 0), and (0, 7). We can set up the integral as follows:

∬R f(x, y) dA = ∫₀² ∫₀ᵧ (8x + 5y) dy dx

Integrating with respect to y first, the inner integral becomes:

∫₀ᵧ (8x + 5y) dy = 8xy + (5y²/2) |₀ᵧ = 8xᵧ + (5ᵧ²/2)

Now integrating with respect to x, the outer integral becomes:

∫₀² (8xᵧ + (5ᵧ²/2)) dx = (4x²ᵧ + (5ᵧ²x)/2) |₀² = (8ᵧ + 10ᵧ² + 20ᵧ)

To find the area of the triangle, we can use the formula for the area of a triangle: A = (1/2) * base * height.

The base of the triangle is 2 and the height is 7.

A = (1/2) * 2 * 7 = 7

Finally, to find the average value, we divide the double integral by the area of the triangle:

Average value = (8ᵧ + 10ᵧ² + 20ᵧ) / 7

Simplifying this expression gives:

Average value = (8 + 10ᵧ + 20ᵧ) / 7 = (8 + 10(7) + 20(7)) / 7 = 142/7 = 20 2/7

Therefore, the correct answer is not listed among the options provided.

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Answer: A

Step-by-step explanation:

The correct option is A.

In mathematics, an exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Given is that a graph,

So, from the graph we can concluded that it is an exponential and positive function,

Therefore, as x increases y also increases.

We know that the exponential function is given by =

y = abˣ

So, when x = 0, y = 100,

100 = a × b⁰

a = 100

When x = 4, y = 150,

150 = 100 × b⁴

b⁴ = 1.5

b = 1.11

y = 100(1.11)ˣ

Change = 110-100 / 100 × 100% = 10%

Therefore, we can say the value of a $100 stock grows in value by 10% each year.

Hence the correct option is A.

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The value of the term 14 times 39 can be expressed as the value of 2.7857.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

Or, how do you increase something by 14 to get 39? If "x" in the phrase "14 times what = 39?" is "what," then the equation to use to solve the issue is as follows:

14 • x = 39

which is spelled out as:

14x = 39

In order to get the x alone, we must take the 14 from the left side of the equation. We multiply both sides by 14 to achieve that.

14x/14 = 39/14

39/14 is 2.7857 and 14x/14 equals x, thus our equation will be as follows:

x = 2.7857

Therefore, the result of 14 times what is 39 is 2.7857.

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Answer:

A, C, E

Step-by-step explanation:

A function cannot have an x-value that produces more than y-value.  Examples would be {(2, 2), (2,3)} and {(1,0), (1,5)}.

A - This could be a function because it follows the above rule.

B - This can not be a function because it has an x-value that has two y-values.

C - This could be a function because it follows the rule.

D - This can not be a function because it has an x-value that has two y-values.

E - This could be a function because it follows the rule.

The system of equations that gives the (7,-3)

2x - 5y = 29

6x + 3y = 33 Option D

We can solve by the method of simultaneous equations so that we can be able to obtain the lines.

We have that;

2x - 5y = 29 ---- (1)

6x + 3y = 33 ---- (2)

Multiply equation (1) by 6 and equation (2) by 2

12x - 30y = 174

-(12x + 6y = 66)

y = -3

From equation 1;

2x = 29 - -5y

Where y = -3

x  =  29 - -5(-3)/2

x = 7

Thus the intersection of the lines that we have in the problem can now be obtained as (7,-3)

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The person who starts Priya does not always win, but rather the outcome depends on whether the total number of players is even or odd.

Let's record the game on paper for different numbers of players and see if the person who starts always wins.

Case 1: Two Players (Priya and Jada)

Round 1: Priya says SAFE.

Round 2: Jada says OUT and leaves the circle.

Priya is the winner. The person who starts (Priya) wins.

Case 2: Three Players (Priya, Jada, and Han)

Round 1: Priya says SAFE.

Round 2: Jada says OUT and leaves the circle.

Round 3: Han says SAFE.

Priya is the winner. The person who starts (Priya) wins.

Case 3: Four Players (Priya, Jada, Han, and Diego)

Round 1: Priya says SAFE.

Round 2: Jada says OUT and leaves the circle.

Round 3: Han says SAFE.

Round 4: Diego says OUT and leaves the circle.

Priya is the winner. The person who starts (Priya) wins.

From these examples, we can see that when the number of players is even, the person who starts always wins.

To find more numbers where the person who starts always wins, let's consider some additional cases:

Case 5: Six Players (Priya, Jada, Han, Diego, Alex, and Mia)

Round 1: Priya says SAFE.

Round 2: Jada says OUT and leaves the circle.

Round 3: Han says SAFE.

Round 4: Diego says OUT and leaves the circle.

Round 5: Alex says SAFE.

Round 6: Mia says OUT and leaves the circle.

Priya is the winner. The person who starts (Priya) wins.

Case 6: Eight Players (Priya, Jada, Han, Diego, Alex, Mia, Ethan, and Lily)

Round 1: Priya says SAFE.

Round 2: Jada says OUT and leaves the circle.

Round 3: Han says SAFE.

Round 4: Diego says OUT and leaves the circle.

Round 5: Alex says SAFE.

Round 6: Mia says OUT and leaves the circle.

Round 7: Ethan says SAFE.

Round 8: Lily says OUT and leaves the circle.

Priya is the winner. The person who starts (Priya) wins.

Based on these examples, we can observe that when the number of players is a multiple of 2, the person who starts always wins. There seems to be a pattern here: if the number of players is even, the starting person wins, while if the number of players is odd, the starting person loses.

Therefore, the person who starts does not always win, but rather the outcome depends on whether the total number of players is even or odd.

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The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.

To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.

To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.

After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:

(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).

These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.

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The boats are approximately 9.4 units apart.

To find the distance between two points in a coordinate plane, we can use the distance formula:

distance =\(\sqrt{((x2 - x1)^2 + (y2 - y1)^2)}\)

Using this formula, we can find the distance between Boat A at (4.2, -2) and Boat B at (-5.2, -2):

distance = \(\sqrt{((-5.2 - 4.2)^2 + (-2 - (-2))^2)}\)

distance = \(\sqrt{((-9.4)^2 + (0)^2)}\)

distance =\(\sqrt{(88.36)}\)

distance ≈ 9.4

Therefore, the boats are approximately 9.4 units apart.

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Answer: 5k +7

Step-by-step explanation: -2k + -7k + 5k is -4K and 2+3=5 -4K +5 and 6k +3k= 9k + 2 then u do -4K plus 9k and get 5k next, 5+2

Answer:

See explanation.

Step-by-step explanation:

An expression is a set of terms that are combined using addition, subtraction, multiplication, or division. The following are examples of expressions:

\(2x-1\)

\(5y+8\)

\(2\)

Note: expressions do not equal anything.

In contrast, equations are expressions that equal at least one term. The following are examples of equations:

\(2y-4=26\)

\(4x-4=0\)

\(x=10\)

\(y=x+2\)

Note: equations do equal a term, as shown in the examples.

The limit is finite and non-zero, the series Σ((-1)^(11n - 3))/(10n + 3) is divergent by the nth term test.

To test the convergence or divergence of the series Σ((-1)^(11n - 3))/(10n + 3) from n = 1 to infinity, we need to find the limit of the expression (11n - 3)/(10n + 3) as n approaches infinity.

To determine the highest power of n in the fraction, we can observe the exponents of n in the numerator and denominator. In this case, the highest power of n is n^1.

Let's calculate the limit:

lim(n→∞) [(11n - 3)/(10n + 3)]

To find the limit, we can divide the numerator and denominator by n:

lim(n→∞) [(11 - 3/n)/(10 + 3/n)]

As n approaches infinity, the terms with 3/n become negligible, and we are left with:

lim(n→∞) [11/10]

The limit evaluates to 11/10, which is a finite value.

Since the limit is finite and non-zero, the series Σ((-1)^(11n - 3))/(10n + 3) is divergent by the nth term test.

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The equation will be:

t = b - 2

And we can see that:

Here we have two variables:

t = taner's age

b = age of Tanner's brother.

The independent variable is the one that does not depend on the other, in this case (for how it is worded) is the brother's age.

The dependent variable depends on the other, on this case, Tanner's age.

Now let's write the equation, we know that Taner's age is 2 years less than his brother, then:

t = b - 2

That is the equation.

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Answer:

\(y = \frac{3}{4} x - 3\)

The slope is 3/4, and the y-intercept is -3.

The value of the missing sides are

x = -12

y = 109

z = -102

Consecutive Interior Angles: These are the angles that are on the same side of the transversal and inside the parallelogram. They are supplementary, which means their sum is 180 degrees.

-z + 1 + 77 = 180

-z = 180 - 1 - 77

-z = 102

z = -102

Alternate Interior Angles: These are the angles that are on opposite sides of the transversal and inside the parallelogram. They are also congruent, meaning they have the same measure.

y - 6 = -z + 1

y - 6 = 102 + 1

y = 103 + 6

y = 109

Also

-6x + 5 = 77

-6x = 77 - 5

-6x = 72

x = -12

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