Which of the following is a rational number?

The extreme value of the function f(x) is the minimum value of the profit, which occurs when x = 15.

The given function f(x) represents the profit in thousands of dollars of selling x items. To find the meaning of the extreme value, we need to find the critical points of the function, which are the values of x where the derivative of the function is equal to zero or undefined.

The derivative of the given function is:

f'(x) = 12x - 180

Setting f'(x) = 0 to find critical points:

12x - 180 = 0

Solving for x, we get:

x = 15

So, x = 15 is the critical point of the function.

Now, we need to determine whether this critical point is a maximum or a minimum.

To do so, we can use the second derivative test. The second derivative of the given function is:

f''(x) = 12

Since f''(15) = 12 > 0, the critical point x = 15 is a minimum.

Therefore, the extreme value of the function f(x) is the minimum value of the profit, which occurs when x = 15. This minimum value represents the least amount of profit that can be earned by selling the items.

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The expressions that are equivalent to 81x² + 180x - 200 = 100 are:  27x² - 60x + 100 = 0, x² + (20/9)x - (100/27) = 0, (x + 1/3)(x + 10/3) = 0, (3x + 1)(3x + 10) = 0.

To find the expressions that are equivalent to 81x² + 180x - 200 = 100, we can simplify and manipulate the equation using basic algebraic operations.

Starting with the given equation:

81x² + 180x - 200 = 100

We can subtract 100 from both sides to get:

81x² + 180x - 300 = 0

Now, we can simplify the left side by dividing each term by their greatest common factor, which is 3:

27x² + 60x - 100 = 0

Next, we can divide each term by 27 to make the coefficient of x² equal to 1:

x² + (60/27)x - (100/27) = 0

Simplifying the fractions, we get:

x² + (20/9)x - (100/27) = 0

Now, we can use the quadratic formula to find the solutions of this equation:

x = (-b ± √(b² - 4ac))/2a

where a = 1, b = 20/9, and c = -100/27.

Plugging in these values, we get:

x = (-20/9 ± √((20/9)² + 4(1)(100/27)))/2(1)

x = (-20/9 ± √(400/81 + 400/27))/2

x = (-20/9 ± √(1600/81))/2

x = (-20/9 ± 40/9)/2

x = (-20 ± 40)/18

x = -1/3, -10/3

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Answer:

9/2

Step-by-step explanation:

To find the gradient of a line passing through two points, we can use the formula:

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

where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.

Using the points (1, 4) and (-1, -5), we have:

m = (-5 - 4)/(-1 - 1)

= (-9)/(-2)

= 9/2

Therefore, the gradient of line L is 9/2.

Answer:

60°

Step-by-step explanation:

Let m<R = x.

Let m<Q = 2x.

m<Q + m<R = 90

2x + x = 90

3x = 90

x = 30

m<Q = 2x = 2(30) = 60

Answer: 60°

The given quadratic function, y=x^2+7x+4, in vertex form is y = (x + 7/2)^2 - 33/4

From the question, we are  to write the given quadratic function in vertex form

To write the quadratic function y = x^2 + 7x + 4 in vertex form, we can complete the square. The vertex form of a quadratic function is y = a(x - h)^2 + k, where (h, k) is the vertex.

To complete the square, we need to add and subtract a constant inside the parentheses so that the expression inside the parentheses becomes a perfect square trinomial. We can do this by adding and subtracting (7/2)^2 = 49/4 inside the parentheses:

y = x^2 + 7x + 4

= (x^2 + 7x + 49/4) - 49/4 + 4 (adding and subtracting 49/4)

= (x + 7/2)^2 - 33/4

Hence, the vertex form is y = (x + 7/2)^2 - 33/4

NOTE: The vertex is (-7/2, -33/4).

Here is the correct question:

Write the quadrat function Y=x^2+7x+4 in vertex form

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Answer:54

Step-by-step explanation:

7 squared + \sqrt{25 }

[tex]7^{2}=49\\and \ \\\sqrt{25}=5[/tex]

49+5=54

Answer:

54

Step-by-step explanation:

[tex]7 ^2 + \sqrt{25} \\= 49 + 5\\= 54[/tex]

Hope this helps!

Brainliest and a like is much appreciated!

Step-by-step explanation:

x + 4y = 10 ---(1)

13x + 5y = 10 ---(2)

(1) x 13 : 13x + 52y = 130 ---(3)

(3)-(2) : 47y = 120

y = 120/47 ---(4)

sub (4) into (1)

x + 4y = 10

x + 4(120/47) = 10

x = -10/47

Check the picture below.

so if we just find the vertex of that parabolic path, we'd get how far up it went and how long it took

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+16}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 16}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (16)^2}{4(-16)}\right) \implies \left( - \cfrac{ 16 }{ -32 }~~,~~0 - \cfrac{ 256 }{ -64 } \right) \\\\\\ \left( \cfrac{ -1 }{ -2 } ~~~~ ,~~~~ 0 +4 \right)\implies \stackrel{seconds ~~ feet }{\left(0.5~~,~~4 \right)}[/tex]

well, as you see in the picture, the horse hits the ground again when h(t) = 0

[tex]\stackrel{h(t)}{0}=-16t^2+16t\implies 0=-16t(t-1)\implies t= \begin{cases} 0\\ 1 \end{cases}[/tex]

so at t=0 and t=1 it's touching the ground, at t=0 when it begins to jump at t=1 when it thumps back down, took that long.

The percentage of the cuboid filled with water is given as follows:

53.85%.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions of the cuboid are given as follows:

The filled dimensions of the cuboid are given as follows:

As only the height is different, the percentage filled is obtained as follows:

7/13 = 53.85%.

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From most minutes of sunlight to least minutes of sunlight during summer, the order would be  Winnepeg, Philadelphia, Houston and Porto Alegre.

The number of sunlight hours increases as you move to the north, indeed in places like Alaska there can be 24 hours of sunlight near the summer solstice. Based on this principle, the correct order for the places given would be:

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The solution for the formula V = πr² is A. r = √(V/(π)).

What is the equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

To solve for r in the formula V = πr², we need to isolate r on one side of the equation.

We can do this by dividing both sides of the equation by π and then taking the square root of both sides:

V/π = r²

√(V/π) = r

Therefore, the solution is A. r = √(V/(π)).

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The correct answer is [tex](\frac{1}{10!} )[/tex] i.e. 0.00002756% , for this we have to learn probability.

Probability of an event which define as the possibility of any event to occur when we perform any event.

Probability is a method to determine how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make assumption about the likelihood or chance of an event happening, or how likely it is.

An event in probability theory is the result of a random experiment or a specified group of its results.

To achieve 10 balls in order we first choose a random ball, then the probability of that ball is i.e. P(1) =  [tex]\frac{1}{10}[/tex] .

Then choose Second ball whose probability is i.e. P(2) =  [tex]\frac{1}{9}[/tex] .

And then [tex]\frac{1}{8}, \frac{1}{7} ,\frac{1}{6} ,\frac{1}{5} .......... finally,\ \frac{1}{1}.[/tex]

[tex]P(1.......10\ in\ order)=\frac{1}{10!}[/tex]

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The Cartesian, parametric, and normal forms for the given line in R2 are y = 5x - 15, x = 2 + t and y = 3 + 5t, and 4x – 5y + 15 = 0, respectively.

Cartesian form: The Cartesian form for this line is y = 5x - 15. This can be calculated by taking the given slope (m = 5) and the given point (3,1), and using the equation y-y1 = m(x-x1) to solve for the y-intercept.

Parametric form: The parametric form for this line is x = 2 + t and y = 3 + 5t. This can be calculated by taking the given x and y intercepts (2,0) and (0,3), and using the equations x = x1 + t and y = y1 + m*t to solve for t.

Normal form: The normal form for this line is 4x – 5y + 15 = 0. This can be calculated by taking the given slope (m = 5) and the given point (3,1), and using the equation Ax + By + C = 0 to solve for A, B, and C.

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If the combined weight is 1.5 kilograms and the weight of the gram weights is 0.5 kilograms, then the mass of the object is 1 kilogram.

Mass is describes the amount of matter it contains. It is usually measured in kilograms or pounds. Mass is distinct from weight, which measures the force of gravity on an object.

To measure the mass of an object that I think has a mass greater than 1 kilogram, I will use a pan balance and kilogram and gram weights.

First, I will set the pan balance to 0 by adjusting the counterweight.

Then, I will place the object on one of the pans and add weights to the other pan until the balance is equal.

I will first use 1 kilogram weights and then add smaller gram weights until the pan balance is equal.

Once the pan balance is equal, the combined weight of the object and the weights will be the mass of the object.

I can then calculate the mass in kilograms by subtracting the weight of the gram weights from the total mass.

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The minimum οf the data is 81, the first quartile is 94, the median οf the data is 105, the third quartile is 129, and the maximum οf the data is 133.

A stem and leaf plοt is a graphical representatiοn οf a dataset that is used tο display and οrganize individual values. The plοt is made up οf twο parts: the "stem" and the "leaf." The stem is the left-hand side οf the plοt and represents the first οne οr twο digits οf the values, while the leaf is the right-hand side οf the plοt and represents the remaining digits.

This plοt shοws the distributiοn οf the data and allοws yοu tο quickly see the range οf values, the shape οf the distributiοn, and any οutliers οr gaps in the data.

The stem and leaf plot represents the following data:

Stem/Leaf                  Value

8 1 3                              813

9 0 3 4 7       903, 934, 974

10 4 7                     104, 107

11 5                                  15

12 9                               129

13                                    13

The five-number summary for the data is as follows:

The minimum of the data is 81.

The first quartile is 94.

The median of the data is 105.

The third quartile is 129.

The maximum of the data is 133.

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Answer:

minimum-81

first Q-95

median-109

third Q-127

maximum-136

Step-by-step explanation:

yurrrrr

Answer:

congruent, same length

Step-by-step explanation:

The three sides of an equilateral triangle are congruent.

They have the same length.

the weights that separate the top 9%of the machine components is 6.33 ounces and the bottom 9% of the machine components is 6.27 ounces.

We know that the weights of the machine components are normally distributed with a mean of 6.3 ounces and a standard deviation of 0.03 ounces.

Let X be the weight of a machine component.

To find the weights that separate the top 9% and the bottom 9%, we need to find the z-scores corresponding to these percentiles and then use them to find the corresponding weights.

Using a standard normal distribution table, we can find that the z-score corresponding to the top 9% is approximately 1.34, and the z-score corresponding to the bottom 9% is approximately -1.34.

Using the formula for converting a value to a z-score:

z = (X - μ) / σ

For the top 9% weight, we have:

1.34 = (X - 6.3) / 0.03

Solving for X, we get:

X = 6.33 ounces

For the bottom 9% weight, we have:

-1.34 = (X - 6.3) / 0.03

Solving for X, we get:

X = 6.27 ounces

Therefore, the weights that separate the top 9% and the bottom 9% of the machine components are 6.33 ounces and 6.27 ounces, respectively. Any components with weights outside of this range may be considered for rejection.

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To find -2A, we simply multiply every element of A by -2. Therefore,

            6   -10   0

-2A  =  -6    4   -2

            2   -8   -14

A matrix is a rectangular array of numbers, arranged in rows and columns. Matrices are used in many areas of mathematics, science, and engineering to represent and manipulate data.

Matrices can have any number of rows and columns, but are typically denoted by the letter A with a subscript indicating the number of rows and columns. For example, a matrix with 2 rows and 3 columns might be denoted as [tex]A_{2x3}[/tex].

To find -2A, we need to multiply every element of matrix A by -2. In other words, we need to apply the scalar multiplication operation to every element in the matrix.

Scalar multiplication is a simple operation where we multiply each element in a matrix by a scalar, which is just a regular number. In this case, our scalar is -2.

To perform scalar multiplication on a matrix, we simply multiply each element of the matrix by the scalar. So, for each element in matrix A, we can write:

(-2) * aij

where i is the row number and j is the column number of the element.

We can use this formula to find each element of -2A. Let's look at the first element, a11:

(-2) * a11 = (-2) * 5 = -10

So the first element of -2A is -10. We can repeat this process for each element in the matrix to get the following result:

            6   -10   0

-2A  =  -6    4   -2

            2   -8   -14

And that's it! We have successfully found -2A by applying scalar multiplication to every element of matrix A.

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x = 2 is not a root of the given function.

We are required to use the Remainder Theorem to determine whether x = 2 is a root of the given function:????(x) = 3x³ − 4x² − 8.Remainder Theorem The Remainder Theorem states that when a polynomial function f(x) is divided by (x - a), the remainder equals f(a).In order to find whether x = 2 is a root of the function or not, we have to apply the Remainder Theorem. We can perform the division in the following manner: Solution The given polynomial function is: ????(x) = 3x³ − 4x² − 8.So, we can perform the division as shown below: On dividing f(x) by (x - a), the remainder is f(a). Hence, the remainder when the given function is divided by (x - 2) is -14.Therefore, x = 2 is not a root of the given function.

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The correct option is (c) i.e. The segments are parallel.

What are parallel lines?

Parallel lines are two lines in a two-dimensional space that never intersect, no matter how far they are extended in either direction. They always maintain the same distance between them and have the same slope. The symbol for parallel lines is "||".

In geometry, parallel lines are important because they create angles that are congruent or equal to each other when intersected by a third line, known as a transversal. This concept is used in many practical applications, such as in construction, engineering, and navigation.

The segments are parallel.

If the slopes of two lines are equal, it means that the lines are either parallel or they are the same line. In this case, since the two segments have zero slope, it means that they are horizontal lines. Horizontal lines are always parallel to each other, so we can conclude that the two segments are parallel.

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Answer:

In 2009, a fire destroyed 85% of the

farmer's crops.

To convert a fraction to a

percentage, you can multiply the

fraction by 100.

17/20 0.85

So, 17/20 is equivalent to 0.85 or

85%.

Answer:

In 2009 a fire destroyed 85% of the farmers crops

Step-by-step explanation:

Answer:

A. Corresponding angles

B. Vertically opposite angles

C. Alternate angles

Step-by-step explanation:

Alternate angles are two angles, not adjoining one another, that are formed on opposite sides of a line that intersects two other lines. If the original two lines are parallel, the alternate angles are equal.

Vertically Opposite Angles are the angles opposite each other when two lines cross "Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down. Example: a° and b° are vertically opposite angles.

Corresponding angles are the angles which occupy the same relative position at each intersection where a straight-line crosses two others. If the two lines are parallel, the corresponding angles are equal.

Answer: b

Step-by-step explanation: b is right

Answer:

  14(y -7/2) = (x -5)²

Step-by-step explanation:

You want an equation for the parabola with focus (5, 7) and directrix y=0.

The vertex of a parabola is halfway between the focus and the directrix. When the directrix is a horizontal line, the y-coordinate of the vertex is the average of the y-coordinates of the focus and directrix. The x-coordinate of the vertex is the same as that of the focus.

The scale factor in the vertex form equation is 1/(4p), where p is the distance from the vertex to the directrix.

Here, the vertex y-coordinate is (7+0)/2 = 3.5. The vertex x-coordinate is 5. The distance from the vertex to the directrix is 3.5 -0 = 3.5.

Then the vertex form equation for the parabola can be written as ...

  y = a(x -h)² +k . . . . . . . . parabola with scale factor 'a' and vertex (h, k)

  y = 1/(4·3.5)·(x -5)² +3.5 . . . . . parabola with scale factor 1/(4·3.5) and vertex (5, 3.5)

The fraction can be eliminated to give the form ...

  14(y -3.5) = (x -5)²

A graph of each inequality is shown in the grid below.

A shape which the solution region represent is a rectangle.

In order to graph the solution to the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;

0.4r ≤ 120     .....equation 1.

r ≥ 4(360/5)    .....equation 2.

By evaluating the given system of inequalities, we have;

r ≤ 120/0.4

r ≤ 300

r ≥ 4(360/5)

r ≥ 4(72)

r ≥ 288

By combining the system of inequalities, we have:

288 ≤ r ≤ 300

Based on the graph shown in the image attached below, we can logically deduce that the solution to the given system of inequalities is within the shaded region between the solid lines, and the point of intersection of these solid lines on the graph.

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The normal distribution is a mathematical model used to describe real-world data that occurs in many scenarios, including restaurant wait times. The normal distribution is characterized by a mean and a standard deviation; in this case, the mean wait time is 20 minutes, and the standard deviation is 4 minutes.

In order to find the maximum wait time for customers so that at most 1% of them would receive their meals for free, we can use the normal distribution graph.

The graph shows the probability of a customer waiting any given amount of time. The mean is the highest point on the graph, while the standard deviation can be seen as two "bumps" on either side of the mean. For this scenario, any customer who waits more than 25.5 minutes will be in the top 1% of wait times, and therefore, should receive their meal for free.

This provides a reasonable time limit for customers to expect their meal, while also helping to dispel any negative perceptions about the speed of service.

In terms of the company's profitability, offering free meals to the top 1% of customers does not present any significant risk. The 25.5 minute wait time is well above the average wait time of 20 minutes, so it's unlikely that the company will incur a significant loss due to this promotion.

To sum up, the maximum wait time to be advertised to customers so that 1% of them will receive their meals for free is 25.5 minutes. The normal distribution graph shows how this wait time is chosen, as it corresponds to the top 1% of wait times.

As the average wait time is much lower than this maximum wait time, this promotion is unlikely to cause the company any significant loss in profit.

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The answer, however, will be less than one because the numerator is less than the denominator. Thus, 1 divided by 2 is equal to 0.5. The right response is hence "0.5."

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

Hence, The answer, however, will be less than one because the numerator is less than the denominator. Thus, 1 divided by 2 is equal to 0.5. The right response is hence "0.5."

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The student's reading level is at the 4.01st percentile. Answer: 4.01.

Given that you are an elementary school teacher and you are evaluating the reading levels of your students. You find an individual that reads 50 word per minute. You do some research and determine that the reading rates for their grade level are normally distributed with a mean of 85 words per minutes and a standard deviation of 20 words per minutes.The percentile of a given value represents the percentage of the distribution that falls below that value.To find the percentile rank of the student's reading level, we can use the Z-score formula:$$z = \frac{X - \mu}{\sigma}$$where X is the student's reading rate, μ is the mean reading rate for the grade level, and σ is the standard deviation of the reading rates for the grade level. Substituting the given values, we get:$$z = \frac{50 - 85}{20} = -1.75$$The negative sign indicates that the student's reading rate is below the mean rate for the grade level. Now we need to find the percentile of the Z-score -1.75.Using a standard normal table or calculator, we can find that the area to the left of -1.75 under the standard normal distribution is 0.0401. Therefore, the student's reading level is at the 4.01st percentile. Answer: 4.01.

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Answer: 4:12

Step-by-step explanation: Since it is squares to total you have to put the amount of squares first. That would be 4. Then, you have to figure out the total which is just adding 4+8=12. That would be the total. Therefore, the answer would be 4 to 12.

The point halfway between (–0.75, –1.25) and (–0.75, –0.25) is (–0.75, –0.75).To find the point halfway between (–0.75, –1.25) and (–0.75, –0.25), we will use the midpoint formula.

To find the point halfway between (–0.75, –1.25) and (–0.75, –0.25), we will use the midpoint formula. The midpoint formula is (x1 + x2) / 2, (y1 + y2) / 2. In this case, x1 and x2 are both –0.75, and y1 is –1.25 and y2 is –0.25. Plugging in the values and doing the math, we get (–0.75 + –0.75) / 2 = –0.75, and (–1.25 + –0.25) / 2 = –0.75. Therefore, the point halfway between (–0.75, –1.25) and (–0.75, –0.25) is (–0.75, –0.75).

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