the function f(x)=6x^2-180x=1000 represents the profit f(x) in thousands of dollars of selling x items. what is the meaning of the extreme value

Using the given information, we found the angles of the right triangle as:

∠R = 56.30º

∠P = 33.7º

∠Q = 90º

What is a right triangle?

A triangle with a right angle, also known as a right-angled triangle or right-angled triangle, more technically an orthogonal triangle, has two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle. A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To describe the sides of right triangles, we utilise specific terminology. The side opposite the right angle is always the hypotenuse of a right triangle.

Given one of the angles of the triangles as 90º.

So it is a right triangle.

PQ = 7.5cm
QR = 5cm
∠Q = 90º

The figure is given below.

Now PR is the hypotenuse.

Hypotenuse = [tex]\sqrt{base^2+height^2}[/tex]

base = 5 = QR

height = 7.5 = PQ

PR = [tex]\sqrt{5^2+7.5^2} = \sqrt{81.25}[/tex] = 9.01 cm

We can find the angles using trigonometric relations.

sin R = PQ/PR = 7.5/9.01 = 0.832

∠R = 56.30º

∠P = 180 - (∠Q+∠R) = 180 - (90+56.30) = 33.7º

Therefore using the given information, we found the angles of the right triangle as:

∠R = 56.30º

∠P = 33.7º

∠Q = 90º

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Answer:

25&36

Step-by-step explanation:

25 is a square number and so is 36 and there product is 900. They are also consecutive.

Just assemble the square numbers from the least i.e 4 and try solving as asked to see if it gives 900.

Thus you'll land on 25&36

Answer:

5² and 6²

Step-by-step explanation:

Use trial and error

Start from the product of 1² and 2²

1×2²

1×4=4

4<900 (incorrect)

2²×3²

4×9=36

36<900(incorrect)

3²×4²

9×16=144

144<900(incorrect)

4²×5²

16×25=400

400<900(incorrect) *but close

5²×6²

25×36 =900

900=900(correct)

: . 5² and 6² are the two consecutive square numbers.

The most specific category that this shape can be sorted into is "Triangle."

What is the triangle?

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

The Venn diagram shows the relationships between different types of triangles.

The Scalene circle represents all the triangles that have no equal sides.

The Isosceles circle represents all the triangles that have two equal sides.

The Equilateral circle represents all the triangles that have three equal sides.

The triangle with a tick mark on each side does not provide enough information to determine whether it is a scalene, isosceles, or equilateral triangle.

Therefore, the most specific category that this shape can be sorted into is "Triangle."

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The correct statement regarding the translation of the functions f(x) and h(x) is given as follows:

The graph of h is a translation of 4 units left and 7 units down of f(x).

A translation happens when either a figure or a function are moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The meaning of each translation from function f(x) to function h(x) is given as follows:

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Step-by-step explanation:

use the function sohcahtoa to solve as all these triangles are right angled

Answer:

It's very difficult

maby

4) Let the polynomial function of degree 4 that has roots 3, 2, 2+ i as its roots be p(x).

So, the required polynomial function is:

p(x)=(x−3)(x−2)(x−(2+i))(x−(2−i))

= (x−3)(x−2)(x^2−(2+i)x−(2−i)x+(2−i)(2+i))

= (x−3)(x−2)(x^2−2x−ix+ix+4)

= (x−3)(x−2)(x^2−2x+4)

= x^4−9x^3+28x^2−36x+24

Thus, the polynomial function of degree 4 that has real coefficients and has 3, 2 and 2+ i as some of its roots is x^4−9x^3+28x^2−36x+24.

Given: x^3−2x^2+36x−72=0 and 6i is a zero of this polynomial function.

So, we can write it as:

x^3−2x^2+36x−72= (x−6i)(x−(−6i))(x−6)

= (x−6i)(x+6i)(x−6)

As this polynomial function has real coefficients, so the imaginary roots occur in conjugate pairs.

Thus, the remaining zeros are:

−6i (as 6i is a zero, so −6i is also a zero due to conjugate pair of complex roots) and 6 (as 6i is one factor of the polynomial function, so x−6i will be its conjugate factor, which will be x+6i. And, the remaining factor will be x−6)

Therefore, the remaining zeros of x^3−2x^2+36x−72 polynomial function are −6i and 6.

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Based on the coordinate plane, the ordered pair for the post office is (9, 9).

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

By critically observing the coordinate plane shown in the image attached below, we can logically deduce that the coordinates of the post office would be located in quadrant I at point (9, 9).

Similarly, the the coordinates of the library is also located in quadrant I and it is represented by the ordered pair (6, 2).

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There are 6 + 9 + 9 + 12 + 9 + 9 + 6 = 60 outcomes where the sum of the three dice is greater than 5.

So, the probability of rolling a sum greater than 5 is given by:

Probability = Number of favorable outcomes / Total number of outcomes
Probability = 60 / 216
Probability = 5 / 18

We know that when a dice is rolled, the numbers that come up on the dice are 1, 2, 3, 4, 5 and 6. Since there are three dice, the total number of possible outcomes when they are tossed is given by 6 * 6 * 6 = 216.

Now we have to find the probability of rolling a sum greater than 5. To find this probability, we need to consider all the cases where the sum of the three dice is greater than 5.

The possible outcomes where the sum of the three dice is greater than 5 are:

Sum of 6: (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1) (Total 6)
Sum of 7: (1, 2, 4), (1, 4, 2), (2, 1, 4), (2, 4, 1), (4, 1, 2), (4, 2, 1), (1, 3, 3), (3, 1, 3), (3, 3, 1) (Total 9)
Sum of 8: (1, 2, 5), (1, 5, 2), (2, 1, 5), (2, 5, 1), (5, 1, 2), (5, 2, 1), (3, 3, 2), (3, 2, 3), (2, 3, 3) (Total 9)
Sum of 9: (1, 3, 5), (1, 5, 3), (3, 1, 5), (3, 5, 1), (5, 1, 3), (5, 3, 1), (4, 2, 3), (4, 3, 2), (2, 4, 3), (3, 4, 2), (2, 3, 4), (3, 2, 4) (Total 12)
Sum of 10: (1, 4, 5), (1, 5, 4), (4, 1, 5), (4, 5, 1), (5, 1, 4), (5, 4, 1), (2, 4, 4), (4, 2, 4), (4, 4, 2) (Total 9)
Sum of 11: (1, 5, 5), (5, 1, 5), (5, 5, 1), (2, 5, 4), (2, 4, 5), (4, 5, 2), (4, 2, 5), (5, 4, 2), (5, 2, 4) (Total 9)
Sum of 12: (3, 4, 5), (3, 5, 4), (4, 3, 5), (4, 5, 3), (5, 3, 4), (5, 4, 3) (Total 6)

Therefore, there are 6 + 9 + 9 + 12 + 9 + 9 + 6 = 60 outcomes where the sum of the three dice is greater than 5.

So, the probability of rolling a sum greater than 5 is given by:

Probability = Number of favorable outcomes / Total number of outcomes
Probability = 60 / 216
Probability = 5 / 18

Hence, the probability of rolling a sum greater than 5 is 5 / 18.

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Answer:

Step-by-step explanation: m miles

Answer:

To determine the best value between chocolate bar A and B, we need to calculate the cost per gram of each chocolate bar.

For chocolate bar A, the cost per gram is:

$1.00 ÷ 80 grams = $0.0125 per gram

For chocolate bar B, the cost per gram is:

$1.20 ÷ 85 grams = $0.0141 per gram

Therefore, chocolate bar A is the better value as it costs less per gram compared to chocolate bar B. While chocolate bar B may weigh slightly more, its higher cost per gram means that you are paying more for each gram of chocolate compared to chocolate bar A.

Answer: x=10/9

Step-by-step explanation:

Based οn this pattern, we can determine the vοlume οf the next figure in the pattern by using a height οf 4 units: 1 x 1 x 4 = 4 cubic units.

A cube is three-dimensiοnal sοlid οbject that has six square faces οf equal size. It is special type οf rectangular prism in which all six faces are squares οf equal size. A cube has twelve edges οf equal length and eight vertices where three edges meet.

Let's analyze each figure separately and find the vοlume using the fοrmula fοr the vοlume οf a rectangular prism: length x width x height.

First figure: The length, width, and height are all 1 unit, sο the vοlume is 1 x 1 x 1 = 1 cubic unit.

Secοnd figure: The length and width are still 1 unit, but the height is nοw 2 units. Sο, the vοlume is 1 x 1 x 2 = 2 cubic units.

Third figure: The length and width are still 1 unit, but the height is nοw 3 units. Sο, the vοlume is 1 x 1 x 3 = 3 cubic units.

Frοm the analysis, we can see that the pattern is that the length and width οf each figure remain cοnstant at 1 unit, while the height increases by 1 unit fοr each successive figure.

Based οn this pattern, we can determine the vοlume οf the next figure in the pattern by using a height οf 4 units: 1 x 1 x 4 = 4 cubic units.

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Answer:

QU is 21, and I *think* that VS would be 8.5.

Answer:

QV = 21 , VS = 8.5

Step-by-step explanation:

QU and RS are medians of Δ PQR

the point V where the medians intersect is the centroid.

on each median the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint.

then

VU = [tex]\frac{1}{2}[/tex] QV = [tex]\frac{1}{2}[/tex] × 14 = 7

so

QU = QV + VU = 14 + 7 = 21

and

VS = [tex]\frac{1}{2}[/tex] RV = [tex]\frac{1}{2}[/tex] × 17 = 8.5

Answer: Let's use algebra to check if Tim is correct.

Let x be the original price of the jeans.

When the jeans are marked down by 20%, the new price becomes:

x - 0.2x = 0.8x

Tim claims that if we increase the new price by 20%, we will get the original price:

0.8x + 0.2(0.8x) = x

Simplifying the left-hand side:

0.8x + 0.16x = x

0.96x = x

This is not true for all values of x, which means that Tim's claim is not correct.

Let's use the given information that the original price is $200 to find out what the new price is after the 20% discount:

New price = Original price - Discount

New price = $200 - 20% of $200

New price = $200 - $40

New price = $160

If we increase the new price of $160 by 20%, we get:

New price + 20% of new price

$160 + 20% of $160

$160 + $32

$192

This is not equal to the original price of $200, so we can conclude that Tim's claim is incorrect.

Answer: -7.6n + 11.1

Step-by-step explanation:

We will simplify the given expression by combining like-terms.

   Given:

3.1 - 4.6n - 3n + 8

  Subtract like-terms:

3.1 - 7.6n + 8

   Add like-terms:

11.1 - 7.6n

Answer:

[tex] \sf \: -7.6n + 11.1 [/tex]

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ 3.1 - 4.6n - 3n + 8

Let's simplify the expression,

→ 3.1 - 4.6n - 3n + 8

→ -4.6n - 3n + 3.1 + 8

→ (-4.6n - 3n) + (3.1 + 8)

→ (-7.6n) + (11.1)

→ -7.6n + 11.1

Hence, the answer is -7.6n + 11.1.

The simplified expression is 8x² + 24x.

The distributive property of multiplication over addition is a fundamental property of arithmetic that relates multiplication and addition. It states that when you multiply a number by the sum of two or more numbers, you can first distribute the multiplication over each addend and then perform the addition.

In other words, if a, b, and c are any numbers, then:

a x (b + c) = (a x b) + (a x c)

To simplify the expression 4x° (2x + 6)°, we can use the distributive property of multiplication over addition.

4x° (2x + 6)°

= 4x° * 2x° + 4x° * 6° (using distributive property)

= 8x² + 24x (simplifying by multiplying)

Therefore, the simplified expression is 8x² + 24x.

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Answer:

13

Step-by-step explanation:

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

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

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

Using this formula, we can find the distance between the points (-3, 6) and (-8, -6) as follows:

d = sqrt((-8 - (-3))^2 + (-6 - 6)^2)

= sqrt((-5)^2 + (-12)^2)

= sqrt(25 + 144)

= sqrt(169)

= 13

Therefore, the distance between the two points in simplest radical form is 13.

ECDF=1/100

The value of the empirical cumulative distribution function (ECDF) at the smallest observation in a sample of 100 observations is 1/100.What is the empirical cumulative distribution function (ECDF)?The empirical cumulative distribution function (ECDF) is a graph that depicts the distribution of a given data set. It is used to illustrate the proportion or percentage of data points that fall below a particular value in the distribution. The ECDF can be used to construct a distribution function for data that do not have an existing theoretical distribution.The ECDF value at the smallest observation in a sample of 100 observations is 1/100. This is because the ECDF takes on a value of 0 for all values that are smaller than the smallest observation. Since there are 100 observations in the sample, each observation has a weight of 1/100. Thus, the ECDF value at the smallest observation is 1/100.

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hypotenuse^2 = 16^2 + 25^2

hypotenuse^2 = 256 + 625

hypotenuse^2 = 881

hypotenuse = sqrt(881)

hypotenuse ≈ 29.67 inches

Now that we know the length of the hypotenuse, we can use the 16-inch side and the hypotenuse as the base and height of the triangle, respectively. Plugging these values into the formula, we get:

Area = (16 x 29.67) / 2

Area ≈ 237.36 square inches

Therefore, the area of the triangle is approximately 237.36 square inches.

If Aaron is 8 years older than Judi, then Aaron's age is 22 years , Judi's age is 14 years and Maree's age is 7 years .

Let Maree's age be = M;

Judi is twice as old as Maree, which means ⇒ Judi's age is 2M;

And Aaron is 8 years older than Judi, which means

⇒ Aaron's age is (2M+8);

We know that the sum of their ages is 43, so we can write an equation:

⇒ M + 2M + (2M + 8) = 43

Simplifying and solving for M:

We get,

⇒ 5M + 8 = 43

⇒ 5M = 35

⇒ M = 7

So, Maree's age is 7 years.

Now, we use this to find Judi's and Aaron's ages:

⇒ Judi = 2M = 2 × 7 = 14

⇒ Aaron = 2M + 8 = 2 × 7 + 8 = 22

Therefore, Judi is 14 years old and Aaron is 22 years old.

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around 13 jars of paint will the farmer need to buy in order to paint the entire exterior of the silo.

To find the number of jars the rancher required to get, you really want to know the surface area of both the cone and cylinder.

The method for finding the SA of the cone would be area =[tex]3.14 x r^2 + 3.14 x r x sqrt(r^2 + h^2)[/tex].

SA= 1976.0617791 [tex]m^2[/tex].

The method for finding the SA of the cylinder under the cone would be 3.14 x d x (d/2 + h).

A = 3097.6103564 [tex]m^2[/tex]

Then, at that point, you need to add 1976.0617791+3097.6103564 which gives you 5,073.8. (5,073 is the total surface area of the storehouse)

Then, the partition that by 400.

5,073.8/400 = 12.7

He would have to purchase around 13 jars of paint to have the option to paint the whole storehouse.

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The new mural dimensions are 267 inches by 273 inches.To find the new dimensions, we must add 33 inches to the original length of 234 inches, giving us a new length of 267 inches.

To calculate the new dimensions of Rhiannon's mural, we must first identify the original dimensions of the mural which are 234 inches by 245 inches. To find the new dimensions, we must add 33 inches to the original length of 234 inches, giving us a new length of 267 inches. We must also add 28 inches to the original width of 245 inches, giving us a new width of 273 inches. Therefore, the new dimensions of Rhiannon's mural are 267 inches by 273 inches.

The complete question is :

A rectangle mural measures 234 inches by 245. Rhiannon creates a new mural that is 33 inches longer. What are the dimensions of Rhiannon's new mural?

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0.3406 (approx)

Given that 60% of all Americans live in cities with population greater than 100,000 people. If 47 Americans are randomly selected, we need to find the probability thata. Exactly 25 of them live in cities with population greater than 100,000 people.b. At most 26 of them live in cities with population greater than 100,000 people.c. At least 30 of them live in cities with population greater than 100,000 people.d. Between 23 and 28 (including 23 and 28) of them live in cities with population greater than 100,000 people.Probability is defined as the ratio of the favorable outcomes to the total outcomes of an event. The formula to calculate probability is given by;Probability = Number of favorable outcomes / Total number of outcomesa. Exactly 25 of them live in cities with a population greater than 100,000 people.Probability of exactly 25 Americans living in cities with population > 100,000 people is given by the probability mass function of the binomial distribution.P( X = 25) = 47 C 25 * (0.6)25 * (0.4)22= 0.1213 (approx)b. At most 26 of them live in cities with population greater than 100,000 people.We need to find the probability of at most 26 Americans living in cities with population greater than 100,000 people. This means the number of Americans living in cities with population greater than 100,000 is 0, 1, 2, ..., 26.P(X ≤ 26) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 26)P(X ≤ 26) = ΣP(X = r)Where r varies from 0 to 26P(X ≤ 26) = Σ (47 C r * (0.6)r * (0.4)47-r )r = 0 to 26= 0.6413 (approx)c. At least 30 of them live in cities with population greater than 100,000 people.We need to find the probability of at least 30 Americans living in cities with population greater than 100,000 people. This means the number of Americans living in cities with population greater than 100,000 is 30, 31, 32, ..., 47.P(X ≥ 30) = P(X = 30) + P(X = 31) + P(X = 32) + ... + P(X = 47)P(X ≥ 30) = ΣP(X = r)Where r varies from 30 to 47P(X ≥ 30) = Σ (47 C r * (0.6)r * (0.4)47-r )r = 30 to 47= 0.0031 (approx)d. Between 23 and 28 (including 23 and 28) of them live in cities with population greater than 100,000 people.We need to find the probability of the number of Americans living in cities with population greater than 100,000 is between 23 and 28 (both inclusive).P(23 ≤ X ≤ 28) = P(X = 23) + P(X = 24) + ... + P(X = 28)P(23 ≤ X ≤ 28) = ΣP(X = r)Where r varies from 23 to 28= Σ (47 C r * (0.6)r * (0.4)47-r )r = 23 to 28= 0.3406 (approx)Hence, the required probabilities are,a. P(X = 25) = 0.1213 (approx)b. P(X ≤ 26) = 0.6413 (approx)c. P(X ≥ 30) = 0.0031 (approx)d. P(23 ≤ X ≤ 28) = 0.3406 (approx)

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The ratio x:y in its simplest form is 7:4.

The ratio x:y can be found by dividing x by y. In this case, we can start with the equation y = 4x/7 and solve for x in terms of y.

Multiplying both sides by 7, we get:

7y = 4x

Dividing both sides by 4, we get:

x = 7y/4

Now we can substitute this expression for x into the ratio x:y:

x:y = (7y/4):y

Simplifying by canceling out the y, we get:

x:y = 7/4

So the ratio x:y in its simplest form is 7:4.

This means that for every 7 units of x, there are 4 units of y. The ratio cannot be simplified further because 7 and 4 do not have any common factors other than 1.

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The length of line JC is 20 miles.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental concept in geometry that states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of sides of triangle.

To find the length of line JC, which is the hypotenuse of the right triangle JSC, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).

In this case, we have:

JS² + SC² = JC²

Substituting the given values, we get:

12² + 16² = JC²

144 + 256 = JC²

400 = JC²

Taking square root both sides, we get:

JC = √400JC = 20

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Answer:

Population: The population is the total demand (sale) of the product over all days.

Variable of interest: The variable of interest is the daily demand (sale) of the product.

To obtain the confidence interval for the average daily demand at a confidence level of 97%, we can use the following formula:

Confidence interval = sample mean ± (t-value x standard error)

where t-value is the value from the t-distribution for the desired confidence level and degrees of freedom, and the standard error is calculated as:

standard error = sample standard deviation / √n

where n is the sample size.

Using the given data, we can calculate:

Sample mean = (35+44+38+55+33+56+60+45+48+40+45+35+42)/12 = 44.5

Sample standard deviation = 9.92

Degrees of freedom = n-1 = 12-1 = 11

From the t-distribution table with 11 degrees of freedom and a confidence level of 97%, the t-value is approximately 2.718.

Therefore, the confidence interval for the average daily demand is:

Confidence interval = 44.5 ± (2.718 x 9.92/√12) = 44.5 ± 9.14

The lower limit is 44.5 - 9.14 = 35.36 and the upper limit is 44.5 + 9.14 = 53.64.

So, we can say with 97% confidence that the true population average daily demand falls within the range of 35.36 to 53.64 thousand units.