A school has 160 students. Only 120 students went to a dance the school had. What percent of students went to the dance?

The polynomial function in standard form with the given zeros x = 5, 6, and 7 is:

f(x) = x^3 - 18x^2 + 107x - 210

To write a polynomial function in standard form with the given zeros x = 5, 6, and 7, we use the fact that if a value x is a zero of a polynomial function, then (x - a) is a factor of the polynomial, where a is the zero.

Using this information, we can construct the polynomial function as follows:

Since the zeros are x = 5, 6, and 7, the factors of the polynomial are (x - 5), (x - 6), and (x - 7).

To obtain the polynomial function, we multiply these factors together:

f(x) = (x - 5)(x - 6)(x - 7)

Expanding this expression, we get:

f(x) = (x^2 - 11x + 30)(x - 7)

Now, let's multiply further:

f(x) = (x^2 - 11x + 30)(x) - 7(x^2 - 11x + 30)

Expanding again:

f(x) = x^3 - 11x^2 + 30x - 7x^2 + 77x - 210

Combining like terms:

f(x) = x^3 - 11x^2 - 7x^2 + 30x + 77x - 210

Simplifying:

f(x) = x^3 - 18x^2 + 107x - 210

Therefore, the polynomial function in standard form with the given zeros x = 5, 6, and 7 is:

f(x) = x^3 - 18x^2 + 107x - 210

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Answer:

(4,4)

Step-by-step explanation:

Answer:

I think is C I hope is right

The correct expressions which are equivalent to the one below is,

⇒ 0

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ log 1 × log 81

Now, We know that;

⇒ log 1 = 0

Hence, The correct expressions which are equivalent to the one below is,

⇒ log 1 × log 81

⇒ 0 × log 81

⇒ 0

Thus, The correct expressions which are equivalent to the one below is,

⇒ 0

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Step-by-step explanation:

the correct answer is option a 6a-7

30.8

you take 25^2 + 18^2 and find the square root of that which is 30.8 for this problem.

please give me brainliest :)

Based on the given information that Caruso, Inc. has an inventory turnover rate of 8 times and a cost of goods sold of $150,000, the company average inventory can be calculated.

To calculate the average inventory, we can use the formula: Average Inventory = Cost of Goods Sold / Inventory Turnover Rate.

Plugging in the values, we have: Average Inventory = $150,000 / 8 = $18,750. Therefore, option c. The company's average inventory is $18,750 is the correct answer.

The inventory turnover rate measures how quickly a company sells its inventory during a specific period. In this case, the turnover rate of 8 times indicates that Caruso, Inc. sells its entire inventory 8 times per year. This suggests that the company has an efficient inventory management system and a relatively high sales volume compared to its inventory level. However, the other options provided (a, b, d) are not supported by the given information and are not accurate in this context.

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Answer:

Right answer = 52

Wrong answers = 8

Step-by-step explanation:

Every correct answer = + 3

Every wrong answer = - 2

Number of correct answers = x

Number of wrong answers = y

x + y = 60 - - - (1)

3x - 2y = 140 - - - (2)

From (1) :

x = 60 - y

Put x = 60 - y into (2)

3(60 - y) - 2y = 140

180 - 3y - 2y = 140

180 - 5y = 140

-5y = 140 - 180

-5y = - 40

y = 8

x = 60 - y

x = 60 - 8

x = 52

Right answer = 52

Wrong answers = 8

Answer:

8

Step-by-step explanation:

0.20 x 40 = 8

Therefore, 20% of 40 is 8

Answer:

(15, 36, 39)

Step-by-step explanation:

Using pythagoreas formula: A^2 * B^2 = C^2

so a=15, b=36, c=39

15^2+36^2=39^2

The measure of side AC is approximately 366.9 inches.

A triangle is a geometric shape that consists of three straight sides and three angles. It is one of the basic shapes in geometry and is often studied as a fundamental building block in mathematics, engineering, and physics. Triangles have several important properties, including:

The sum of the angles in a triangle is always 180 degrees.

The longest side of a triangle is opposite to the largest angle, and the shortest side is opposite to the smallest angle.

The area of a triangle can be calculated using the formula: area = 1/2 x base x height, where the base is one of the sides and the height is the perpendicular distance from the base to the opposite vertex.

Triangles can be classified based on the length of their sides and the measure of their angles. For example, a triangle with all three sides of equal length is called an equilateral triangle, while a triangle with two sides of equal length is called an isosceles triangle.

To find the measure of side AC, which is denoted by "b", we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. Specifically, the Law of Cosines states that:

c² = a² + b² - 2ab cos(C)

where "a" and "b" are the lengths of the other two sides of the triangle, and "C" is the angle opposite to side "c".

In this case, we know that side AB has length "c" (290 inches), and side AC is denoted by "b". We also know that the angle opposite to side AB has measure 42 degrees. Therefore, we can write:

c² = a² + b² - 2ab cos(C)

290² = a² + b² - 2ab cos(42)

Simplifying this equation and solving for b, we get:

b² - 2ab cos(42) + (290² - a²) = 0

This is a quadratic equation in "b", which we can solve using the quadratic formula:

b = [2a cos(42) ± √((2a cos(42))² - 4(290² - a²)]/2

Simplifying this expression, we get:

b = a cos(42) ± √(a² cos²(42) - (290² - a²))

We don't know the value of "a", so we cannot find the exact value of "b". However, we can use the fact that "b" is a length of a triangle, so it must be positive. Therefore, we can discard the negative square root, and we get:

b = a cos(42) + sqrt(a² cos²(42) - (290² - a²))

Since "b" is positive, we can set the expression inside the square root to zero and solve for "a":

a² cos²(42) - (290² - a²) = 0

Simplifying and solving for "a", we get:

a = 290/sin(42)

Substituting this value of "a" back into the equation for "b", we get:

b = (290/sin(42)) cos(42) + sqrt((290/sin(42))² cos²(42) - 290² + (290/sin(42))²)

Simplifying this expression, we get:

b ≈ 366.9 inches

Therefore, the measure of side AC is approximately 366.9 inches.

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Answer:

8.5

Step-by-step explanation:

Applying pythagora's theorem,

hypotenuse^2 = opposite^2 + adjacent^2

but, hypotenuse = 9

opposite = X

adjacent = 1/2(base of triangle)= 1/2(6)

adjacent = 3

9^2 = X^2 + 3^2

X^2 = 81 - 9

X^2 = 72

X = 8.5

Answer:

slope = \(\frac{1}{5}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 4, - 3) and (x₂, y₂ ) = (11, 0) ← 2 ordered pairs from the table

m = \(\frac{0-(-3)}{11-(-4)}\) = \(\frac{0+3}{11+4}\) = \(\frac{3}{15}\) = \(\frac{1}{5}\)

The unit tangent vector T and the principal unit normal vector N can be computed for the given vector-valued function r(t) = (sin(t) + 2, cos(t) + 10, 6t). The unit tangent vector T represents the direction of the curve at each point, while the principal unit normal vector N is perpendicular to the tangent vector and points towards the center of curvature.

To find the unit tangent vector T, we differentiate r(t) with respect to t and divide by its magnitude:

r'(t) = (cos(t), -sin(t), 6)

||r'(t)|| = sqrt((cos(t))^2 + (-sin(t))^2 + 6^2) = sqrt(1 + 1 + 36) = sqrt(38)

Therefore, the unit tangent vector T is given by:

T = r'(t) / ||r'(t)|| = (cos(t)/sqrt(38), -sin(t)/sqrt(38), 6/sqrt(38))

To find the principal unit normal vector N, we differentiate T with respect to t and divide by its magnitude:

T'(t) = (-sin(t)/sqrt(38), -cos(t)/sqrt(38), 0)

||T'(t)|| = sqrt((sin(t)/sqrt(38))^2 + (-cos(t)/sqrt(38))^2) = sqrt(1/38 + 1/38) = sqrt(2/38) = sqrt(1/19)

Therefore, the principal unit normal vector N is given by:

N = T'(t) / ||T'(t)|| = (-sin(t)/sqrt(19), -cos(t)/sqrt(19), 0)

In summary, the unit tangent vector T for the given vector-valued function is (cos(t)/sqrt(38), -sin(t)/sqrt(38), 6/sqrt(38)), and the principal unit normal vector N is (-sin(t)/sqrt(19), -cos(t)/sqrt(19), 0). These vectors represent the direction and perpendicular direction to the curve defined by r(t).

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The median of X is 1;  P(X > 2) = 0; P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0; Var(X) is approximately 0.33; E(X) is 1 and  the value of q such that P(X < q) = 0.95 is 1.9.

(a) To find the median of X, we need to find the value of x for which the cumulative distribution function (CDF) equals 0.5.

Since the PDF is given as f(x) = 1/2 for 0 < x < 2 and 0 otherwise, the CDF is the integral of the PDF from 0 to x.

For 0 < x < 2, the CDF is:

F(x) = ∫(0 to x) f(t) dt = ∫(0 to x) 1/2 dt = (1/2) * (t) | (0 to x) = (1/2) * x

Setting (1/2) * x = 0.5 and solving for x:

(1/2) * x = 0.5;  x = 1

Therefore, the median of X is 1.

(b) To find P(X > x), we need to calculate the integral of the PDF from x to infinity.

For x > 2, the PDF is 0, so P(X > x) = 0.

Therefore, P(X > 2) = 0.

(c) To find the probability that one observation is less than 2 and the other is greater than 2, we need to consider the possibilities of the first observation being less than 2 and the second observation being greater than 2, and vice versa.

P(one observation < 2 and the other > 2) = P(X < 2 and X > 2)

Since X follows a continuous uniform distribution from 0 to 2, the probability of X being exactly 2 is 0.

Therefore, P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0.

(d) The variance of X can be calculated using the formula:

Var(X) = E(X²) - [E(X)]²

To find E(X²), we need to calculate the integral of x² * f(x) from 0 to 2:

E(X²) = ∫(0 to 2) x² * (1/2) dx = (1/2) * (x³/3) | (0 to 2) = (1/2) * (8/3) = 4/3

To find E(X), we need to calculate the integral of x * f(x) from 0 to 2:

E(X) = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1

Now we can calculate the variance:

Var(X) = E(X²) - [E(X)]² = 4/3 - (1)² = 4/3 - 1 = 1/3 ≈ 0.33

Therefore, Var(X) is approximately 0.33.

(e) The expected value of X, E(X), is given by:

E(X) = ∫(0 to 2) x * f(x) dx = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1

Therefore, E(X) is 1.

(f) The value of q such that P(X < q) = 0.95 can be found by solving the following equation:

∫(0 to q) f(x) dx = 0.95

Since the PDF is constant at 1/2 for 0 < x < 2, we have:

(1/2) * (x) | (0 to q) = 0.95

(1/2) * q = 0.95

q = 0.95 * 2 = 1.9

Therefore, the value of q such that P(X < q) = 0.95 is 1.9.

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Answer:

sorry I don't understand can somebody help him??

The Multiplicative Inverse of postive 146 is  0.00684932.

What is Multiplicative Inverse?

The reciprocal of a particular integer is referred to as the multiplicative inverse. It is employed to make mathematical expressions simpler. The word "inverse" denotes an opposing or opposed action, arrangement, position, or direction. A number becomes 1 when it is multiplied by its multiplicative inverse.

When a number is multiplied by the original number, the result is 1, that number is said to be the multiplicative inverse of that number. A-1, or 1/a, stands for the multiplicative inverse of the letter "a". In other terms, two numbers are said to be multiplicative inverses of one another when their product is 1.

The division of 1 by a number yields the multiplicative inverse of that number. The number's reciprocal is another name for it. According to the multiplicative inverse formula, a number's product with its reciprocal is 1.

Given number for the multiplicative inverse is 146;

so, If the Multiplicative Inverse of 146 is x

then , the problem can be written as a function as follows:

146(x) = 1

Thus, to get the answer, we divide 1 by 146 like this:

1 / 146 = 0.00684932

Therefore,the Multiplicative Inverse of postive 146 is  0.00684932.

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Aggregate Demand (AD) is a macroeconomic concept that represents the total demand for goods and services in an economy. The X factor in the AD equation represents exports, which are an important part of the economy.

AD is calculated by adding up the individual components of demand, which include consumer spending (C), investment spending (I), government spending (G), and net exports (X-M). The X-M component represents the difference between exports (X) and imports (M).

The X component in the equation represents exports, which are the goods and services produced domestically and sold to foreign countries. Exports are an important part of the economy as they generate income and create jobs. The M component in the equation represents imports, which are the goods and services purchased from foreign countries and consumed domestically. Imports can have a negative impact on the economy as they represent a drain on resources and can lead to a trade deficit. The X factor in the equation is used to represent exports because it is a variable that can change over time. Factors that can affect exports include exchange rates, tariffs, and global demand for certain products. If the exchange rate between two currencies changes, it can make exports more or less expensive for foreign buyers, which can affect the level of exports. Tariffs are taxes on imports, which can make domestic products more competitive in foreign markets.

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Answer:

1 foot = 12 inches

Step-by-step explanation:

Answer: x= -3

Step-by-step explanation:

You would use the formulas b^x=y <----> log∨b(y)=x

b=4

x=?

y=1/64

Plug in:

log(∨4)(1/64)= x

then you use...

log(y)/log(b)=x

log(1/64)/log(4)

plug into calculator and you would get -3 for x

hope that helps :)

The correct option is function g(x), the minimum is at y = -2.

The minimum will be at the vertex (always that the quadratic has a positive leading coefficient).

For the graphed one, the vertex is at (0, 0).

For the one in the table, the minimum is at 2.5 and it is a value near zero (but smaller).

For a standard quadratic:

y = ax² + bx + c

The minimum is at:

x = -b/2a

So for the first function,  y= 6x² + 5x - 2

The minimum is at:_

x = -5/2*6 = -5/12

Evaluating there we get:

y = 6*(-5/12)² + 5*(-5/12) - 2

y = -87/72

Finally, for the one that is in vertex form:

y = 6*(x - 2)² -2

The vertex is at (2, -2)

so this one has the smaller y-value.

That is the correct option.

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To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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Answer:

B. Yes.

C. Yes.

Step-by-step explanation:

B. In this, it is saying basically is "2b + b = 3b." Well yes, because 2b + b = 3b. So 3b = 3b? Yes.

C. So same thing. 2b + b = 3b. 3b = 3b. they are equivalent.

Answer:

P (1 + r/n)^(nt)

Step-by-step explanation:

Answer:

A = P(1+r/n)nt

(note the r/n is a fraction)

Step-by-step explanation:

3)  since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.

(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:

Total payment A = Monthly installment * Number of installments

              = $375 * 36

              = $13,500

Therefore, Adrian paid a total of $13,500 over the course of 36 months.

(2) In the simple interest formula I = Prt, the letters used represent the following variables:

I: Interest (the amount of interest paid)

P: Principal (the initial amount, or in this case, the car worth)

r: Rate of interest (expressed as a decimal)

t: Time (in years)

(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:

r = (I / Pt) * 100

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Unfortunately, I am unable to directly interpret or visualize figures or images. However, I can provide you with a general explanation. In a discretized reservoir using block-centered grids, the standard ordering refers to the arrangement of grid cells or blocks in a particular pattern.

This pattern is often used to establish the connectivity and adjacency relationships between the cells in the reservoir model. Typically, the standard ordering arranges the grid cells in a sequential manner, starting from the top-left corner and moving row by row. Each grid cell represents a discrete volume or unit in the reservoir. The non-zero elements, indicated by the "x" positions in the coefficient matrix, would correspond to the active or connected cells within the reservoir model. These active cells are the ones that contribute to fluid flow and other reservoir properties. To visualize the discretized reservoir using the standard ordering, you would need to refer to the coefficient matrix and determine the dimensions of the reservoir model, such as the number of rows and columns. Then, starting from the top-left corner, you can represent each active cell or block using a graphical representation, such as a square or rectangle, in a sequential manner based on the standard ordering. This way, you can construct a visual representation of the discretized reservoir model.

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Answer:

Monomial

Step-by-step explanation:

It only has 1 term.

A binomial has 2 terms. Ex 2x + 1

A trinomial has 3 terms. Ex. 3x² + 2x + 1

A polynomial has 4+ terms. Ex. 7x^5 + 7x³ + 2x² + x - 1

The area of the rectangle is 11.76 cm². However, when rounding to two significant figures, the area becomes 11.8 cm². This rounded value should be used as the area of the base when calculating the answer for Part C. Option A

When calculating the area of a rectangle, we multiply the length by the width. Given that the rectangle has a width of 2.1 cm and a length of 5.6 cm, multiplying these values gives us an area of 11.76 cm². However, we are asked to round the answer to two significant figures.

To round to two significant figures, we look at the digit immediately after the second significant figure. In this case, the digit is 7. Since 7 is equal to or greater than 5, we round up the preceding digit, which is 6. Thus, when rounding to two significant figures, the area becomes 11.8 cm².

Therefore, the value to be used as the area of the base when calculating the answer for Part C is 11.8 cm². It is important to use the rounded value to maintain the appropriate significant figures in the final answer.

Option A

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The missing Value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

The missing value that, when multiplied by 5/3^4, gives the result of 5^4, we can set up the equation:

(5/3^4) * x = 5^4

To solve for x, we can simplify both sides of the equation. First, let's simplify the right side:

5^4 = 5 * 5 * 5 * 5 = 625

Now, let's simplify the left side:

5/3^4 = 5/(3 * 3 * 3 * 3) = 5/81

Now we have:

(5/81) * x = 625

To solve for x, we can multiply both sides of the equation by the reciprocal of 5/81, which is 81/5:

(81/5) * (5/81) * x = (81/5) * 625

On the left side, the fraction (81/5) * (5/81) simplifies to 1, leaving us with:

1 * x = (81/5) * 625

Simplifying the right side:

(81/5) * 625 = 13125

Therefore, the missing value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

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main answer: yes, translated triangles are congruent

supporting answer

what is congruent triangles?

Two triangles are said to be congruent if all three corresponding sides and angles are equal in size. These triangles can be moved, rotated, flipped, and turned to look exactly the same. They coincide with each other.

body of the answer:

when all corresponding sides and corresponding angles of two triangles of same measure,then it is said to be congruent triangle

shapes that have been rotated or translated are congruent shapes.this does not mean that they are not exactly the same.

final answer:hence the translated triangles are congruent

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Yes, translated triangles are congruent.

What are congruent triangles?

Two triangles are said to be congruent if all three corresponding sides and angles are equal in size. These triangles can be moved, rotated, flipped, and turned to look exactly the same. They coincide with each other.

When all corresponding sides and corresponding angles of two triangles are of the same measure, then it is said to be a congruent triangle.

The rules of congruent triangles are SSS, SAS, AA, and ASA.

Shapes that have been rotated or translated are congruent shapes. This does not mean that they are not exactly the same.

Hence the translated triangles are congruent.

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