To indirectly measure the distance across a lake, Dominic makes use of a couple landmarks at points � B and � C. He measures � � AD, � � DB, and � � DE as marked. Find the distance across the lake ( � � ) (BC), rounding your answer to the nearest hundredth of a meter.

The oak tree is 35.5 feet tall.

A mathematical expression known as an algebraic expression can include variables, numbers, and operations (such as addition, subtraction, multiplication, and division). If the values of the variables are known, it indicates a value that can be calculated. Although an algebraic expression lacks an equal sign and cannot be solved like an equation, algebraic methods can be used to simplify or manipulate it. For example, the expression 2x + 3y is an algebraic expression, where x and y are variables.

a) To solve this problem, we can draw a diagram to represent the situation:

In this diagram, "A" represents Benjamin's position, "B" represents the mirror, and "C" represents the top of the oak tree. Let's call the height of the oak tree "h".

b) We can use Angle-Angle Similarity to solve for h. In this case, we have two similar right triangles: ABC and ABD. We can write an equation to relate their sides:

(AB)/(BC) = (AD)/(CD)

c) Plugging in the known values:

(5)/(40) = (5.75)/(h + 5.75)

Expanding and solving for h:

h = (40 * 5.75)/5 - 5.75

h = 35.5 feet

So, the oak tree is 35.5 feet tall.

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Answer: h=12  r=√12

Step-by-step explanation:

volume of cone=πr^2 h/3

πr^2 h/3=48π

πhr^2=144π

hr^2=144

h=12  r=√12

The ingredient you need to serve, round the amount of an ingredient instead of using an exact amount, is vanilla extract.

Rounding is a process to estimate a particular number in a context.

Given that, a recipe serving 10 persons, but you need to serve 30, we need to multiply the amount of each ingredient by to adjust the recipe

Here we have a recipe that works for 10 serves.

Then, if we want to make 30 servings, we need to use that recipe 3 times. (because x·10 = 30, then x = 30/10 = 3)

This would be equivalent to multiply each ingredient by 3.

for 30 cupcakes, we need:

3 cups of vegetable oil.

3 cups of all-purpose flour

(because for each one of these ingredients, we needed only 1 cup to make 10 cupcakes).

for 10 cupcakes, we need 1 teaspoon of vanilla.

for 30 cupcakes we need 3 teaspoons of vanilla, the difference is 3 - 1 = 2.

So the difference is 2 teaspoons.

About which quantities we should round are those where we may have mixed numbers or big numbers.

For example, we have 4 tablespoons of sour cream for 10 servings, then for 30 servings we should have:

3×4 = 12 tablespoons.

We could round this down to 10 tablespoons.

Hence, the ingredient you need to serve, round the amount of an ingredient instead of using an exact amount, is vanilla extract.

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The linear inequalities in the given graph  is [tex]y\geq \frac{1}{2} -1[/tex] and  y< -1/2x -3.

Linear inequalities:

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These quantities may be numerical, algebraic, or a combination of the two.

The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality has the same appearance as a linear equation, but uses a different symbol to link the two expressions.

In the given graph, the area above solid line,

points, (-2 , -2) , (0 , -1)

slope = [tex]\frac{-1-(-2)}{0-(-2)}[/tex]= [tex]\frac{1}{2}[/tex]

so,  [tex]y\geq \frac{1}{2} -1[/tex]

The area below dashed line ,

points, (-2 ,-2) , (0 ,-3)

slope= [tex]\frac{-3-(-2)}{0-(-2)}= \frac{-1}{2}[/tex]

so, y< -1/2x -3.

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The measures of the three angles are 60 degrees, 75 degrees and 45 degrees.

A semi-circle has a total angle measure of 180 degrees. The sum of the angles formed by the two arcs must equal the total angle measure of the semi-circle.

Let's call the angle formed by the first arc "angle A" and the angle formed by the second arc "angle B".

From the given information, we know that:

angle A = 60 degrees

angle B = 75 degrees

So, angle A + angle B = 60 degrees + 75 degrees = 135 degrees

Since the total angle measure of the semi-circle is 180 degrees, the measure of the remaining angle is:

180 degrees - 135 degrees = 45 degrees

Therefore, the measures of the three angles are:

angle A = 60 degrees

angle B = 75 degrees

angle C = 45 degrees

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Question: Ned made the design at the right. Use a protractor. Find and write the measure of the 3rd angle with given 60 and 75 degrees.

In order to determine the exact nature of the distribution, Professor X would need to analyze the data in more detail, for example, by creating a histogram or other visual representation of the grades, and conducting statistical tests to determine the nature of the distribution.

If Professor X finds that the grades on the first exam for their statistics class either did really well or really poorly, it suggests that the distribution of grades is bi-modal, meaning there are two distinct peaks in the distribution. This means that some students did very well on the exam and scored high grades, while others did very poorly and scored low grades, with very few students scoring grades in between these two groups.

A bi-modal distribution is not a common occurrence in a typical exam setting, as most exams tend to have a normal or bell-shaped distribution with a single peak, where the majority of students score around the average or mean grade. The bi-modal distribution found by Professor X could be due to a variety of factors, such as students having widely differing levels of prior knowledge, or students' varying levels of preparation for the exam.

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Answer:

150.72 cubic inches

Step-by-step explanation:

The volume of a cylinder can be calculated using the formula:

V = π * r^2 * h

where V is the volume, π (pi) is approximately equal to 3.14, r is the radius, and h is the height.

For the cylinder with a radius of 4 inches and a height of 3 inches, the volume can be calculated as follows:

V = π * r^2 * h = π * 4^2 * 3 = 3.14 * 16 * 3 = 3.14 * 48 = 150.72 cubic inches.

So the volume of the cylinder is approximately 150.72 cubic inches.

Therefore , the solution of the given problem of equation comes out to be the equation of the parabola in standard form is x² - 10x - 12y + 13 = 0

In arithmetic equations, the identical figure (=) is used to denote the equivalence of two assertions. It is demonstrated that mathematical methods, which have acted as manifestations of reality, can be used to assess a variety of numerical factors. The equal sign actually splits the number 12 into two separate pieces, despite the fact that the result is y + 6 = 12.

Here,

The distance between the focus and vertex is the same as the distance between the vertex and directrix, which is |-4 - (-1)| = 3. This distance is also equal to the absolute value of the coefficient "a" in the equation of the parabola.

Therefore, the equation of the parabola in vertex form is:

(x - 5)² = 4p(y + 1)

where "p" is the distance between the vertex and the focus, which is 3. Substituting this value into the equation gives:

(x - 5)² = 4(3)(y + 1)

Simplifying:

(x - 5)² = 12y + 12

Expanding the left side:

x² - 10x + 25 = 12y + 12

Moving all the terms to one side:

x² - 10x - 12y + 13 = 0

So the equation of the parabola in standard form is:

x^2 - 10x - 12y + 13 = 0

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The number of computer chips produced in 3 months will be 2515.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the function f(x) = 5x + 2,500 models the number of computer chips produced by a manufacturing plant each month during its first year.

The number of chips will be calculated as:-

f(x) = 5x + 2,500

f(3) = 5 x 3 + 2500

f(3) = 15 + 2500

f(3) = 2515

Therefore, the number of chips will be 2515.

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The comparison of m∠B to m∠E is that both angles are congruent

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

A dilation with a scale factor of 2 maps ΔABC to ΔDEF

When a shape is dilated to form another, the corresponsing sides change while the corresponding angles remain the same

Using the above as a guide, we have the following:

Angle B cprresponds to angle E

Hence, the are equal angles

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Answer:

The ratio of flies to all insects is 1:5

For every 1 bee, there are 10 insects

Step-by-step explanation:

give brainlist please

Answer: 345 + n

For finding the total, we have to add 345 with n.

Answer:-1/2

Step-by-step explanation:

Take two points and use the formula (y2-y1)/(x2-x1). I used (0,4) and (4,2) as my set of coordinate pts.

For 5 batches, 65 cups of chocolate chips are needed.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that Marie’s recipe for one batch of chocolate chip cookies calls for 13 cup of chocolate chips. If Marie is making 5 batches of cookies.

For 1 batch - 13 cups of chocolate chips are needed.

For 5 batches - (13 x 5) = 65 cups of chocolate chips are needed.

Therefore, for 5 batches, 65 cups of chocolate chips are needed.

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The corresponding side in the smaller triangle is 10 cm.

When two or more objects or figures appear the same or equal due to their shape, this property is known as a similarity.

Given that, the ratio of similitude in two similar triangles is 3:1. the side in the larger triangle measures 30 cm, we are asked to find the measure of the corresponding side in the smaller triangle.

Let the corresponding side in the smaller triangle be x,

Since, the ratio similitude is 3:1, therefore, the ratio of the corresponding sides of both the triangle will be in same ratio,

Therefore,

1 / 3 = x / 30

x = 30 / 3

x = 10

Hence, the corresponding side in the smaller triangle is 10 cm.

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The end behaviour of the polynomial function p(x) = -9x⁹ + 6x⁶ - 3x³ + 1 is

A polynomial function is a function in which the lowest power of the unknown is 2.

Since the graph p hs the polynomial function p(x) = -9x⁹ + 6x⁶ - 3x³ + 1.

To determine its values as x → ∞, we see that the -9x⁹ term is the dominant term in the polynomial function.

So, p(x) ≅  -9x⁹

So, substituting x = ∞ into the equation, we have that

p(x) ≅  -9x⁹

p(∞) ≅  -9(∞)⁹

p(∞) ≅  -9(∞)

p(∞) ≅  -∞

So, as  x → ∞, P(x) → ∞

Also, to determine its values as x → -∞, we see that the -9x⁹ term is the dominant term in the polynomial function.

So, p(x) ≅  -9x⁹

So, substituting x = -∞ into the equation, we have that

p(x) ≅  -9x⁹

p(∞) ≅  -9(-∞)⁹

p(∞) ≅  -9(-∞)

p(∞) ≅  9∞

p(∞) ≅  ∞

So, as  x → -∞, P(x) → ∞

So, the end behaviour is

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Answer: To divide 9x³ - 18x² - x + 2 by 3x + 1 using long division, we can follow the following steps:

Step 1: Divide the first term of the dividend 9x³ by the first term of the divisor 3x. The result is 3x².

Step 2: Multiply the divisor 3x + 1 by 3x². The result is 9x³ + 3x².

Step 3: Subtract 9x³ + 3x² from 9x³ - 18x² - x + 2. The result is -18x² - 4x + 2.

Step 4: Repeat the division and multiplication process by dividing the first term of the new dividend, -18x², by the first term of the divisor, 3x. The result is -6x.

Step 5: Multiply the divisor 3x + 1 by -6x. The result is -18x + 6.

Step 6: Subtract -18x + 6 from -18x² - 4x + 2. The result is -4x² + 10.

Step 7: Repeat the division and multiplication process by dividing the first term of the new dividend, -4x², by the first term of the divisor, 3x. The result is -4/3 x.

Step 8: Multiply the divisor 3x + 1 by -4/3 x. The result is -4/3 x + 4/3.

Step 9: Subtract -4/3 x + 4/3 from -4x² + 10. The result is 10 - 4/3.

Thus, the final answer is:

(9x³ - 18x² - x + 2) / (3x + 1) = 3x² - 6x - 4/3 x + 4/3 + 10

Step-by-step explanation:

The solution is Option A.

The inequality equation is -2 ≤ x < -11

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the first inequality equation be represented as A

Now , the value of A is

4x + 7  ≤ -37   be equation (1)

Let the second inequality equation be represented as B

5x + 3 > -7   be equation (2)

On simplifying the equation , we get

From equation (1) , Subtracting 7 on both sides of the equation , we get

4x ≤ -44

Divide by 4 on both sides of the equation , we get

x ≤ -11

And , from equation (2) , Subtracting 3 on both sides of the equation ,

5x > -10

Divide by 5 on both sides of the equation , we get

x > -2

Hence , the inequality equation is -2 ≤ x < -11

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The length of chord BC is 3 cm

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

The angle in a semicircle is 90 degrees

This means that

B = 90 degrees

Using the pythagorean theorem, we have

AC^2 = AB^2 + BC^2

This gives

5^2 = 4^2 + BC^2

So, we have

BC^2 = 9

This gives

BC = 3

Hence, the length s 3 units

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Answer:

(-3.1)^8

Step-by-step explanation:

(-3.1)^4•(-3.1)^4

Because they have the same base is -3.1, we can add the ^4 with ^4 and get

(-3.1)^8

So, the answer is (-3.1)^8

This years tuition is $1900

Let us assume that the next year tuition fee be x dollars.

The next year's tuition will be $2000 which is $600 more than this year's tuition fee.

Chana will pay $2000 which is 80 percent of her college tuition.

Using percentage formula we get an equation,

x × (80/100) = 2000

we solve this equation for x.

x = (2000 × 100)/80

x = 2500

If the next year's tuition fee is $600 more than this year's tuition fee, then this year's tuition fee would be,

2500 - 600 = 1900 dollars

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The volume of cuboid is 180 cubic centimeters.

As we know the formula for the volume of the cuboid is given as:

V = l × w × h

where, V is the volume of the cuboid

l is the length of the cuboid

w is the  width of the cuboid

and h is the height of the cuboid

Here, the dimensions of the cuboid are: 9cm × 4cm × 5cm

Let the length of the cuboid is l = 9 cm,

the width of the cuboid is w = 4 cm

and the height of the cuboid is h = 5 cm

Using above formula of volume of cuboid,

V = l × w × h

substitute values, l = 9, w = 4 and h = 5

⇒ V = 9 × 4 × 5

⇒ V = 180 cm³

Therefore, the volume of cuboid 180 cubic centimeters

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The volume of the prism formed of two rectangles is 528 cm³

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Volume of the prism is the amount of space that it occupied. From the prism shown:

Volume of prism = area of L shaped base * height

Area of L shaped base = (2 cm * 6 cm) + (8 cm * 15 cm) = 132 cm²

Volume of prism = 132 cm² * 4 cm = 528 cm³

The volume of the prism is 528 cm³

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Factor of the expression are,

⇒ (x - 1) (x - 12) (x - 10)

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 equation is,

⇒ x³ - 23x² + 142x - 120 = 0

Now, Put x = 1;

⇒ x³ - 23x² + 142x - 120 = 0

⇒ 1 - 23 + 142 - 120 = 0

⇒ 0 = 0

Thus, One factor of the equation is,

⇒ (x - 1)

Now, After divide we get;

⇒ (x³ - 23x² + 142x - 120 ) ÷ (x - 1)

⇒ x² - 22x + 120

⇒ x² - (12 + 10)x + 120

⇒ x² - 12x - 10x + 120

⇒ x (x - 12) - 10 (x - 12)

⇒ (x - 12) (x - 10)

Thus, Factor of the expression are,

⇒ (x - 1) (x - 12) (x - 10)

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The perimeter of the figure composed of a semicircle and rectangle is 59.7 inches

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The perimeter of a figure is the total distance along the boundary of that figure.

From the image attached:

Perimeter of circle = π * radius = 3.14 * 5 = 15.7 inches.

Perimeter of rectangle = 2(length + breadth) = 2(12 + 10) = 44 inches

Perimeter of figure = Perimeter of circle + Perimeter of rectangle = 15.7 + 44 = 59.7 inches

The perimeter of the figure is 59.7 inches

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The required [tex]f(x) = x/10[/tex] is a valid probability distribution function for a discrete random variable X which can take on the values 0, 1, 2, 3, or 4.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

For a function f(x) to be a valid probability distribution function (pdf) for a discrete random variable X, it must satisfy the following conditions:

Non-negativity: [tex]f(x) = x/k[/tex] is non-negative for all x when k > 0.

Normalization: We need to find the value of k such that the sum of the probabilities for x = 0, 1, 2, 3, 4 is equal to 1.

[tex]f(x) = x/k[/tex] for x = 0, 1, 2, 3, 4.

The sum of the probabilities is given by:

[tex](0/k) + (1/k) + (2/k) + (3/k) + (4/k) = 1[/tex]
[tex]10/k = 1[/tex]

So, k = 10.

Thus,[tex]f(x) = x/10[/tex] is a valid probability distribution function for a discrete random variable X which can take on the values 0, 1, 2, 3, or 4.

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Answer:

18 Rials

Step-by-step explanation:

54 divided by 3= 18

The Board of Trustees can choose a president and a provost in 1000 different ways because there are 1000 professors on the college's faculty. The concept used in this is permutations and combinations.

What are combinations?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations). Three fruits, such as an apple, an orange, and a pear, for instance, can be combined into three different pairs: an apple and a pear, an apple and an orange, or a pear and an orange. A k-combination of a set S is officially defined as a subset of S's k unique elements. So, if and only if each combination contains the same elements, two combinations are said to be identical.

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Correct question:

Suppose that a college has 1000 professors.

a) In how many ways can the Board of Trustees pick a president? The president should be one of the 1000 professors.

The correlation coefficient that represents the strongest downward trend in a data set is -0.83.

The correlation coefficient measures the strength and direction of the relationship between two variables, with values ranging from -1 to 1. A negative correlation coefficient indicates a downward trend, meaning as one variable increases, the other decreases.

The magnitude of the coefficient represents the strength of the relationship, with values close to -1 indicating a strong downward trend and values close to 0 indicating a weak or nonexistent relationship. In this case, among the options provided, the correlation coefficient of -0.83 represents the strongest downward trend.

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