The table shows the number of 6th grade students who prefer each kind of juice at lunch time. Draw a circle graph to display the information. 6th Grade Juice Choices: Grape Juice 8, Orange Juice 6, Fruit Punch 6, Apple Juice 20.

If AD = 12 and BD = 36 in the right triangle ABC with altitude BD was drawn to hypotenuse AC, then the length of AC is 12√82.

What is the similarity law for triangles?

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the complementary angles are congruent.

We can use the property of similar triangles to find the length of AC.

Since BD is an altitude of triangle ABC, we can write:

(AD)(DC) = (BD)²

Substituting the given values, we get:

12(DC) = 36²

Solving for DC, we get:

DC = (36)²/12 = 3 x 36 = 108

Now, using the Pythagorean theorem, we can write:

(AC)² = (AD)² + (DC)²

Substituting the given values, we get:

(AC)² = 12² + 108²

Simplifying and solving for AC, we get:

AC = √(12² + 108²) = √(12² x (1 + 9²)) = 12 x √(1 + 9²) = 12 x √(82)

Therefore,  If AD = 12 and BD = 36 in right triangle ABC with altitude

BD was drawn to hypotenuse AC, then the length of AC is 12√82.

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Solving the provided question, we can say that By, Pythagorean theorem PR = √277 and b = 11.31

The Pythagοrean Theorem, sometimes known as the Pythagοrean Theorem, is the basic Euclidean geοmetry relationship between a right triangle's three sides. Accοrding to this rule, the area of a square with the hypotenuse side equals the sum οf the areas of squares with the other twο sides. The Pythagοrean Theorem, often knοwn as the generic algebraic nοtation a² + b² = c², states that the square that crοsses the hypotenuse οf a right triangle οpposite the right angle equals the sum of the squares that span the sides of a right triangle.

By, Pythagοrean theorem

PR² = PQ² + QR²

PR² = 14² + 9²

PR² = 196 + 81

PR = √277

Again by Pythagorean theorem

c² - a² = b²

18² - 14² = b²

b² = 324 - 196

b = √128

b = 11.31

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Answer:

5,840,000

Step-by-step explanation:

Let P be the population after x years. The population after 24 years is 2P. So, we have:

P = 365,000 * 2^(x/24)

To find the population after 96 years, we plug in x = 96:

P = 365,000 * 2^(96/24) = 365,000 * 2^4 = 365,000 * 16 = 5,840,000

So, the population of the city will be 5,840,000 after 96 years.

Answer:

Step-by-step explanation:

[tex]\cot\left(\frac{\pi}{2}-\theta\right)=\tan(\theta) \hspace{5em}\cos\left(\frac{\pi}{2}-\theta\right)=\sin(\theta) \\\\\\ \textit{Symmetry Identities} \\\\ \sin(-\theta )=-\sin(\theta) \hspace{5em}\cos(-\theta )=\cos(\theta )\hspace{4em} \tan(-\theta)=-\tan(\theta ) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cot\left(\frac{\pi}{2}-x\right)=-1.84\implies \tan(x)=-1.84 \\\\\\ \tan(-x)\implies -\tan(x)\implies -(-1.84)\implies \text{\LARGE 1.84} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\sin(\theta )=-0.57\implies \cos\left(\frac{\pi}{2}-\theta\right)=-0.57 \\\\\\ \boxed{\alpha = \frac{\pi}{2}-\theta} \hspace{5em}\cos(-\alpha)= \cos(\alpha) \\\\\\ \cos\left[ -\left(\frac{\pi}{2}-\theta\right) \right]\implies \cos\left(\theta -\frac{\pi}{2}\right)=\cos\left(\frac{\pi}{2}-\theta\right) \implies \cos\left(\theta -\frac{\pi}{2}\right)=\text{\LARGE -0.57}[/tex]

The future value is 6,495,554.308.

What has compounded annually?

The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound and simple interest is this.

Compound interest can be calculated in math in a variety of ways depending on the circumstances. To make the calculations simpler, we can use the compound interest formula. We need to know the amount and the principal in order to calculate compound interest. The distinction is between the amount and the principal.

Given that  $12,000 is invested in a project at 7% for 9 years.

The formula of compound interest is

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

A = amount

P = principal

r = rate of interest

t = time

n =  number of compound interest per annum

For the given problem:

P =12,000, r = 7%, t = 9, n = 365:

The amount after 9 years will be:

A = 12,000(1+0.07/365)^(365×9)

A = 6,495,554.308

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Answer:

To solve it, you need to use probability. Let me show you how.

We can use a tree diagram to represent the possible outcomes of the last ball. Here is the diagram:

```

Haris Rauf

/        \

yorker   full toss

0.8       0.2

/  \      /  \

boundary no boundary boundary no boundary

0.2  0.8  0.9  0.1

```

The probability of a boundary is the sum of the probabilities of the branches that end with a boundary. To find the probability of each branch, we multiply the probabilities along the branch. For example, the probability of a yorker and a boundary is 0.8 × 0.2 = 0.16.

So, the probability of a boundary is:

0.8 × 0.2 + 0.2 × 0.9 = 0.16 + 0.18 = 0.34

Therefore, the probability that a boundary will be scored of the last ball is 0.34 or 34%.

Step-by-step explanation:

The original price of the upright bike is $3,600.

Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign that is used to represent percentages is %. Percentage is a measure of frequency.

Original price of the upright bike = sales price / percent discount

= $720 / (20/100)

$720 / 0.2

= $3,600

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The measure of the angles m∠BOX = 77.5° and  m∠AOX = 77.5°.

What is the angle bisector of an angle?

The angle bisector of an angle is a line or line segment that divides the angle into two equal parts, creating two smaller angles that are congruent (i.e., have the same measure). The angle bisector starts from the vertex of the angle and extends to the opposite side or ray of the angle, dividing the angle into two smaller angles that have the same number of degrees.

By the definition of the angle bisector of an angle, the angle bisector divides the angle in two equal measures.

As m∠AOB = 155°

m∠BOX = 1/2 * m∠AOB

m∠BOX = 1/2 * 155

m∠BOX = 77.5°

also m∠AOX = 77.5°

Hence, the measure of the angles m∠BOX = 77.5° and m∠AOX = 77.5°.

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There are 2(3/16) cups of shredded cheese on each pizza.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Large pizza = 1(1/4) cups of sauce

Now,

1(3/4) of the sauce = shredded cheese

The amount of shredded cheese.

= 1(3/4) x 1(1/4)

= 7/4 x 5/4

= 35/16

= 2(3/16)

Thus,

The amount of shredded cheese is 2(3/16).

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The measured value x = 13.

What is parallelogram?

A unique variety of quadrilateral made up of parallel lines is known as a parallelogram. A parallelogram can have any angle between its adjacent sides as long as its opposite sides are parallel. If two opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both pairs of opposite sides are parallel and equal is known as a parallelogram.

We can solve this easily using alternative interior angles. A parallelogram's interior is always 360 degrees, right?

In the given parallelogram the side vy = yx

VY = YX = 80 = 6x+2

6x = 80-2=78

x = 78/6= 13

Hence The measured value x = 13.

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The graph of the quadratic function is given below.

Quadratic functions are polynomial functions consisting of variables and exponents and the degree of the variable is 2.

The general form of a quadratic function is f(x) = ax² + b x + c.

Given is a quadratic function.

y = 3x² + 1

We know that graph of a quadratic function is a parabola.

Since the leading coefficient is +3, positive. So the graph opens upward.

Vertex = (-b/2a, f(-b/2a))

-b/2a = -0/(2 × 3) = 0

f(-b/2a) = (3 × 0) + 1 = 1

(0, 1) is the vertex.

x = 1, then y = 3 + 1 = 4

x = -1, then y = 3 + 1 = 4

x = 2, then y = 12 + 1 = 13

x = -2, then y = 12 + 1 = 13

x = 3, then y = 27 + 1 = 28

x = -3, then y = 27 + 1 = 28

Some of the points are (-3, 28), (-2, 13), (-1, 4). (0, 1), (1, 4), (2, 13) and (3, 28).

Hence the graph through the given points is given below.

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The probability that a randomly selected cat has no treatment and no fleas is 43/87.

It is a branch of mathematics that deals with the occurrence of a random event.

Total number of cats = (cats sprayed with flea deterrent + cats with no treatment)

= (33+6 + 43+5)

=87

we need to find the number of cats with no treatment and no fleas, and divide it by the total number of cats.

Now we can see that the number of cats with no treatment and no fleas is 43.

Therefore, the probability that a randomly selected cat has no treatment and no fleas is:

P(no treatment and no fleas) = number of cats with no treatment and no fleas / total number of cats

= 43 / 87

Hence, the probability that a randomly selected cat has no treatment and no fleas is 43/87.

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The value of the piecewise function f(-2) + 2f(-1) - f(3) is -14

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

The definition of a piecewise function

Given that

f(-2) + 2f(-1) - f(3)

Using the definition of the piecewise function and the domain values. we have

f(-2) + 2f(-1) - f(3) = -(-2)^2 + 3(-2) + 2(4(-1)^3) + [(3 + 5)/(3 - 1)]

Evaluate

f(-2) + 2f(-1) - f(3) = -14

Hence, the solution is -14

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Answer:

The triangle has an area of 192cm^2

Step-by-step explanation:

Given;

the formula to find the area of the triangle,

[tex]A=\frac{h_{b}b }{2}[/tex]

We can insert the values,

[tex]A=\frac{24*16}{2} \\\\\\A=\frac{384}{2} \\\\A=192cm^2[/tex]

The area of the triangle is 192cm^2.

The side length of the square with the same area as the circle is given as follows:

9.75 cm.

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr²

The radius for this problem is of 5.5 cm, hence the area of the circle is given as follows:

A = π x 5.5²

A = 95.03 cm².

For a square of side length s, the area is given by the side length squared, that is:

A = s².

Hence the desired side length is obtained as follows:

s² = 95.03

s = sqrt(95.03)

s = 9.75 cm.

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Answer:

Below

Step-by-step explanation:

If you draw this diagram you will see a right triangle with legs = height

    and   10 miles

for the 6 degree angle  ( in the right triangle)

   tan ( 6) = opposite leg / adjacent leg

      tan (6) = height / 10

       or    10 * tan 6 = height     ( in miles)

                      1.05 miles high

A sorting algorithm is defined as an algorithm that sorts the elements of a list. The most commonly used sequences are numerical sequence and lexicographical sequence, ascending or descending.

A sorting algorithm is used to reorder an array or list of elements according to an element comparison operator. Comparison operators are used to define a new order of elements in that data structure. Consider example, The above list of characters is sorted in ascending order by their value. That is, characters with lower values are placed before characters with higher values. It is important in real life because it supports the development of the scientific concept that things can be owned and organized into distinct groups (e.g. creatures, cars, weather types, etc.). We will now discuss some real-world examples of using sorting algorithms.

1) Your phone's contact list is sorted. This means that your data is organized in this way so you can easily access the contacts you want from your phone. That is, "I ordered."

2) Paper sorting : Imagine a teacher sorting students' work alphabetically by student name. This type of operation is similar to the functionality of sorting algorithms such as bucket sort. Sorting is more efficient process.

3) Traffic lights : Traffic lights are a good example of how algorithms are used in the real world around us. Next time you get stuck in a car at a red light, think about the algorithm that traffic lights run." Most traffic lights don't automatically switch between green, yellow, and red. This algorithm is a well-established turn-by-turn algorithm that directs traffic correctly. It's in order (it may not seem that way when you're sitting at a red light).

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multiply the second equation by -1, you get

y=5x-10

-y=3x-14

add both of the equations together

0=8x-24

then

24=8x

x=3

to find y replace x in one of the original equations

y=5x-10

y=5(3)-10

y=15-10

y=5

(x,y)

(3,5)

Note that the size of angle x = 115°. This is a problem relating to the sum of angles in a circle. See the computation below.

The sum of angles in a circle is always equal to 360 degrees or 2π radians.

This means that the sum of the measures of the angles formed by any number of rays or line segments that meet at a common point, or vertex, and whose endpoints lie on the circle, will always add up to 360 degrees or 2π radians. This property is often used in geometry and trigonometry to solve problems involving circles and angles.

With regard to the above problem,

We are given three angles in a circle named as follows:

a) 81°

b) 164°

c) x

The above rule state that

81 + 164 + x = 360°

thus, x = 360 - 81 - 164

x = 360 -245

x = 115°

Thus the value of ∠x is  115°

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Full Question:

See attached image.

The probability of drawing an orange marble and then a green marble without replacement  is (a) 1/15 .

The probability of drawing an orange marble on the first draw = 2/10 because there are 2 orange marbles out of total of 10 marbles .

After 1 orange marble is drawn, there are 9 marbles left in the box, of which 3 are green.

So, the probability of drawing a green marble on the second draw, given that an orange marble was drawn on the first draw, is 3/9.

⇒ P(orange, green) = P(orange) × P(green | orange was drawn)

⇒ P(orange, green) = (2/10) × (3/9) = 6/90 = 1/15  ;

Therefore , the value of P(Orange , Green) is = 1/15 .

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The given question is incomplete , the complete question is

A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. Draws are made without replacement. P(orange ,green)

(a) 1/15

(b) 2/15

(c) 3/31

(d) 1/5

The unknown in the similar triangles are as follows;

x = 15 units

x = 16 units

Two triangles are said to be similar when they have two corresponding angles congruent and the sides proportional to each other.

Let's solve for x in the triangles as follows:

using the proportion,

2.

9 / x = x / 25

cross multiply

25 × 9 = x²

x² = 225

x = √225

x = 15 units

3.

x / 12 = 12 / 9

cross multiply

9x = 144

x = 144 / 9

x = 16 units

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The triangles are congruent using: 1. LM = LO - segments of the same length as given. 2. LN = LN - common segment. 3. Angle MLN = Angle OLN - LN bisects the angle. 4. ΔMLN ≅ ΔOLN - SAS criteria.

A triangle is a closed polygon with three line segments that intersect at each of its three angles.

When the sides and angles of two triangles match, the triangles are said to be congruent. Thus, two triangles can be placed side by side and angle by angle on top of one another.

Given that the segments LM = LO, and LN bisects angle MLO.

Thus,

1. LM = LO - segments of the same length as given.

2. LN = LN - common segment

3. Angle MLN = Angle OLN - LN bisects the angle.

4. ΔMLN ≅ ΔOLN - SAS criteria.

Hence, the triangles are congruent using: 1. LM = LO - segments of the same length as given. 2. LN = LN - common segment. 3. Angle MLN = Angle OLN - LN bisects the angle. 4. ΔMLN ≅ ΔOLN - SAS criteria.

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Answer:

7.5dollars

Step-by-step explanation:

25%/100×$30

The annual percentage rate is 19.59%.

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Repayment months =  48

Interest rate = 10%

The annual percentage rate.

=  (2 x repayment months x interest rate) ÷ (repayment months + 1)

= (2 x 48 x 10/100) / (48 + 1) x 100

= (2 x 48 x 0.10) / 49 x 100

= 9.6/49 x 100

= 0.1959 x 100

= 19.59%

Thus,

The annual percentage rate is 19.59%.

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The domain of f  * g is the set of all real numbers x such that x ≤ 6.

In interval notation, we can write:

Domain of f * g = (-∞, 6].

What is the domain of the function?

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The domain of the function f(x) = √(6-x) is the set of all real numbers x such that 6-x ≥ 0, which is x ≤ 6.

The domain of the function g(x) = x² - x is the set of all real numbers x, since there are no restrictions on the input.

To find the domain of the function f * g, we need to consider the values of x for which the expression f(x) * g(x) is defined.

We have:

f(x)g(x) = √(6-x)(x² - x)

The expression is defined only if both factors are defined.

For the first factor, √(6-x) to be defined, we need 6-x ≥ 0. This means that x ≤ 6.

For the second factor, x² - x to be defined, there are no restrictions on the input.

Therefore, the domain of f * g is the set of all real numbers x such that x ≤ 6.

In interval notation, we can write:

Domain of f * g = (-∞, 6].

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if the ratio of two sample variances exceeds the critical value of f at a defined confidence level, then the level of confidence also exceeds the critical level.

All tests that make use of the F-distribution are collectively referred to as "F Tests." The F-Test to Compare Two Variances is often what is meant when the term "F-Test" is used. However, a number of tests, including regression analysis, the Chow test, and the Scheffe test, use the f-statistic. If we are conducting an F-Test, we might employ a variety of technological tools. since doing an F-test manually while accounting for variations is a difficult and time-consuming operation.

if the ratio of two sample variances exceeds the critical value of f at a defined confidence level, then the level of confidence also exceeds the critical level.

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Answer: 15 pounds

Step-by-step explanation:

10.4(x)+4.3(10)=7.96(x+10)

10.4x+43=7.96x+79.6

2.44x=36.6

x=15 pounds

(check my work. I may have done something wrong, but the equation should be correct.)

Answer:

Step-by-step explanation:

sinX = 18/32

sinX = 0.5625

X = 34.23

We cannot make any definitive inferences about the entire school population, however, so the answer is E. None of the above.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The total number of students are 10+11+23+6=50

Based on the survey of 50 students about their preference for an additional sports team, we can observe that lacrosse is the most popular sport among the surveyed students, with 23 supporters.

It is likely that there would be enough interest to form an ice hockey team, as there were 11 supporters.

We cannot make any definitive inferences about the entire school population, however, so the answer is E. None of the above.

Hence, We cannot make any definitive inferences about the entire school population, so the answer is E. None of the above.

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The table shown below represents the results from a sample group of 50 students

surveyed about a preference for an additional sports team.

Sports Team    Number

Gymnastics       10

Ice hockey         11

Lacrosse             23

Swimming           6

If the school has 500 students, what can be inferred from the survey?

A. There would not be enough students to form a 20-person ice hockey

team.

B. About half of the students prefer lacrosse to the other sports.

C. Fewer than ten students in the school prefer swimming to the other

sports.

D. About 10% of the students prefer gymnastics.

E. None of these