Perform the operation and reduce the answer fully. Make sure to
express your answer as a simplified fraction.
1
3
1
2

Applying the tangent ratio, the value of x in the image, rounded to the nearest thousandth is: 15.824.

The tangent ratio, commonly referred to as "tangent," is a trigonometric function that relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle. It is expressed as:

tan (∅) = opposite/adjacent

We have the following:

Reference angle (∅) = 53 degrees

Length of opposite side = 21

Length of adjacent side = x

Plug in the values:

tan 53 = 21/x

x * tan 53 = 21

x = 21 / tan 53

x = 15.824

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Answer:

8- foot shadow? i am not sure

Answer:

i believe its 12 feet!

Step-by-step explanation:

assuming that the difference from the 6 foot giraffe with a four foot shadow is two feet, the 10 foot shadow would be two feet less then the giraffes height.

Answer:

the area of the shape is 48m

Step-by-step explanation:

10*4=40

2*4=8

40+8=48

brake it up into two triangles. one is a triangle that is 10m tall and 8m wide at the top. you can solve that by doing 4*10=40. the other triangle is 4m wide at the bottom and 2m tall. you can solve that by doing 2*4=8. and 40+8=48.

The first step in evaluating the expression 3x{9-(4+2)/2 is to simplify the innermost parentheses. By performing operations within parentheses first, we can simplify the expression and make it easier to evaluate.

To begin, we evaluate the expression within the parentheses (4+2), which equals 6. Thus, the original expression becomes 3x{9-6/2}.

The next step is to simplify the division operation. We divide 6 by 2, resulting in 3. Now the expression becomes 3x{9-3}.

The subsequent step is to simplify the subtraction operation. We subtract 3 from 9, giving us 6. The expression now becomes 3x6.

Finally, we multiply 3 by 6, yielding a final result of 18. Therefore, the evaluation of the expression 3x{9-(4+2)/2 is equal to 18.

By simplifying the parentheses, performing the division, and evaluating the subtraction, we systematically reduce the expression to its simplest form. Following the order of operations (also known as PEMDAS or BODMAS), which prioritizes parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right), ensures an accurate evaluation of the expression.

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A la sala de cine ingresaron 180 niños y 165 adultos.

De acuerdo con el enunciado, la sala de cine tiene capacidad para 345 espectadores y cobra 3 dólares por cada niño y 5 dólares por cada adulto. Asimismo, esta sala tiene un recaudo diario de 1365 dólares. La situación puede ser sintetizada en la siguiente ecuación algebraica:

3 · x + 5 · (345 - x) = 1365

Donde x es el número de niños que asistieron a la sala de cine.

Ahora despejamos la variable correspondiente mediante propiedades algebraicas:

3 · x + 1725 - 5 · x = 1365

1725 - 2 · x = 1365

2 · x = 1725 - 1365

2 · x = 360

x = 180

Ahora, el número de adultos es:

y = 345 - 180

y = 165

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\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(\stackrel{\textit{"F" inversely proportional to }\sqrt{g}}{F=\cfrac{k}{\sqrt{g}}}\qquad \textit{we also know that} \begin{cases} F=18\\ g=9 \end{cases} \\\\\\ 18=\cfrac{k}{\sqrt{9}}\implies 18=\cfrac{k}{3}\implies 54=k~\hfill\boxed{ F=\cfrac{54}{\sqrt{g}}} \\\\\\ \textit{when g = 36, what is "F"?}\qquad F=\cfrac{54}{\sqrt{36}}\implies F=\cfrac{54}{6}\implies F=9\)

Answer:

f = 9

Step-by-step explanation:

f = k/square root of g (k is the constant) so 18 = k/square root of 9.

We can rearrange this to find k, so 18*square root of 9 = k

Consequently, k = 54

We can put k in our equation to now find f. f = 54/square root of 36

Therefore, f is 9

a. The probability that the time spent resolving the complaint is less than 10 minutes is 0.6255.

b. The probability that the time spent resolving the complaint is longer than 5 minutes is 0.9742.

c. The probability that the time spent resolving the complaint is between 8 and 15 minutes is approximately 0.7180.

(a) First, we calculate the standardized score (z-score) using the formula:

z = (x - μ) / σ

z = (10 - 9.3) / 2.2 = 0.3182

Using a standard normal distribution table or calculator, we can find the probability corresponding to a z-score of 0.3182, which is approximately 0.6255.

(b) Probability of spending longer than 5 minutes:

We need to find P(X > 5).

Similarly, we calculate the z-score:

z = (5 - 9.3) / 2.2 = -1.9545

Looking up the probability for a z-score of -1.9545, we find approximately 0.0258.

However, we need to find the probability of spending longer than 5 minutes, so we need to subtract this value from 1:

P(X > 5) = 1 - 0.0258

= 0.9742

(c) Probability of spending between 8 and 15 minutes:

We need to find P(8 < X < 15).

First, we calculate the z-scores for each value:

z1 = (8 - 9.3) / 2.2 = -0.5909

z2 = (15 - 9.3) / 2.2 = 2.5909

Using the standard normal distribution table or calculator, we find the probabilities for each z-score:

P(X < 8) = P(z < -0.5909) ≈ 0.2776

P(X < 15) = P(z < 2.5909) ≈ 0.9956

P(8 < X < 15) = P(X < 15) - P(X < 8)

= 0.9956 - 0.2776

≈ 0.7180

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Answer:

the correct answer is y=-3x+8

Answer:

4.5 quarts, because one cup is 0.25 quarts

Step-by-step explanation:

Answer:

V≈1.25664×10^6

Step-by-step explanation:

The formula for the volume of a cylinder is V=πr2h, so if you plug in the values for radius and height (V=πr2h=π·100^2·40), you get .25664×10^6)

Answer:

The volume of cylinder is 314000 ft³.

Step-by-step explanation:

Solution :

Here we have given that :

We need to find the volume of cylinder.

Here's the required formula to find volume of cylinder :

\(\longrightarrow{\pmb{\sf{Volume_{(Cylinder)}= \pi{r}^{2}h}}}\)

Substituting all the given values in the formula to find the volume of cylinder :

\(\longrightarrow{\sf{Volume_{(Cylinder)}= \pi{r}^{2}h}}\)

\(\longrightarrow{\sf{Volume_{(Cylinder)}= 3.14{(50)}^{2}40}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)}= 3.14{(50 \times 50)}40}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)}= 3.14{(2500)}40}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)}= 3.14 \times 2500 \times 40}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)}= 3.14 \times 100000}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)}= \dfrac{314}{100} \times 100000}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)}= \dfrac{314 \times 100000}{100}}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)}= \dfrac{31400000}{100}}}}\)

\({\longrightarrow{\sf{Volume_{(Cylinder)}= 314000 \: {ft}^{3}}}}\)

\(\star{\underline{\boxed{\sf{\purple{Volume_{(Cylinder)}= 314000 \: {ft}^{3}}}}}}\)

Hence, the volume of cylinder is 314000 ft³.

\(\rule{300}{2.5}\)

Answer:

Step by step below

Step-by-step explanation:

0 000 007

0 004  007

0 204 007

0 204  047

0 204  647

0 224 647

4 224 647

The polynomial function of least degree with only real coefficients will be;  y = x³ - 8 · x² + 22 · x - 20.

Algebraic expressions called polynomials include constants and indeterminates. Polynomials can be thought of as a type of mathematics.

The statement indicates that the polynomial has  real coefficients having zeros 3 and 1 - 32 and a lead coefficient of 1.

By algebra of quadratic equations, equations with real coefficients with complex roots are α + i β and α - i β. Then we get;

y = 1 · (x - 3) · (x - 3 - i) · (x - 3 + i)

y = (x - 3) · [x² - 3 · x - i · x - 3 · x + i · x + (3 + i) · (3 - i)]

y = (x - 3) · (x² - 6 · x + 9 - i²)

y = (x - 3) · (x² - 6 · x + 10)

y = x³ - 6 · x² + 10 · x - 2 · x² + 12 · x - 20

y = x³ - 8 · x² + 22 · x - 20

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Answer:

\(p(x)=x^3-5x^2+16x-30\)

Step-by-step explanation:

Given information:

For any complex number  \(z = a+bi\) , the complex conjugate of the number is defined as  \(z^*=a-bi\).  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if p(x) is a polynomial with real coefficients, and (1 - 3i) is a root of p(x)=0, then its complex conjugate (1 + 3i) is also a root of p(x)=0.

Therefore, the polynomial in factored form is:

\(p(x)=a(x-3)(x-(1-3i))(x-(1+3i))\)

As the leading coefficient is 1, then a = 1:

\(p(x)=(x-3)(x-(1-3i))(x-(1+3i))\)

Expand the polynomial:

\(\implies p(x)=(x-3)(x-(1-3i))(x-(1+3i))\)

\(\implies p(x)=(x-3)(x-1+3i)(x-1-3i)\)

\(\implies p(x)=(x-3)(x^2-x-3xi-x+1+3i+3ix-3i-9i^2)\)

\(\implies p(x)=(x-3)(x^2-x-x-3xi+3ix+1+3i-3i-9i^2)\)

\(\implies p(x)=(x-3)(x^2-2x+1-9(-1))\)

\(\implies p(x)=(x-3)(x^2-2x+10)\)

\(\implies p(x)=x^3-2x^2+10x-3x^2+6x-30\)

\(\implies p(x)=x^3-2x^2-3x^2+10x+6x-30\)

\(\implies p(x)=x^3-5x^2+16x-30\)

Loudness, pitch, and timbre are the three psychological aspects of sound that are influenced by the physical properties of sound waves.

When energy moves through a medium (such as air, water, or any other liquid or solid matter), it creates a pattern of disturbance known as a sound wave that propagates away from the sound source.

When an object vibrates, sound waves are produced that are similar to pressure waves, like when a phone rings.

Pitch, intensity, and timbre are three key components of the field of sound psychology or psychoacoustics. People can distinguish the harmonics of a complex periodic sound wave under certain conditions thanks to the way that humans perceive sound and music.

Thus, loudness, pitch, and timbre are the three psychological aspects of sound that are influenced by the physical properties of sound waves.

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The Answer:

Width = 6

Step-by-step explanation:

Let width be w

(3w + 8) x w = 156

3 \(w^{2}\) x 8n - 156 = 0

(w + 8 x 6) (w-6) = 0

w = 6

The height of the pile increasing at the rate of  4.56 inches per minute when the pile is 10 ft high.

In given situation, the rate of change of height is equal to the rate of change of volume, divided by the base area.

First we find the base area.

base area = (π/4)d²

base area = (π/4)10²

base area = 25π ft²

base area ≈ 78.5 ft²

Then the rate of change of height would be,

(30 ft³/min)/(78.5 ft²)

≈ 0.38 ft/min

= 4.56 inches / minute

Therefore, the height of the pile increasing at the rate of  4.56 inches per minute when the pile is 10 ft high.

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Step-by-step explanation:

y+6=-2(x-4)

if it is wrong i am sorry

Answer:

1.57

Step-by-step explanation:

Answer:

1.57

Step-by-step explanation:

Circumference = 2pi(r) = 2(3.14)1 = 6.28

1/4x6.28=1.57

Answer:

Y intercepts: (0, 3)
X Intercepts: (-1, 0), (3, 0)

Step-by-step explanation:

The y-intercepts are the points of the proabola that cross the y-axis and the x-intercepts are the points that cross the x-axis. Hope this helps!

Answer:

D

Step-by-step explanation:

a quartic function is a polynomial of the 4th degree. that means that in the function expression the highest exponent of a term of x is 4.

y = ax⁴ + bx³ + cx² + dx + e

with a not 0.

the degree of a polynomial expression defines also how many zeroes (x values that create y = 0, that means points where the graph intersects the x-axis) there are.

a function has as many zeroes as the degree of the polynomial.

so, we are looking for potentially 4 zeroes.

the only graph that fulfills that is D.

the left "touch" of the graph on the x-axis counts for 2 (but equal) zeroes.

you can always test by virtually shifting the graph up or down and see, what are the max. x-axis intersections you can create.

if shifting D down a little bit you see, that this left "touch" turns into 2 intersections.

the same would apply for a "bend" or turn in the graph that does not even touch the x-axis.

if the original graph has not enough real x-axis intersections, it means that the remaining zeroes are then "imaginary" complex numbers (based on the sqrt(-1) = i).

a polynomial of the nth degree, must have n zeroes.

as a consequence it must have n-1 turns (even if the corresponding curve segments don't intersect with the x-axis in the real number space).

Answer:graph d

Step-by-step explanation:

just took the test

The value of the missing data point is 10. Option C

The data set has 8 data points, and the median is given as 12. The median is the middle value when the data points are arranged in ascending or descending order.

Let's arrange the data set in ascending order:

6, 8, ?, 8, 14, 15, 16, 18

Since the median is 12, it should be the fourth data point when arranged in ascending order. Therefore, the missing data point must be the fourth value in the sorted data set.

From the given options, the only whole number that could fit as the fourth value in the data set is 10.

Thus, the value of the missing data point is C. 10.

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Answer:

14

Step-by-step explanation:

8 pencils in each package.

28 children in all.

each child gets 4.

two children is one whole package.

28 divided by 2 is 14.

that means 14 packs will give each student 4 pencils.

Hope this helped!

Answer:

a

Step-by-step explanation:

Answer: the students are smarter than she thinks

Step-by-step explanation:

more people passed

Answer:

166

Step-by-step explanation:

:)

Answer:

5km

Step-by-step explanation:

A - her office

E - her home

AB = 1km; BC = CE = 4km

AE - the shortest disctance between her office and home.

ADE - right triangle, where AD = 4km, ED = 3 (EC - CD) =>

According to the Pythagorean theorem , we make up the equation:

AE = √ED^2 + AD^2 = √25 = 5km

Answer:

2×2×7=28

Step-by-step explanation:

28÷2=14

14÷2=7

Prime numbers 2, 2, and 7 make 28

Answer:

r≈4.775

Step-by-step explanation:

the formula for this is: r=(3V /4π)^⅓

Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

3.1 Activity: Procedural and Conceptual Understanding in Action

Content Area: Fractions

Problem: Comparing Fractions

Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.

Activity Steps:

Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).

Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.

After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:

What does it mean for one fraction to be greater than or less than another?

Can you explain why we need a common denominator when comparing fractions?

How can you visually represent and compare fractions to better understand their relative sizes?

Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.

Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.

Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.

Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.

By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.

3.2 Example: Conceptual Knowledge vs. Procedural Knowledge

Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.

Example: Division of Fractions

Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.

Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.

In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

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Answer:

twenty million

Step-by-step explanation:

there are 7 zeros so the "20" part would be one number then there would be a comma and the 3 zeros and then another comma then the other 3 zeros