3. Find the sine of angle in the triangle below.
8
7

Answer:

AB ≈ 4.73

Step-by-step explanation:

using the sine ratio in the right triangle

sin25° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{2}{AB}[/tex] ( multiply both sides by AB )

AB × sin25° = 2 ( divide both sides by sin25° )

AB = [tex]\frac{2}{sin25}[/tex] ≈ 4.73 ( to the nearest hundredth )

The correct answer is three squares. To represent 3/5, 3 out of 5 squares need to be shaded.

Fractions written using a numerator (the number on top) and a denominator (the number on the bottom) that indicate how many parts make up the whole.

This can be seen visually if you draw 5 squares in a row and shade in 3 of them. Since fractions are a representation of the part-whole relationship, the numerator of the fraction (3) indicates the number of parts of the whole (5) that are shaded.

Fractions can be used to represent a variety of ratios, from unit fractions (1/2 or 1/3) to more complex fractions (3/5 or 7/9). To answer the question, "How many squares would need to be shaded to represent 3/5?", it is important to understand that the numerator of the fraction (3) indicates the number of parts of the whole (5) that are shaded.

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We need to shade 3/5 or 60% of the small squares in the bigger square which is 54 small squares.

Fractions written using a numerator (the number on top) and a denominator (the number on the bottom) that indicate how many parts make up the whole.

For this problem, we need to shade 3/5 or 60% of the small squares in the bigger square.

To calculate the number of small squares that need to be shaded, we must first calculate the total number of small squares within the bigger square.

We can do this by multiplying the number of squares in the rows(10) by the number of squares in the columns(9), which in this case is

10 x 9 = 90.

Now that we know the total number of small squares, we can calculate the number of small squares that need to be shaded.

To do this, we need to multiply the total number of small squares (90) by  by the fraction we are trying to represent (3/5).

90 x 3/5 = 54.

This means that 54 small squares need to be shaded to represent 3/5.

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Answer:

The other is 75/7.

Step-by-step explanation:

Let the other rational number be x, then:

(-7/15) * x =  -5

x = -5 * -15/7

  = 75/7

The angle BOC on the line AOC is found to be 47 degrees in magnitude.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together.

Hence, AOC is a straight angle, BOC is equal to 6x+29°, and AOB is equal to 3x+124°.

It is common knowledge that a straight angle measures 180 degrees.

As the angle ∠BOC+∠AOB=∠AOC is essentially a straight line, we are assuming that it is 180 degrees, which also satisfies the requirement that all angles on the line add to 180 degrees.

6x+29°+3x+124°=180°

9x+153°=180°

9x=27°

x=3°

Hence, ∠BOC=6x+29°

=6×3+29°

= 47°

So, the value of ∠BOC is 47°.

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The probability distribution that X has is a binomial distribution, and the expected score on the exam is 20.

a. The correct probability distribution is a binomial distribution.

This is because the multiple-choice exam consists of 100 questions with 5 possible responses to each question.

The discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome, is known as the binomial distribution with parameters n and p in probability theory and statistics: success (with probability p) or failure (with probability q= 1 - p)

Therefore, this is a classic example of a binomial distribution where there are two outcomes in each trial (success and failure) and the trials are independent of each other.

(b) The expected score on the exam

The expected value of X is given by the formula;

Expected value (E) = np

n is the number of trials (100)

p is the probability of getting the correct answer (1/5).

Therefore, Expected value (E) = np

= 100 × (1/5) = 20

So, your expected score on the exam is 20.

A score of 50 is z = 6 standard deviations above the mean.

Therefore, it is extremely unlikely that you would score over 50 on this exam.

In conclusion, a binomial distribution is the probability that X has. Meanwhile, 20 is the expected score.

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Therefore, you would be more likely to win the game by choosing option (2) - winning if the spinners do not match.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many areas of mathematics, science, engineering, finance, and other fields to model and analyze uncertain situations. It helps to make predictions, to assess risks and opportunities, and to make informed decisions based on available information. Probability theory provides a foundation for statistical inference, which is used to draw conclusions from data and to test hypotheses about the underlying population.

Here,

In the "Two Spinner Game", there are two possible outcomes for each spin - a match or a non-match. The probability of the spinners matching is the probability of both spinners landing on the same color. Let's say that there are 3 red sections, 3 blue sections, and 2 green sections on each spinner.

The probability of the first spinner landing on red is 3/8, and the probability of the second spinner landing on red is also 3/8. Therefore, the probability of both spinners landing on red (a match) is (3/8) x (3/8) = 9/64.

Similarly, the probability of both spinners landing on blue (another match) is (3/8) x (3/8) = 9/64, and the probability of both spinners landing on green (a match) is (2/8) x (2/8) = 4/64.

The probability of the spinners not matching is the probability of them landing on different colors. There are 3 different pairs of colors that are not a match: red-blue, red-green, and blue-green. The probability of each of these pairs is (3/8) x (3/8) = 9/64.

So, there are 6 possible outcomes, and the probability of winning by a match is 9/64 + 9/64 + 4/64 = 22/64, or about 34.4%. The probability of winning by a non-match is 3 x 9/64 = 27/64, or about 42.2%.

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Distance from the base of tower to the airplane = 706ft.

The term "angle of depression" called   angle created when an observer looks down at an item and the horizontal line intersects with the line of sight. It determines how our field of vision shifts as we glance down. Say you are standing in your kitchen and gazing straight, and suddenly you spy an insect crawling on the floor.

Given, Angle of Depression=12°

Height of tower=150ft

For AB parallel to CD

∠ACD=∠cAB=12°

Tan12°=BC/AB

AB=BC/Tan12°

AB=706ft

Hence, Distance from the base of tower to the airplane = 706ft.

Diagram is attached below;

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The probability that fewer than 3 of them use their smartphones in meetings or classes is 0.0366.

The binomial probability distribution is a discrete probability law with two parameters: trial number (n) and success probability (p) (p). When there are two mutually exclusive outcomes of finite trials, the binomial distribution is utilised.

The probability that a specific 3 people all use their smartphones in meetings or class is 0.53³.

Probability that remaining 7 people do not use their phone is 0.47⁷

¹⁰C₃ = 10*9*8/(3*2*1) = 120.

Thus, the probability of exactly 3 people using their smartphones in meetings or in class is 10C3*0.533*0.477, or 0.0905.

So, adding up the 3 possibilities (that 0 of them, 1 of them, or 2 of them use their smartphones in meetings or class) we get

¹⁰C₀*0.530*0.4710 + ¹⁰C₁*0.531*0.479 + ¹⁰C₂*0.532*0.478 = 0.0366.

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Complete question:

Assume that when adults with smartphones are randomly​ selected, 53​% use them in meetings or classes. If 10 adult smartphone users are randomly​ selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes.

Since the volume of the sphere V = 36π cm³is greater than that of the cone, V' = 21π cm³ the ice cream will overflow.

The volume of a sphere is given by V = 4πr³/3 where r = radius of sphere

Now if the ice cream above is going to melt when it does, will it fit in the cone or will it overflow? Since the ice cream is a sphere, the ice cream will not overflow if the volume of the ice cream equals the volume of the cone. If is greater than the volume of the cone, it will overflow.

Now, since the ice cream is a sphere, its volume is given by V = 4πr³/3 where r = radius of sphere = 3 cm

So, substituting this into the equation, we have that

V = 4πr³/3

V = 4π(3 cm)³/3

V = 4π × 27 cm³/3  

= 4π × 9 cm³

= 36π cm³

Also, since the volume of the cone is given by V' = 1/3πr²h where r = radius of cone = 3 cm and h = height of cone = 7 cm

So, substituting the value of the variables into the equation, we have that

V' = 1/3πr²h

V' = 1/3π(3 cm)² × 7 cm

= 1/3π × 9 cm² × 7 cm

= 3π cm² × 7 cm

= 21π cm³

We see that V = 36π cm³ > V' = 21π cm³

Since the volume of the sphere is greater than that of the cone, the ice cream will overflow.

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The result of each trigonometric functions are:

a) sin X = 7√149 / 149

b) sin Z = 10√149 / 149

c) cos X = 10√149 / 149

d) cos Z = 7√149 / 149

In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse, and the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. Using this trigonometric functions, we can calculate sin X, sin Z, cos X, and cos Z as follows

sin X = YZ / XZ = 7 / √149

cos X = XY / XZ = 10 / √149

sin Z = XY / XZ = 10 / √149

cos Z = YZ / XZ = 7 / √149

To simplify these fractions, we can rationalize the denominator by multiplying the numerator and denominator by √149:

sin X = 7√149 / 149

cos X = 10√149 / 149

sin Z = 10√149 / 149

cos Z = 7√149 / 149

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The given question is incomplete, the complete question is:

Find sin X, sin Z, cos X, and cos Z. Write each answer as a simplified fraction.

Answer:

<b> <i>

Step-by-step explanation:

The given expression is

[tex]15 + c = 17.50[/tex]

We can use this expression to model the cost for a service.

Let's say that your gardener charges an initial amount of $15, and an additional per hour. If the gardener worked only for one hour, and the total cost charged was $17.50, how much was the additional cost?

So, the given expression models this real life situation, we can answer the problem by just solving the equation for [tex]c[/tex]

[tex]15 + c = 17.50[/tex]

[tex]c=17.50-15[/tex]

[tex]c=2.50[/tex]

Answer: Well C equals 2.5. You could use...

You have 3 sticks. one stick is 15 inches long and the other is 17.50. You want to get a small stick to add to the first one so that the first and last stick is equal to the 2nd stick.  C is the third stick.  15+C = 17.50. What is the length of C?

Step-by-step explanation:

EASY

Move all terms not containing C to the right side of the equation. C = 2.5

The required perimeter of the trapezoid is22 units.

The given vertices of the trapezoid are (1,3), (4,7), (9,7), and (9,3). To find the perimeter of the trapezoid, we need to add up the lengths of all four sides.

We can use the distance formula to find the length of each side of the trapezoid:

[tex]{Side 1: }&(1,3) \text{ to } (4,7) \&d = \sqrt{(4 - 1)^2 + (7 - 3)^2} = \sqrt{9 + 16} = 5 \\\text{Side 2: }&(4,7) \text{ to } (9,7) \&d = \sqrt{(9 - 4)^2 + (7 - 7)^2} = \sqrt{25} = 5 \\\text{Side 3: }&(9,7) \text{ to } (9,3) \&d = \sqrt{(9 - 9)^2 + (3 - 7)^2} = \sqrt{16} = 4 \\\text{Side 4: }&(9,3) \text{ to } (1,3) \&d = \sqrt{(1 - 9)^2 + (3 - 3)^2} = \sqrt{64} = 8\end{align*}[/tex]

Therefore, the perimeter of the trapezoid is:

[tex]$\begin{align*}P &= \text{Side 1} + \text{Side 2} + \text{Side 3} + \text{Side 4} \&= 5 + 5 + 4 + 8 \&= 22\end{align*}[/tex]

Thus, the perimeter of the trapezoid is22 units.

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Answer:

0.33

Step-by-step explanation:

To solve this, you first write the problem as an algebra equation as follows: 3x + 4 = 5

Then you solve the equation by subtracting 4 from both sides, and then divide both sides by 3. Here is the math to illustrate better:

3x + 4 = 5

3x + 4 - 4 = 5 - 4

3x = 1

3x/3 = 1/3

x = 0.33

Answer = 0.33

It will take 16 seconds to get to your class.

[tex]\bold{Distance}=\bold{Speed }\times \bold{Time}[/tex]

[tex]200m = 1.5m\div s \times t[/tex]

[tex]24=1.5\times t[/tex] (We want to get t by itself, so lets get rid of the [tex]\times1.5[/tex] by dividing both sides by 1.5)

[tex]t = 16 \ \text{seconds}[/tex]

Therefore, it will take 16 seconds to get to your class.

The percentage of the original sample left after 85 days is approximately 30.73%.

The rate of decay of a radioactive substance is proportional to the amount of substance present. The radioactive decay law states that the amount of a radioactive substance left after t days is given by the formula N(t) = N₀ e^(-kt). Here, N₀ is the initial amount of the substance, and k is the decay constant.

We know that the half-life of the substance is 50 days. This means that N(t) = N₀/2 when t = 50. Therefore, we can use this information to find the decay constant k as follows:

N(50) = N₀ e^(-50k)

N₀/2 = N₀ e^(-50k)

1/2 = e^(-50k)

ln(1/2) = -50kln(e)

ln(1/2) = -50k

0.693 = 50k

k = -0.01386 (approx.)

Therefore, the formula for the amount of substance left after t days is given by N(t) = N₀ e^(-0.01386t). Now, we can use this formula to find the percentage of the original sample left after 85 days as follows:

N(85) = N₀ e^(-0.01386 * 85)

N(85) = N₀ e^(-1.1771)

N(85)/N₀ = e^(-1.1771)

N(85)/N₀ = 0.3073 (approx.)

Therefore, the percentage of the original sample left after 85 days is 30.73% (approx.). The answer is 30.73%.

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Answer:

9

Step-by-step explanation:

-5 + (-18) +32

-23 + 32

32 -23

The correct definition for the lines drawn to circle with centre C are:

A circle is a spherical shape without boundaries or edges.

Thus, on the basis of propertied of circle, the correct definition for the lines drawn to circle with centre C are:

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Step-by-step explanation:

20% off means you pay 80 % of the original price for two books

80% * ( 2 x 19.95 ) = .8 ( 39.90) = $ 31.92

4x - 4/4x² + x is the value of linear equation.

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.  

                                   Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

28x³ - 28x²/28x⁴ + 7x³

= 28x²( x - 1 )/7x³( 4x + 1)

= 4( x - 1)/x( 4x + 1)

= 4x - 4/4x² + x

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The option that is NOT an augmented functional dependency is: Q --> P, because it removes the attribute from the left-hand side of the existing functional dependency, which is not allowed in an augmented dependency.

Functional dependency: It is a concept in database management systems that describes the relationship between two attributes or sets of attributes in a table. In a functional dependency A → B, A is the determinant or the attribute(s) that uniquely determines the value of B.

Augmented functional dependency : It is formed by adding one or more attributes to the determinant side of an existing functional dependency.

From the given options, the only one that is not an augmented functional dependency is "Q → P". This is because it does not involve adding any attributes to the determinant side of an existing functional dependency.

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The two numbers that are in both sequences and between 10 and 30 are 14 and 26.

An ordered set of numbers that adhere to a pattern or rule is referred to as a sequence in mathematics. Sequences can be defined in a variety of ways, such as a formula or a recursive definition, and they can be finite or infinite. Several branches of mathematics, including calculus, algebra, and number theory, employ sequences to explore and answer problems related to the behaviour of functions. For instance, sequences may be used to create fractals and other geometric patterns, predict the rise of populations or the spread of illnesses, and examine the distribution of prime numbers.

The given sequence is 4n - 5, and the nth term is 3n + 2.

For numbers between 10 and 30 in the sequence we have:

4n - 5 ≥ 10

4n ≥ 15

n ≥ 3.75

And,

4n - 5 ≤ 30

4n ≤ 35

n ≤ 8.75

Now, we calculate the sequence for n from 4 to 8:

When n = 4, 3n + 2 = 14

When n = 5, 3n + 2 = 17

When n = 6, 3n + 2 = 20

When n = 7, 3n + 2 = 23

When n = 8, 3n + 2 = 26

Hence, the two numbers that are in both sequences and between 10 and 30 are 14 and 26.

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Answer:

<1= 61

<2= 61

<3= 119

Step-by-step explanation:

The length of the side on the prism is 5cm. The area of the shaded region is 72 cm².

Area is the total amount of area occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the region that its boundary encloses. The quantity of unit squares that span a closed figure's surface is its area. Square units like cm² and m² are used to quantify area. A shape's area is a two-dimensional measurement.

The region inside the perimeter or boundary of a closed shape is referred to as the "area". Such a shape has at least three sides that can be joined together to create a boundary. The "area" formula is used in mathematics to describe this type of space symbolically.

In this figure,

The 5cm flap will be adjacent to the side x. Therefore,

Length of the side x= 5cm

Area of the shaded region= l×b

because the shaded region is a rectangle.

area= 9*x

       =9*5= 45 cm²

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The quotient of 6. 208 × 10⁹ and 9. 7 × 10⁴ expressed in scientific notation is 6.4 × 10¹².

Quotient:

The quotient is the answer we get when we divide one number by another. For example, if we divide the number 6 by 3, we get 2, the quotient. The quotient can be integer or decimal. For an exact division like 10 ÷ 5 = 2, we have a whole number as the quotient, and for a division like 12 ÷ 5 = 2.4, the quotient is a decimal number. The quotient can be greater than the divisor, but always less than the dividend.

Based on the given conditions, Formulate:

6.208× 10⁹ /9.7×10⁴

Simply using exponent rule with same base:

[tex]a^n. a^m = a^(n+m)[/tex]

= 6.208 × 1/9.7

Now,

the sum or difference = [tex]6.208*\frac{1}{9.7}[/tex] × 10¹³

Now solving, we get:

6.208/9.7 × 10¹³

Converting fraction into decimal, we get:

  0.64× 10¹³

⇒ 6.4 × 10¹²

Therefore,

The quotient of 6. 208 × 10⁹ and 9. 7 × 10⁴ expressed in scientific notation is 6.4 × 10¹².

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Answer:

Step-by-step explanation:

2(-4) - 3(-2) = -2

 -8 + 6 = -2

   -2 = -2

Answer:

22

Step-by-step explanation:

2-4i and i=6

2-4(6)

=22

Answer:

-12 is the y intercept while your slope is -4

Step-by-step explanation: