In the diagram, the measurements that are labeled are known, while the other measurements are unknown. Which measurement of acute triangle ABC can you find by direct substitution of the labeled measures in the Law of Sines?

Answer:16

Step-by-step explanation:

The solution of the equations are as follows:

A. x = 11

B. No solution

C. Many solution

D. x = 0

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

The solution of the following variables can be found as follows:

A variable is a number represented with letter in an equation. Hence, let's find the variables of the equations.

x - 4 = 1 / 2 (x + 3)

x - 4 = 1 / 2 x + 3 / 2

x - 1 / 2x = 3 / 2 + 4

1 / 2 x = 11 / 2

cross multiply

2x = 22

x = 22 / 2

x = 11

-4x = 1 / 2 (-8x + 2)

-4x = -4x + 1

-4x + 4x = 1

0 = 1

No solution

3 - 2(-3x + 1) = 6x + 1

3 + 6x - 2 = 6x + 1

1 + 6x = 6x = 1

1 - 1 = 6x - 6x

0 = 0

Many solutions

0.5(x + 3) = -3(x - 0.5)

0.5x + 1.5 = -3x + 1.5

0.5x + 3x = 1.5 - 1.5

3.5x = 0

x = 0

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Theodore will have $17.5 more from the bank than the travel agent.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Theodore wants to exchange £350 for dollars ($).

Bank's exchange rate is £1 = $1.32.

So, £350 = $1.32×350.

= $462.

Travel agent's exchange rate is £1 = $1.27.

So,  £350 = $1.27×350.

= $444.5.

Therefore, He will get $(462 - 444.5) = $17.5 more.

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For each ordered pair (x,y),

the solution is (-8, 7).

The correct option is D.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

We have an inequality:

y > 2.

From the given choices of ordered pair (x, y):

Substituting the values to the inequality.

And then,

7 > -8.

Therefore, the solution is (-8, 7).

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The volume of this cylinder is equal to 675 cm².

Mathematically, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Substituting the given parameters into the volume of a cylinder formula, we have the following;

Volume of a cylinder, V = πr²h

Volume of a cylinder, V = 3 × 5² × 9

Volume of a cylinder, V = 3 × 25 × 9

Volume of a cylinder, V = 675 cm².

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The measure of the angles of a quadrilateral in ratio 3:20 is 15 and 100 degrees.

A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners. The angles at the vertices of a quadrilateral ABCD are A, B, C, and D. A quadrilateral has the following sides: AB, BC, CD, and DA.

Given that the 2 angles are in the ratio 3 : 20, then the measure of the angle can be taken as 3x and 20x.

We know that the sum of the internal angles of a quadrilateral is 360 thus:

160 + 85 + 3x + 20x = 360

23x = 115

x = 5

The measure of the angles are:

3x = 3(5) = 15

20x = 20(5) = 100

Hence, the measure of the angles of a quadrilateral in ratio 3:20 is 15 and 100 degrees.

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The total number of proper subsets of a set consisting of n elements is 2^n - 1.

A proper subset of a set is a subset that contains fewer elements than the original set. The total number of proper subsets of a set consisting of n elements is given by 2^n - 1.

This is because each element in the set can either be included or excluded in a subset, leading to 2^n possible combinations. However, the empty set (i.e., the subset with no elements) is not considered a proper subset, hence the total number of proper subsets is 2^n - 1.

For example, if n = 3, then the set has 8 possible subsets: {}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, and {1, 2, 3}. Out of these, only 7 are proper subsets. Hence,

the total number of proper subsets of a set consisting of 3 elements is 2^3 - 1 = 7.

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This form of number of trade illustrates an example of comparative advantage, where each country specializes in the production of goods that they are more efficient at producing and then trading those goods with each other.

Comparative advantage is a concept in economics that states that countries that specialize in goods they are more efficient at producing will be able to produce those goods at a lower cost than countries that do not specialize in that good. In this form of trade, China specializes in the production of silk, while Germany specializes in the production of automobiles. By trading these goods with each other, both countries are able to benefit from the number of  specialization of each other, as they can produce silk or automobiles more efficiently and at a lower cost than the other country.

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Lama paid $3,510 to Social Security and Medicare in 1990.

Earnings typically refer to the salary or wages received by an employee for their labor. It can also include bonuses, commission, and other forms of compensation.

Since Lama's earnings were below the threshold of $52,000, the 7.8% rate applied to all of her earnings. To calculate the amount she paid to Social Security and Medicare, multiply her earnings by the rate:

$45,000 x 7.8% = $3,510

So, Lama paid $3,510 to Social Security and Medicare in 1990.

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The probability that 0 or fewer students will withdraw from the course is 26.68%.

Let x be the number of students that withdraw from the introductory statistics course.

We can use a binomial distribution to solve this problem. The binomial distribution formula is:

P(x) = nCx * p^x * (1-p)^(n-x)

Where n is the number of trials, p is the probability of success, and x is the number of successes.

In this case, n = 100 (the number of students registered for the course), p = 0.4 (the probability of a student withdrawing from the course), and x = 0, 1, 2, ..., 100 (the number of students that withdraw from the course).

We want to calculate the probability that 0 or fewer students will withdraw from the course. This can be calculated by summing all the probabilities of x = 0, 1, 2, ..., 100:

[tex]P(x ≤ 0) = P(x = 0) + P(x = 1) + P(x = 2) + ... + P(x = 100)\\P(x ≤ 0) = nCx * p^x * (1-p)^(n-x)\\P(x ≤ 0) = 100C0 * 0.4^0 * (1 - 0.4)^100\\P(x ≤ 0) = 0.2668 = 26.68%[/tex]

The probability that 0 or fewer students will withdraw from the course is 26.68%.

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So the probability of winning $300 is 1/1315 & the probability of winning $201 is 7/196.

The probability of winning $300:

There are a total of 5 $100 bills + 8 $20 bills + 18 $5 bills + 35 $1 bills = 66 bills in the bag.

The probability of winning $300 by drawing 3 bills is the number of ways to select 3 $100 bills divided by the total number of possible combinations of 3 bills, which is:

(5 choose 3) / (66 choose 3) = (5! / (3! * (5-3)!) ) / (66! / (3! * (66-3)!)) = 10 / 13,145 = 1/1315

So the probability of winning $300 is 1/1315.

The probability of winning $201:

We can win $201 by drawing a $100 bill, a $50 bill (which can be achieved by drawing two $20 bills and putting back one), and a $1 bill.

The probability of winning $201 is the number of ways to select 1 $100 bill, 2 $20 bills (which can be rearranged into 1 $50 bill), and 1 $1 bill divided by the total number of possible combinations of 3 bills, which is:

(5 choose 1) * (8 choose 2) * (35 choose 1) / (66 choose 3) = (5 * 28 * 35) / 13,145 = 4900 / 13,145 = 7/196

So the probability of winning $201 is 7/196.

Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain to occur. A probability of 0.5, for example, indicates that an event is equally likely to occur or not occur.

Probabilities can be calculated based on the number of favorable outcomes divided by the number of possible outcomes in a given scenario. For example, if you roll a die, the probability of rolling a 6 is 1/6 because there is only 1 favorable outcome (rolling a 6) out of 6 possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).

Probability is a key concept in statistics and is used to make predictions and decisions in fields such as finance, insurance, engineering, and more.

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The ratio of 6:8 in the simplest form is 3:4. The result is obtained by dividing the ratio by the same number.

A ratio is a comparison between two quantities with the same units. The ratio is generally expressed as

a:b (read: a is to be)

Where

The antecedent and consequent of ratio can be multiplied or divided by the same number. It will make the same value of the ratio. The simplest form of the ratio is when the antecedent and consequent cannot be divided by any positif whole number anymore.

We have 6:8. Find the simplest form!

6 and 8 can be divided by 2.

6:8 = 6/2 : 8/2

6:8 = 3:4

Hence, the simplest form of the expression 6:8 is 3:4.

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Answer:

-2x+24

Step-by-step explanation:

The graph for the proportional equation y = 125m is shown in image by red line.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

We have to given that;

The proportional equation is,

⇒ y = 125m

Clearly, The equation shows the equation of line.

Hence, The graph for the proportional equation y = 125m is shown in image by red line.

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Answer:

One time I was challenged by a math assignment was when I was performing rotations, and reflections. It was confusing to know what coordinates needed to change based on  each rule. After studying and asking for help, I was able to complete this assignment. At time, I thought I didn't know enough to complete the assignment, but I am happy to say that I improved. Working through your problems can help you succeed and have more confidence in yourself as a student.

The first special right triangle with angle 45° has the adjacent side equal to 16. The second special right triangle has the third angle equal to 60°, and the opposite and adjacent sides equal to 5 and 5√3 respectively, using the trigonometric ratios of sine and cosine.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

cos45 = adjacent/8√2 {adjacent/hypotenuse}

recall cos45 = √2

so;

adjacent = √2 × 8√2 {cross multiplication}

adjacent = 8 × 2

adjacent side = 16

The third angle for the second right triangle is derived as;

180° - (30 + 90)° = 60°

considering the angle 30°;

sin30 = opposite/10

recall sin30° = 1/2

opposite = 10/2 {cross multiplication}

opposite side = 5

cos30 = adjacent/10 {adjacent/hypotenuse}

recall cos30 = √3/2

adjacent = 10 × √3/2 {cross multiplication}

adjacent side = 5√3

Therefore, the first special right triangle with angle 45° has the adjacent side equal to 16. The second special right triangle has the third angle equal to 60°, and the opposite and adjacent sides equal to 5 and 5√3 respectively, using the trigonometric ratios of sine and cosine.

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Answer:

see below

Step-by-step explanation:

basically it's asking you the triangle long side if they r the same

PQ length: need to know the diff b/w 2 x's n 2y's

-3+6 = 3

-4-0=-4

so 3²+4² =5² - you should memorize this.

QR length - same thing

-3+3=0

1+4=5

so 0²+5² =5²

Same.  done.

The value of the expression 7 - 9 using subtraction will be negative 2.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The numbers are given below.

7 and 9

Then the difference between the numbers 7 and 9 will be given by putting a minus sign between them. Then we have

⇒ 7 - 9

⇒ - 2

The value of the expression 7 - 9 using subtraction will be negative 2.

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How much water supporting the hydrostatic skeleton and the constriction of round muscles.

Hydrostatic skeletons (some of the time recently called "hydrostats") utilize a depression loaded up with water; the water is incompressible, so the organic entity can utilize it to apply power or change shape. Plants utilize osmotic pressure to compress the pit, while creatures do it with muscle layers in the hydrostat's walls.

The most widely recognized muscle game plan is to have a layer with longwise or longitudinal filaments and a layer with roundabout or circumferential strands.

Most hydrostatic skeletons are pretty much tube shaped, so longitudinal muscles will more often than not abbreviate them and furthermore enlarge them because of consistent volume, though circumferential muscles will generally do the inverse. The longitudinal and circumferential muscles are in this manner antagonistic.

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A standard normal random variable has a 0.3814 percent chance of falling between 0.3 and 3.2, according to the z table.

The probability is calculated by dividing the total number of outcomes by the total number of events.

Odds and probability are two different concepts.

Divide the probability of an event occurring by the probability that it won't happen to calculate chances.

The four main types of probability that mathematicians study are axiomatic, classical, empirical, and subjective.

So, the probability that a standard normal random variable will occur with a probability ranging from 0.3 to 3.2 must therefore be calculated.

First, a mean and standard deviation are introduced for a standard normal random variable.

The probability that a standard normal random variable will fall between 0.3 and 3.2 needs to be calculated.

Therefore, it should be more likely that:

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

Using the usual value of z:

P(0.3<z<3.2)=0.9993−0.6179

Justify by saying:

P(0.3<z<3.2)=0.3814

Therefore, a standard normal random variable has a 0.3814 percent chance of falling between 0.3 and 3.2, according to the z table.

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no is not a parrel is a standard line

Answer: No

Step-by-step explanation: Parallel lines have the same slope but different y-intercepts. By using the table, we find out that the slope of the second line is 1/2. the slope of the first one is -1/2 so they are not the same.

Answer:  45

Step-by-step explanation:

We can label 5/9 of 81 as Numerator/Denominator of a whole number.

To solve the problem, we multiply the Numerator by the whole number and leave the Denominator as is:

(5 x 81) / 9 = 405/9 = 45

Therefore, the answer to 5/9 of 81 in its lowest form is:

The measure of the value of 'x' from the expression is 8.8712

The given image is a triangle with the following parameters:

Opposite = 8

Hypotenuse = x

acute angle = 46 degrees

Required

The measure of the angle 'x'

Applying the rule of trigonometry

sin theta = opposite/hypotenuse

sin 46 = 8/x

x = 8/sin46

x = 8.8713

Hence the value of x from then given triangle is 8.8712

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The point B'' after the transformation is (-4, 13).

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

A figure when undergoes reflection becomes it's mirror image.

A point (x, y) after a reflection across the line y = -x is (-y, -x).

Given point is B(-8, 3).

After the reflection, it changes to B'(-3, 8).

Then the point undergoes translation by (-1, 5).

B'(-3, 8) is translated to B''(-3 - 1, 8 + 5) = B''(-4, 13).

Hence the point B(-8, 3) after the reflection and translation gives the point B''(-4, 13).

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The maximum probability of victory in this scenario is 50%.

Each player has an equal chance of rolling any number from 1 to 6, so the probability of rolling a specific number is 1/6.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.

Since the players cannot see their own outcome but can see the outcome of the other player, they must guess their own roll based on the observed roll of the other player. If the two players roll different numbers, one of them will have the correct guess, and their probability of winning is 1/6.

If the two players roll the same number, then both players have the same information and the probability of either player winning is still 1/6.

The maximum probability of victory is (1/6) + (1/6) = 1/3 + 1/3 = 2/3 = 50%.

Therefore, the probability is 50%.

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Considering the expression of a line, the slope of the line that passes through the points (2,4) and (9,12) is 8/7.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line is calculated as:

m= (y₂ - y₁)÷ (x₂ - x₁)

In this case, being (x₁, y₁)= (2,4) and (x₂, y₂)= (9,12), the slope m can be calculated as:

m= (12 -4)÷ (9 -2)

Solving:

m= 8÷ 7= 8/7

Finally, the slope of the line is 8/7.

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The angle measure of n is 74°.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

An irregular pentagon is shown below.

The sum of the exterior angles of a polygon is 360°.

So,

n + 72 + 39 + 85 + 90 = 360

n = 360 - 286

n = 74°

Therefore, the angle measure of n is 74°.

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290 people Apple wants to visit the store every day after Layla’s marketing campaign.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given Apple wants to increase the number of people who enter in stores in London every day,

let X be Apple’s target amount of people,

380 is double the difference between, the target amount of people which apple wants to visit the store every day and 100

difference between the target amount of people and 100 is

X - 100

double the equation = 2(X - 100)

the equation is equal to 380

2(X - 100) = 380

divide both sides by 2

X - 100 = 380/2

X - 100 = 190

X = 190 + 100

x  = 290

Hence  Apple’s target amount of people is 290.

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