Solve the following system of equations algebraically:x+y=7, x+2y=11

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 )

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

The calculated value of x in the similar triangles is 14 and it is calculated from the ratio 10 : x = 20 : 28

Given the triangle

The triangle is a superset of similar triangles

So, we have the following equivalent ratio that can be used to determine teh value of x

The set up of teh ratio is

10 : x = 10 + 10 : 28

Evaluating the like terms, we get

10 : x = 20 : 28

So, we have

x/10 = 28/20

Multiply both sides by 10

x = 14

Hence, the value of x is 14

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(x-bar) refers to the sample means in statistics. It is the average of all the data values in a sample. It is calculated by dividing the sum of all the data values by the sample size.

The distribution of (x-bar) follows a normal distribution, and its expected value is equal to the population mean. The standard error of (x-bar) is calculated by dividing the population standard deviation by the square root of the sample size. It is used to estimate how much the sample mean varies from the population mean.

Sample mean (x-bar) is a statistical concept used to calculate the average of a sample, and standard error is a measure of the variability of the sample mean. The distribution of the sample mean is a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

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Answer:

Step-by-step explanation:

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

 -8 + 6 = -2

   -2 = -2

The exponential function that represents the population in the next six years is given as follows:

[tex]39366(1.028)^6[/tex]

The standard definition of an exponential function is given as follows:

[tex]A(t) = A(0)b^{\frac{t}{n}}[/tex]

The parameters of the exponential function are given as follows:

In 2010, the population of Belvedere was estimated to be 39,366 people, hence the parameter a is given as follows:

a = 39366.

The yearly increase rate is of 2.8%, hence the parameter values for b and n are given as follows:

b = 0.028, n = 1.

Then the expression giving the population after t years is of:

[tex]P(t) = 39366(1.028)^t[/tex]

After six years, the expression is given as follows:

[tex]39366(1.028)^6[/tex]

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The length of the side labeled x is 75.3 when rounded to the nearest tenth which can be determined by using Pythagorean theorem.

The Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

To find the length of the side labeled x, we will first need to calculate the length of the other two sides.

For the first triangle, the hypotenuse is equal to the side labeled x, so the length of the side labeled x can be calculated using the formula:

x = √(35² + 42²) = 50.1

For the second triangle, the hypotenuse is the side opposite the right angle, which is equal to the side labeled x. We can calculate the length of the side labeled x using the formula:

x = √(60² + 50²) = 75.3

For the third triangle, the hypotenuse is the side opposite the right angle, which is equal to the side labeled x. We can calculate the length of the side labeled x using the formula:

x = √(28² + 34²) = 39.6

Therefore, the length of the side labeled x is 75.3 when rounded to the nearest tenth.

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The rounded value of x in the triangles is:

25) x ≈ 76

27) x ≈ 21

29) x ≈ 104

All trigonometric identities are based on six trigonometric ratios. Sine, cosine, tangent, cosecant, secant, and cotangent. All these trigonometric ratios are defined using the sides of a right triangle as follows: Adjacent side, opposite side, and hypotenuse side.

25) Since, Sinθ = Opposite side/hypotenuse

Sin35° = 39/hypotenuse

hypotenuse = 39/Sin35°

Sin35° = 0.57

hypotenuse = 39/0.57

hypotenuse = 68.42

Now, using Pythagoras theorem:

hypotenuse² = base² + perpendicular²

68.42² = 39² + perpendicular²

4681.29 - 1521 = perpendicular²

4681.29 - 1521 = perpendicular²

3160.29 = perpendicular²

√3160.29 = perpendicular

56.21 = perpendicular

For the calculation of x:

Cosθ = Adjacent side/hypotenuse

Cos42° = 56.21/x

0.74 = 56.21/x

x = 56.21/0.74

x = 75.95

x ≈ 76

27) Cosθ = Adjacent side/hypotenuse

Cos60° = 14/hypotenuse

0.5 = 14/hypotenuse

hypotenuse = 14/0.5

hypotenuse = 28

Now, using Pythagoras theorem:

hypotenuse² = base² + perpendicular²

28² = 14² + perpendicular²

784 - 196 = perpendicular²

588 = perpendicular²

√588 = 24.24

perpendicular = 24.24

For the calculation of x:

Sinθ = Opposite side/hypotenuse

Sin50 = 24.24/hypotenuse

0.76 = 24.24/hypotenuse

hypotenuse = 24.24/0.76

hypotenuse = 31.89

Using Pythagoras theorem:

hypotenuse² = base² + perpendicular²

31.89² = x² + 24.24²

1016.97 = x² + 587.57

x² = 1016.97 - 587.57

x² = 429.4

x = √429.4

x = 20.72

x ≈ 21

29) Sinθ = Opposite side/hypotenuse

Sin28° = 44/hypotenuse

0.46 = 44/hypotenuse

hypotenuse = 44/0.46

hypotenuse = 95.65

Using Pythagoras theorem:

hypotenuse² = base² + perpendicular²

95.65² = 44² + perpendicular²

perpendicular² = 9148.92 - 1936

perpendicular² = 7212.92

perpendicular = √7212.92

perpendicular = 84.92

For the calculation of x:

Cosθ = Adjacent side/hypotenuse

Cos34 = 84.92/x

x = 84.92/0.82

x = 103.56

x ≈ 104

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These limitations are represented by the inequalities x 500 + 2y and 35x + 50y > 225002.

How do equations work?

An equation is an expression that shows the relationship between two or more numbers and variables. Numerical constants, symbolic names, mathematical operators, functions, and conditional expressions are all examples of components that can be included in expressions.

If x stands for the quantity of product A and y for the quantity of product B, then:

x ≤ 500 + 2y (1) (1)

Also:

35x + 50y > 22500² (2) (2)

These limitations are represented by the inequalities x 500 + 2y and 35x + 50y > 225002.

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The length of AN is equal to: C. 32 units.

In Mathematics and Geometry, a perpendicular bisector can be defined as a type of line that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

Based on the information provided about the triangles, we can logically deduce that the perpendicular bisector of FN is AB. Therefore, we can calculate the length of AN by equating the length of AN to the length of A-F as follows;

5r - 3 = r + 25

5r - r = 25 + 3

4r = 28

r = 28/4

r = 7.

For the length of AN, we have:

AN = r + 25

AN = 7 + 25

AN = 32 units.

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Answer:

$11.22

Step-by-step explanation:

20% of 56.09 = 1/5 of 56.09

Now, we divide 56.09 by 5 to get our answer which when rounded becomes 11.22.

Answer:

$11.22

Step-by-step explanation:

20% = 0.2

We Take

56.09 x 0.2 = $11.218

Round $11.218 will be $11.22

So, the tip amount is $11.22

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 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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Using the equation [tex]y = $7.32(1.04)^t[/tex], the amount of time after which the employee will be earning $10.00 is about 9.64 years, or approximately 9 years and 8 months.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

We can start by setting up the equation for the employee's hourly wage y after t years -

[tex]y = $7.32(1.04)^t[/tex]

We want to find the amount of time t after which the employee will be earning $10.00 per hour, so we can set y equal to 10 and solve for t -

[tex]10 = $7.32(1.04)^t[/tex]

Dividing both sides by $7.32, we get -

[tex]1.367 = 1.04^t[/tex]

Taking the natural logarithm of both sides, we get -

[tex]ln(1.367) = ln(1.04^t)[/tex]

Using the property of logarithms that [tex]ln(a^b) = b ln(a)[/tex], we can simplify the right-hand side -

ln(1.367) = t ln(1.04)

Dividing both sides by ln(1.04), we get -

t = ln(1.367)/ln(1.04) ≈ 9.64

Therefore, the employee will be earning $10.00 per hour after about 9.64 years.

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Step-by-step explanation:

it is completely vertical.

the slope is the ratio

y coordinate change / x coordinate change

when going from one point on the line to another.

but in such a case x is not changing at all. x is a constant for all y values.

so the slope is

y difference / 0

this is undefined (or in some ways described as infinity).

The slοpe οf the flagpοle in the figure is nοt defined.

Here, the pοle is similar tο the Y-axis οf the graph.

Angle the pοle makes with Y-axis = 90 degree

( as it is vertically standing straight )

Thus, the slοpe οf the pοle

= [tex]tan90[/tex]

= not defined

Hence, the slope of the given flag pole is not defined.

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Complete question;

What is the slope of the flagpole in the image shown below? _________

The p-value for the Box-Ljung Q test of returns is greater than 5%, which means that we do not reject the null hypothesis and find no evidence of volatility clustering in the raw returns.

In statistics, p-value is a measure of the strength of evidence against the null hypothesis. It is defined as the probability of obtaining the observed results, or results more extreme, assuming that the null hypothesis is true.

The null hypothesis is a statement that assumes there is no significant difference or relationship between two groups or variables being compared. The alternative hypothesis is the statement that there is a significant difference or relationship.

Given by the question.

Based on the information provided, we can conclude that there is evidence of volatility clustering in the IBM data using 15 lags. This is indicated by the p-value being less than 5% for the Box-Ljung Q test of squared returns. Therefore, we reject the null hypothesis and find evidence of volatility clustering.

However, since the test is conducted on squared returns, it is the p-value for this test that is more relevant in assessing volatility clustering.

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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

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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Answer:

720

Step-by-step explanation:

20% of 600 is 120, so add them together and you get 720

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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The net sales in the department during the month of april is $15960.

Sell-thru perecentage rate = Units sold / Units recieved

In our case:

Net sales = (Sell-thru rate)*(opening inventory)

Net sales = (0.28)*($57000)

= $15960

Net sales refer to the total amount of revenue generated by a company from its primary business operations, minus any returns, allowances, and discounts. This figure reflects the actual revenue earned by a company after accounting for any deductions and is a critical metric for evaluating the financial performance of a business.

Net sales are reported on a company's income statement and are a key component of the top line, which also includes other sources of revenue, such as interest income or gains from the sale of assets. Understanding a company's net sales is essential for assessing its growth potential, profitability, and overall financial health. Investors, creditors, and other stakeholders use net sales as a metric to evaluate a company's ability to generate revenue from its core operations, as well as its ability to compete effectively in its industry.

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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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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:

22

Step-by-step explanation:

2-4i and i=6

2-4(6)

=22

The solution to the equation (3√x) - √(9x-17) = 1 is x = 9.

Given the equation in the question (3√x) - √(9x-17) = 1.

To solve for x in the given equation:

(3√x) - √(9x-17) = 1

We can start by isolating the square root term on one side of the equation. Adding √(9x - 17) to both sides, we get:

(3√x) = √(9x - 17) + 1

Squaring both sides of the equation, we get:

(3√x)² = (√(9x - 17) + 1)²

9x = -16 + 2√(9x - 17) + 9x

Solve for 2√(9x - 17)

2√(9x - 17) = 16

36x - 68 = 256

Add 68 to both sides

36x - 68 + 68 = 256 + 68

36x = 324

x = 324/36

x = 9

Therefore, the solution is x = 9.

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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

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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Answer:

<b> <i>

Step-by-step explanation:

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 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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