what is x - 3 = 21? show your wok

The linear equation in standard form is 19x - 14y = -182.

What is Linear equation?

A linear equation is a mathematical equation that describes a straight line on a graph. In other words, it is an equation that relates a variable or variables to a constant through a linear function, where the highest power of the variable is one. A general form of a linear equation is:

y = mx + b

To write the linear equation in standard form Ax + By = C, where A, B, and C are integers and A is positive, we need to get rid of the fraction in the equation.

To do this, we can multiply both sides of the equation by the denominator of the fraction, which is 14. This gives:

14y = 19x + 182

Next, we can rearrange this equation by subtracting 19x from both sides:

-19x + 14y = 182

Finally, we can multiply both sides of the equation by -1 to make the coefficient of x positive:

19x - 14y = -182

So, the linear equation in standard form is 19x - 14y = -182.

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Accοrding tο the Pythagοrean theοrem, the length οf the suppοrting guy wires frοm the tοp οf the 45 ft. tall cell phοne tοwer, if they are secured tο the grοund 28 ft. hοrizοntally frοm the base οf the tοwer, is 53 ft.

The Pythagοrean theοrem is a fundamental result in Euclidean geοmetry that describes the relatiοnship between the three sides οf a right-angled triangle.

In equatiοn fοrm, this can be written as:

c² = a² + b²

where c is the length οf the hypοtenuse, and a and b are the lengths οf the οther twο sides (alsο knοwn as the legs) οf the right-angled triangle.

In this case, the tοwer, the grοund, and the guy wire fοrm a right triangle. We knοw the height οf the tοwer is 45 ft, and the hοrizοntal distance frοm the base οf the tοwer tο where the guy wire is secured tο the grοund is 28 ft. Let's call the length οf the guy wire c. Then, we have:

a = 28 ft (hοrizοntal distance frοm the base οf the tοwer tο where the guy wire is secured)

b = 45 ft (height οf the tοwer)

c = length οf the guy wire (hypοtenuse)

Using the Pythagοrean theοrem, we can sοlve fοr c:

[tex]a^2 + b^2 = c^2[/tex]

[tex]28^2 + 45^2 = c^2[/tex]

[tex]784 + 2025 = c^2[/tex]

[tex]2809 = c^2[/tex]

[tex]c = \sqrt{(2809)[/tex]

c ≈ 53 ft

Therefοre, the length οf the suppοrting guy wires frοm the tοp οf the 45 ft. tall cell phοne tοwer, if they are secured tο the grοund 28 ft. hοrizοntally frοm the base οf the tοwer, is apprοximately 53 ft.

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In response to stated question, we may state that You will need to stitch about 5.0089 metres of piping around the outside border of the area tablecloth, rounded to the closest 0.1 m, for a total length of 5.0 m.

The size of just an area on either a surface can be represented as an area. The area of an open surface or the border of a two half object is called to as the surface area, meanwhile the area of a horizontal region or planar region pertains to the area of a shape or planar layer. The entire amount of space occupied by a horizontal (2-D) surface or form of an item is referred as its area. With a pencil, draw an square on a sheet of paper. A two-dimensional character. The area of a form on paper is the quantity of area it takes up. Consider the square to be made up of smaller unit squares.

Begin by calculating the radius of the circular tablecloth. We know that the formula A = r2 gives the area of a circle, where A is the area and r is the radius. Hence we may rearrange this formula to find r:

r = √(A/π) = √(2/π) ≈ 0.7979 m (rounded to four decimal places) (rounded to four decimal places)

Now we must determine the circumference of the circle, which is the distance around the tablecloth's outside border. The circumference is calculated using the formula C = 2r.

C = 2π(0.7979) ≈ 5.0089 m

You will need to stitch about 5.0089 metres of piping around the outside border of the tablecloth, rounded to the closest 0.1 m, for a total length of 5.0 m.

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Answer:

Step-by-step explanation:

To find the difference between the temperatures, we need to subtract the night temperature from the day temperature.

Difference = Day temperature - Night temperature

Difference = 36.6°F - (-18.6°F) (Note: Subtracting a negative number is the same as adding the positive number)

Difference = 36.6°F + 18.6°F

Difference = 55.2°F

Therefore, the difference in temperature between day and night in the town is 55.2°F.

Answer:

(x, y) = (cos(2π/5), sin(2π/5)) = ((1/4)(-1 + √5), (1/4)(2√5 + 2))

Step-by-step explanation:

In standard position, the initial side of an angle lies on the positive x-axis, and the terminal side rotates counterclockwise from the initial side.

Since the angle measures 2π/5 radians, we need to find the point on the unit circle that is π/5 radians past the positive x-axis.

Let (x, y) be the coordinates of the point on the unit circle where the terminal side intersects. We can use the following trigonometric identities to find the values of x and y:

cos(2π/5) = x

sin(2π/5) = y

These values can be determined using either a calculator or the unit circle. Alternatively, we can use the fact that the angle 2π/5 is a special angle and can be expressed exactly in terms of square roots:

cos(2π/5) = (1/4)(-1 + √5)

sin(2π/5) = (1/4)(2√5 + 2)

Therefore, the exact coordinates of the point where the terminal side intersects the unit circle are

(x, y) = (cos(2π/5), sin(2π/5)) = ((1/4)(-1 + √5), (1/4)(2√5 + 2))

The equation of the trend line is y = (-1/2)x + 14.

The overall pattern or trend in a collection of data is represented by a trend line, sometimes referred to as a regression line. In statistics, it is frequently used to illustrate the connection between two variables, one of which is the independent variable and the other the dependant variable. Regression analysis, which determines the line that most accurately fits the data points based on their connection, is used to compute the trend line. In order to anticipate or estimate future values of the dependant variable based on the independent variable, the equation of the trend line may then be utilised.

The slope of the line can be found using the formula:

slope = (change in y) / (change in x)

slope = (8 - 12) / (12 - 4)

slope = -4 / 8

slope = -1/2

Using the point slope form:

y - y1 = m(x - x1)

y - 12 = (-1/2)(x - 4)

y = (-1/2)x + 14

Hence, the equation of the trend line is y = (-1/2)x + 14.

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The factors that affect the width of a confidence interval are a. population variation, c. sample size, and d. confidence level

Confidence interval refers to a statistical measure that attempts to estimate the range of values that could plausibly contain the true value of a population parameter. A confidence interval, in other words, is a statistical range that tells us how sure we are that a statistical estimate we're interested in lies between two values.

There are several factors that can affect the width of a confidence interval. Here are some of them:

The Question was Incomplete, Find the full content below :

what factors of the following affect the width of a confidence interval?

a. population variation

b. none of them

c. sample size

d. confidence level

e. sample mean

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The probability that the student will finish her trip in 60 minutes or less is 0.4

To find the probability that the student will finish her trip in 60 minutes or less, we need to find the proportion of the total area under the uniform distribution curve that lies to the left of 60 minutes.

Since the travel time is uniformly distributed between 40 and 90 minutes, the probability density function is

f(x) = 1/(90-40) = 1/50, for 40 ≤ x ≤ 90

The probability of finishing the trip in 60 minutes or less is therefore

P(X ≤ 60) = ∫[40, 60] f(x) dx

= (60-40)/50

Do the arithmetic operations

= 0.4

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Hence, the answer is (4, 3, 1).In conclusion The answer provided above is concise and ng factually correct, and it addresses the question directly.

In order to determine the number of total electron groups, bondiroups, and lone pairs for geometry (a), we need to use the VSEPR theory. According to this theory, the electron groups around a central atom in a molecule will arrange themselves in a way that minimizes their repulsion. The total number of electron groups includes both the bonding and lone pairs of electrons.To determine the number of electron groups for geometry (a), we first need to determine the molecular geometry of the molecule.

From the given name, we can assume that geometry (a) is tetrahedral. In a tetrahedral molecule, there are four electron groups: three bonding groups and one lone pair. Therefore, the number of total electron groups for geometry (a) is four, the number of bonding groups is three, and the number of lone pairs is one.

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The height of the density curve for the given graph is 1/4.

A density curve is an idealised depiction of a distribution in which the area under the curve is defined to be 1. Although normality is not required, the normal density curve will be the most helpful to us. The "shape" of a distribution, including whether or not it includes one or more "peaks" of often occurring values and whether it is skewed to the left or right, may be determined using a density curve.

For a density curve the area under the curve must be equal to 1.

That is,

base (height) = 1

Here, the base = 4 units

Substituting the value we have:

(4) height = 1

height = 1/4

Hence, the height of the density curve is 1/4.

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(a) The point estimate of the population mean is 8

(b) The point estimate of the population standard deviation is 2.1

Detailed explanation of the answers.

(a) To find the point estimate of the population mean, you need to calculate the sample mean. Here's how:
Step 1: Add up all the values in the sample: 6 + 8 + 10 + 7 + 11 + 6 = 48.
Step 2: Divide the sum by the number of values (the sample size): 48 / 6 = 8.
The point estimate of the population mean is 8.

(b) To find the point estimate of the population standard deviation, follow these steps:
Step 1: Calculate the mean, which we already did in part (a) - it's 8.
Step 2: Subtract the mean from each value and square the result: (6-8)² = 4, (8-8)² = 0, (10-8)² = 4, (7-8)² = 1, (11-8)² = 9, (6-8)² = 4.
Step 3: Add up the squared differences: 4 + 0 + 4 + 1 + 9 + 4 = 22.
Step 4: Divide the sum by the sample size minus 1: 22 / (6-1) = 22 / 5 = 4.4.
Step 5: Take the square root of the result: √4.4 ≈ 2.1 (rounded to one decimal place).
The point estimate of the population standard deviation is 2.1.

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The area of the pie is approximately 113.0 square inches.

The ratio of a circle's circumference to its diameter is denoted by the mathematical constant pi . It is roughly equivalent to 3.14159 and is not repetitive or terminal. As pi is an irrational number, it cannot be written as an exact fraction of two integers and its decimal representation never ends. Pi is used to compute the characteristics of circles, spheres, cylinders, and other curved objects in many branches of mathematics and science, including geometry, trigonometry, calculus, physics, and engineering.

The area of the circle is given as:

A = πr²

Here, diameter = 12, thus radius is 6 inches.

Substituting the values:

area = 3.14 x (6)²

area = 113.04 square inches

Hence, the area of the pie is approximately 113.0 square inches.

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The experimental probability of landing on blue is found by dividing the number of times blue was landed on by the total number of spins.

Experimental probability of landing on blue = Number of times blue was landed on / Total number of spins

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Therefore, the experimental probability of landing on blue is 4/9 or approximately 0.444 or 44.4% (rounded to the nearest tenth or percentage).

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The surface area of the playhouse is 564 square feet.

Frank is building a playhouse for his daughter.

The playhouse is a composite figure with a floor and no windows.

The playhouse is a rectangular prism and a triangular prism.

The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh,

where l is the length,

w is the width,

and h is the height.

Therefore, the surface area of the rectangular prism portion of the playhouse can be calculated by substituting the given values into the formula.

Surface area of the rectangular prism = 2lw + 2lh + 2wh

For the rectangular prism, l = 10 feet, w = 8 feet, and h = 6 feet.

Substituting the values in the formula.

Surface area of the rectangular prism

= 2lw + 2lh + 2wh

= 2 (10 feet × 8 feet) + 2 (10 feet × 6 feet) + 2 (8 feet × 6 feet)

= 160 feet2 + 120 feet2 + 96 feet2= 376 feet2

The surface area of the rectangular prism of the playhouse is 376 square feet.

The formula for the surface area of a triangular prism is 2lw + lh + ph,

where l is the length, w is the width, h is the height, and p is the slant height.

Therefore, the surface area of the triangular prism portion of the playhouse can be calculated by substituting the given values into the formula.

Surface area of the triangular prism = 2lw + lh + ph

For the triangular prism, l = 8 feet, w = 5 feet, h = 6 feet, and p = 10 feet.

Substituting the values in the formula.

Surface area of the triangular prism = 2lw + lh + ph= 2 (8 feet × 5 feet) + (8 feet × 6 feet) + (10 feet × 6 feet)= 80 feet2 + 48 feet2 + 60 feet2= 188 feet2

The surface area of the triangular prism of the playhouse is 188 square feet.

The total surface area of the playhouse can be found by adding the surface area of the rectangular prism and the surface area of the triangular prism.

Surface area of the playhouse = surface area of rectangular prism + surface area of triangular prism.

= 376 square feet + 188 square feet

= 564 square feet.

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Answer:

To solve the inequality x^2-5x-36>0, we need to find the values of x for which the expression is greater than zero.

One way to do this is by factoring the quadratic expression:

x^2-5x-36 = (x-9)(x+4)

The expression is positive when either both factors are positive or both factors are negative.

When both factors are positive: x-9 > 0 and x+4 > 0

Solving for x, we get x > 9 and x > -4. Therefore, x > 9.

When both factors are negative: x-9 < 0 and x+4 < 0

Solving for x, we get x < 9 and x < -4. Therefore, x < -4.

Now, we have two intervals: x < -4 and x > 9. To check whether the expression is positive within these intervals, we can pick a value within each interval and plug it into the expression.

Let's choose x = -5 (within x < -4) and x = 10 (within x > 9).

For x = -5:

x^2-5x-36 = (-5)^2-5(-5)-36

= 25+25-36

= 14

Since 14 is greater than zero, the expression is positive when x = -5.

For x = 10:

x^2-5x-36 = 10^2-5(10)-36

= 100-50-36

= 14

Since 14 is greater than zero, the expression is also positive when x = 10.

Therefore, the solution to the inequality x^2-5x-36>0 is x < -4 or x > 9, which can be written in interval notation as (-∞,-4) ∪ (9,∞).

The second urn contains 16 green balls and 46 blue balls.

Let's first find the probability of drawing two green balls, which we'll denote as P(G,G).

We can break it down into two cases:

Case 1: A green ball is drawn from the first urn and a green ball is drawn from the second urn.

The probability of drawing a green ball from the first urn is 4/10, and the probability of drawing a green ball from the second urn is 16/(16+N). Therefore, the probability of this case is (4/10) x (16/(16+N)).

Case 2: A blue ball is drawn from the first urn and a blue ball is drawn from the second urn.

The probability of drawing a blue ball from the first urn is 6/10, and the probability of drawing a blue ball from the second urn is N/(16+N). Therefore, the probability of this case is

(6/10) x (N/(16+N))

The probability of drawing two balls of the same color is the sum of the probabilities of these two cases, which we know to be 0.58:

P(G,G) + P(B,B) = 0.58

We can solve for P(G,G) as follows:

P(G,G) = 0.58 - P(B,B)

= 0.58 - (6/10) x (N/(16+N))

Now, we can set P(G,G) equal to the probability of drawing two green balls from the urns that we found earlier:

(4/10) x (16/(16+N)) = 0.58 - (6/10) x (N/(16+N))

By simplifying this equation, we get:

64 = 58(16+N) - 60N

By solving for N, we get:

N = 46

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Question:

An urn contains 4 green balls and 6 blue balls. A second urn contains 16

green and N blue balls. A single ball is drawn at random from each urn. The probability that both balls are of the same colour is 0.58. Find N.

From the given information provided, the value of fog(3) and fog(4) is 0.971 and 27/40 respectively.

a) To find fog(3), we first need to find g(3) and then evaluate f(g(3)).

To find g(3), we substitute x=3 into the formula for g(x):

g(3) = (5(3) - 2)/(3 + 2) = 13/5

Now, we can evaluate f(g(3)) by substituting g(3) into the formula for f(x):

f(g(3)) = f(13/5) = 3(13/5)² / (4(13/5)² + 4) = 0.971

Therefore, fog(3) = 0.971.

b) To find fog(4), we follow the same process. First, we find g(4):

g(4) = (5(4) - 2)/(4 + 2) = 18/6 = 3

Now, we can evaluate f(g(4)) by substituting g(4) into the formula for f(x):

f(g(4)) = f(3) = 3(3)² / (4(3)² + 4) = 27/40

Therefore, fog(4) = 27/40.

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The range of scores is 0 to 10. Since everyone in the class scored 6 out of 10, the lowest possible score is 0 and the highest possible score is 10.

The range is the difference between the highest and the lowest of the  given scores. In this case, it's 4 (10-6).

Therefore, the range of scores is 0 to 10. It is important to note that the range is a measure of the spread of scores in a dataset, and in this case, the spread is from the lowest possible score of 0 to the highest possible score of 10.

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The information indicates that the correct answer is 9.76% annually.

The area of mathematics that deals with the characteristics of surrounding space, spatial interactions between distinct objects, and the shape of particular items.

It would take 19 years between 1996 and 2015 in all.

We are aware that the equation: gives a geometric mean of a collection of n positive numbers.

GM =  [tex]((x1)(x2)(x3).............)^{1/n}[/tex]

This would provide us with the product of these values' nth roots.

Thus, the following would be the formula indicating rate of rise over time: -

GM =  [tex](value at the end of the period / value at the start of the period)^{1/n} -1[/tex]

[value at the end of the period / value at the start of the period

Value at the conclusion of the time is equal to 241,364,256, hence the statement stands.

The initial value was 40,257,000.

n = 19

Using values, we obtain:

=[tex](241,364,256/40,257,000)^{1/19} -1[/tex]

= (5.995)1/19 - 1

= 0.0976

= 9.76% per year

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Answer:

x=2

Step-by-step explanation:

10÷2=5

Answer: x=2

Step-by-step explanation:

5x2 = 10

10÷5 = 2

hope this helped

Answer:

The slope of the line passing through the points (1, -1) and (4, 8) is 3.

Step-by-step explanation:

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the following formula:

[tex]slope = (y2 - y1) / (x2 - x1)[/tex]

Here, the given points are (1, -1) and (4, 8). So,

[tex]slope = (8 - (-1)) / (4 - 1) = 9 / 3 = 3[/tex]

Therefore, the slope of the line passing through the points (1, -1) and (4, 8) is 3.

the expectation of buying one ticket is $2

Expectation if a person buys one ticket A person is interested in buying a ticket for a lottery that offers one $1000 prize, one $500 prize, and five $100 prizes. One thousand tickets are sold at $3 each. The expected return is calculated using the following formula:

Expectation = (Probability of winning Prize 1 × Value of Prize 1) + (Probability of winning Prize 2 × Value of Prize 2) + (Probability of winning Prize 3 × Value of Prize 3)To determine the expectation, we must first determine the probability of winning each of the three prizes.

Since one thousand tickets are sold and only one person can win the first prize, the probability of winning the $1000 prize is 1/1000 or 0.001. Similarly, the probability of winning the $500 prize is 1/1000 or 0.001. Since five $100 prizes are available and only one person can win each prize, the probability of winning any one of the five $100 prizes is 5/1000 or 0.005.

Therefore, the expectation is calculated as follows: Expectation = (0.001 × $1000) + (0.001 × $500) + (0.005 × $100)Expectation = $1 + $0.50 + $0.50Expectation = $2Thus, the expectation of buying one ticket is $2. This means that the average value of a ticket is $2, and a person can expect to win $2 on average by purchasing a ticket. Since the cost of a ticket is $3, the expected return is less than the cost of the ticket, and therefore, it is not a good investment from a financial standpoint.

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Answer:

Apparently it's 4800 according to desmos.

Step-by-step explanation:

Step-by-step explanation:

x y

-3 150

-2 300

-1 600

0 4800

As you can see, for negative values of x, the area burned becomes smaller and smaller as x becomes more negative. This is because the equation y = 4800(2)^x has a base of 2, which means that as x becomes more negative, 2^x becomes smaller and smaller, causing y to become smaller and smaller as well.

The expression that best represents the total cost of the charter bus for the field trip is 12n + 50

The total cost of the charter bus for the field trip consists of a $50 reservation fee and an additional $12 per student.

If n represents the number of students going on the field trip, then the expression for the total cost can be written as:

Total cost = 12n + 50

This expression represents the variable cost of the charter bus, which depends on the number of students going on the field trip.

The fixed cost of $50 is added to the variable cost to give the total cost.

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For the Yoko Fund, the Treynor ratio is 6.0%, although none of the answer choices provided is a close approximation, we can choose option c. 6.750

The Treynor ratio measures the excess return earned by an investment per unit of systematic risk (i.e., beta). It is calculated as the difference between the return of the investment and the risk-free rate, divided by the investment's beta.

The formula for the Treynor ratio is:

Treynor Ratio = (Return of the Investment - Risk-Free Rate) / Beta

In this case, the return of the Yoko Fund is 11.2%, the risk-free rate is 3.1%, the beta is 1.20, and we are given the standard deviation of the Yoko Fund's returns, which is 17.5%.

Using the formula, we get:

Treynor Ratio = (11.2% - 3.1%) / 1.20

= 6.0%

Therefore, the Treynor ratio for the Yoko Fund is 6.0%.

None of the answer choices is exactly equal to 6.0%, but the closest one is (c) 6.750.


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 This is an example of resonance where all three structures contribute to the description of the anion and none of them are more accurate than the others. The sum of the formal charges for each of the resonance structures is equal to the net charge of the anion.

The carbonate anion can be represented by three equivalent resonance structures. These structures differ in the placement of electrons and the distribution of formal charges on the individual atoms. Structure B has a formal charge of -0.67 on the oxygen atom and a formal charge of 0.33 on the carbon atom.

Structure D has a formal charge of 0.33 on the oxygen atom and a formal charge of -0.67 on the carbon atom. Structure E has a formal charge of 0.67 on the oxygen atom and a formal charge of -0.67 on the carbon atom.

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Answer: 200

Step-by-step explanation: x = 90 ÷ 0.45

x = 200