AB = 2x-2, BC = 3 and AC = 3x-5 find x

Let the magazine be m and the eraser be e. Then the total cost is 25.

The equation can now be shown as follows;

Therefore each eraser cost $5

The increase in the selling price is 1.818.

Test statistic:

A test statistic is a statistic used in statistical hypothesis testing. A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test.

The given values are:

a = 0.1

x = 94

μ = 90

The formula for test statistic will be:

t = ((x- μ) / ([tex]\frac{s}{vn}[/tex])

Now put the values in the given equation we have:

t = (94-90) / ([tex]\frac{22}{10}[/tex])

 = 4/2.2

  = 1.818

Therefore the increase in the selling price is 1.818.

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ANSWERS

a) 58

b) 62.2

EXPLANATION

a) The median is the middle value. It separates the data set in two. To find the median we have to put the data in order, from least to greatest:

The number of data is odd, this means that the median will be one of the values of the data set and not a mean between two of them. If there are 9 values, the median is the 5th value - so we have 4 values to the left and 4 values to the right.

The first 4 values are 44,49,53,54, so the median is 58.

b) The mean is the sum of all values of the data set divided by the amount of data:

Rounded to one decimal place, the mean is 62.2

Alana's conclusion from the study is not appropriate.

Why is Alana's conclusion from the study is not appropriate?

What is an appropriate study?

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Coterminal Angles are angles that share the same initial side and terminal sides.

Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.

QUESTION A

The angle is given as 600°.

To find the coterminal angle between 0° and 360°, we subtract 360° from the angle.

Therefore,

The coterminal angle is 240°.

QUESTION B

The angle is given as

To get an angle between 0 and 2π, we will add 2π to it.

Hence, we have

The coterminal angle is π/2.

Step-by-step explanation:

Meow island get's their population multiplied by 3 per year

Purr island get's and additional 4 cats per year

The population of cats on each island in the mathematical form is:

Meow island:

f(0) = 2

And,

f(x) = 3f(x - 1)

Where x is the number of years from x = 1, 2, 3 ,,,,

Purr island:

y = 4x + 2

Where x is the number of years from x = 0, 1, 2, 3 ,,,,

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

We will make ordered pair of number of years x and number of cats y as

(x, y).

Meow island:

We see that the number of cats is increasing 3 times the previous number of cats.

So,

f(0) = 2

And,

f(x) = 3f(x - 1)

Where x is the number of years from x = 1, 2, 3 ,,,,

Purr island:

(0, 2), (1, 6), (2, 10), (3, 14) ....

The equation for the table.

y = mx + c

m = (6 - 2) / (2 - 1) = 4/1 = 4

(0, 2) = (x, y)

2 = 4 x 0 + c

c = 2

Now,

y = 4x + 2

Thus,

The population of cats on each island in mathematical form is given above.

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To get the inverse of this function you need two steps. First, we leave the variable [tex]x[/tex] alone in the function. Finally, write [tex]f^{-1}(x)[/tex] where you see the letter [tex]x[/tex] and [tex]x[/tex] where you see the letter [tex]y[/tex].

Leave the variable [tex]x[/tex] alone.

Make lettering according to the rule above.

Answer:

where's the rest of the question⁉️

The kite's height above the earth is 287 feet.

A right-angled triangle is formed by the length of the string, the height of the kite (h) above ground, and the perpendicular distance from the end of the kite string to the man.

The link between the lengths and angles of a right-angled triangle is demonstrated through trigonometry.

Using trigonometric ratios,

the height of the kite above the ground is

sin(55) = h ÷ 350

h = 287 ft

As a result, the kite's height above ground is 287 feet.

A trigonometric function is a real function in mathematics that relates the angle of a right triangle to the ratio of the lengths of the sides. They are frequently used in earth sciences such as navigation, structural mechanics, astrophysics, geography, and many other fields.

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Answer:

Step-by-step explanation:

Let the green graph be G and the blue graph, be B:

1) Be cognate of the fact that the function in blue is completely negative, while the upper green graph is positive

Note: First, we should note that the blue function must therefore be a transformation of the Green function.

This means B takes the form:

y = (s)*a*|X+b|

We are required to find a, b, and s, where s is the sign.

2) From (1), we can deduce that, if graph G was transformed into B, then the first transformation begins by reflecting G along the X-axis (multiplying by -1).

Therefore, s = -1

3) From (2), it follows that the first transformation produces the following effect:

y = |X| transformed to y = -|X|

and B now takes the form y = -a*|X+b|

4) We notice again that the apexes of both functions do not touch. This means G was not only reflected along the X-axis but was also shifted or translated along the X-axis.

5) Building from (4), we notice that the Blue function takes a value of 0 when x is 1. If we put this in the general equation for B;

y = -a*|X+b| implies;

0= -a*|1+b|      

|1+b| = 0/-a

|1+b| = 0

1+b = 0

and y becomes:

Notice also that when the x is 5, the Blue function now takes a value of -1. If we put this in a general equation for B;

y = -a*|X-1|

-1 = -a*|5-1|

-1 = -a*|4|

-4a = -1

Blaise M.

SOLUTION

The question is

Now let's solve. This becomes

This becomes

So we have our x as

The Conditional Probability that the coin is weighted towards heads is 0.25/0.75 . Conditional probability is the result of Bayes’ Theorem .

A coin is tossed twice . So, total outcomes are { HH , TH , HT, TT} that is 4 .

Probability= favourable outcomes / total outcomes

Probability of getting two heads = ¼ = 0.25

Favourable outcomes are { HH , HT, TH}

Probability of getting at least one head = ¾ = 0.75

Conditional probability is measure of the probability of an event occurring, given that another event has already occurred.

Formula , P(A|B) = P(A and B)/ P(B)

Here, p(A|B) is conditional probability of A given B

P(B) is probability of event B occur

P(A and B) is probability of both events A and B occur

We have to find conditional probability that coin is weighted towards heads and it is = Probability of getting both heads / probability of getting at least one head

= ¼ / ¾ = 0.25 / 0.75

Which is required result .

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Answer:

Bottom right

Step-by-step explanation

Answer:

first answer is correct

It is to be noted that the absolute expression that shows how far the student's score is from the average is given as: "| x - 74| (Option C)

The student obtained a score of x% based on the question. As a result, x% might be larger or lower than the average score of 74%.

To establish how distant the student's score is from the average, we must subtract the student's score from the average score; i.e. (x - 74)

This difference, however, might be negative: as a result, the absolute value of (x - 78) must be calculated, yielding |x - 74|.

As a result, the phrase that may be used to assess how distant the student's score is from the average is as follows: |x - 74| which is the same as option c - An Absolute expression.

Absolute expressions are or modulus of a real number x, abbreviated |x| in mathematics, is the non-negative value of x regardless of its sign.

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The equation of u when it is the subject is u = 9/t - 12at

From the question, the original equation is given as

9 = 12at2 + ut

Next, we rewrite the equation to show the exponents

This is represented as

9 = 12at² + ut

To solve further, we simply isolate the variable term ut

This is done by subtracting 12at²  from both sides of the equation

So, we have the following equation

9 - 12at² = 12at² - 12at² ut

Evaluate the like terms in the equation

So, we have

9 - 12at² = ut

Lastly, divide both sides of the equation by t

So, we have

(9 - 12at²)/t = ut/t

Evaluate the quotients

9/t - 12at = u

Make us the subject

u = 9/t - 12at

Hence, the solution for the equation for u is u = 9/t - 12at

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The possible coordinates of the other points are (1, -1) and (5, 1)

From the question, we have

Where (1, y) represents the other points

The distance between the points is then calculated using the following distance formula

d = √[(x₁ - x₂)²+ (y₁ - y₂)²]

Where x and y are the coordinates of the two points

Substitute the known values in the above equation

So, we have

d = √[(-3 - 1)²+ (-2 - y)²]

Evaluate

d = √[16+ (-2 - y)²]

The distance is 5 units

So, we have

√[16+ (-2 - y)²] = 5

Square both sides

16+ (-2 - y)² = 25

This gives

(-2 - y)² = 9

Square root of both sides

-2 - y = +/-3

So, we have

y = -2+/-3

Evaluate

y = -1 and y = 5

Hence, the coordinates are (1, -1) and (5, 1)

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Answer: m = 24

Step-by-step explanation:

The right side of the table is the x value, and the left side is the y value.

Pick two points, I will pick (1,35) and (3,83).

Once you pick the points, input them in the rise over run formula:

y2-y1/x2-x1

83-35/3-1 = 48/2 = 24

Answer:

2 hours

Step-by-step explanation:

10+10= 20, so $20 fee

2+2= 4, so a fee for every hour she has the bike.

20+4= $24, so 2 hours maximum

If you tried adding another hour (which would be $12) that would equal $36 which is over her budget.

Consider the following problem.

A student library has 24 tables, X tables with 4 seats each, Y tables with 6 seats each, and Z tables with 10 seats each. The total seating capacity of the cafeteria is 148. For a special student academic meeting, half of the X tables, 1/4 of the Y tables, and 1/3 of the Z tables will be used, for a total of 9 tables. Determine X, Y, and Z.

The conditions of this problem give rise to the following system of equations

Multiplying the second equation by 1/2 and the third equation by 12, we get:

Now, multiply the first equation by -2 and add it to the second equation. In this way we obtain:

Multiply the first equation by -6 and add it to the last equation. In this way we obtain:

Finally, the process is completed by adding the second multiplied by 3 to the third equation.

then, if we perform back substitution we get the desired solutions:

and

We can conclude that the correct answer is:

Problem:

A student cafeteria has 24 tables, X tables with 4 seats each, Y tables with 6 seats each, and Z tables with 10 seats each. The total seating capacity of the cafeteria is 148. For a special student meeting, half of the X tables, 1/4 of the Y tables, and 1/3 of the Z tables will be used, for a total of 9 tables. Determine X, Y, and Z.

System of equations:

Solution for this system of equations:

7069 are the minimum number of balls that must be drawn without replacement to complete the requirement that all balls of a single color be drawn.

First of all, we’ll look at the worst possible scenario and determine the minimum number of balls needed. We know that the color we are looking for is not blue, nor white, nor black (as there are less than 1515 of the same color when talking about those). In our worst possible scenario, we’ll first pull out all the blue, white, and black balls. Add them up. That means that we’ll definitely pull out 2523 balls( 1111 white + 1313 blue + 99 black). We are not done yet. From all the given balls, we are left with red, green, and yellow colored balls. In our worst scenario, we’ll pull out 1514 balls of every single color, and then we’ll finish it with one color (it doesn’t matter which). Since, we have 3 different colors left, that’s 3*1515+1 = 4545+1 = 4546 that is 4546 more balls.

To finish, we simply add the first 2523 balls with 4546, yielding 2523+4546 = 7069 balls.

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The most appropriate choice for function will be given by -

g(x) = -|x| is the correct function

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

f(x) = |x| is the given function.

f(x) has been transformed to g(x) according to  the graph given in the figure

In the figure, the range is negative real number.

So the transformation g(x) = - |x|

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Answer:

3=6 5=10 7=14

Step-by-step explanation:

here's how to do it u wwould have to sum (+) up all the ratios then it would give u 15 after then u divide the sum by 15 hen u multiply by ratios .

Answer: [tex]x=90[/tex]

Step-by-step explanation:

Using the alternate exterior angles theorem,

[tex]180-x=x\\\\180=2x\\\\x=90[/tex]

Question:

Solution:

The definition of parallel lines tells us that if two lines are parallel, they have the same slope. On the other hand, the slope-intercept form of a line is given by the following formula:

y = mx+b

where m is the slope of a line. In this case, the slope of the given line would be m = -2/3. Then the correct answer would be:

Solution;

y=5x

Explanation;

To construct the graph of the hyperbola, the procedure is as follows:

The equation of a vertical hyperbola with center (x*, y*) is given according to the following equation:

(y - y*)²/a² - (x - x*)²/b² = 1.

A vertical hyperbola opens up and down.

In this problem, the equation is:

(y + 2)²/36 - (x + 5)²/64 = 1.

Hence the center is:

(-5, 2).

The value of coefficient a is:

a² = 36 -> a = 6.

Then the vertices of the hyperbola are:

The slopes of the asymptotes of the parabola are given as follows:

±a/b.

Hence:

Since the asymptotes pass through the center, the equation is:

y - 2 = ± 3/4(x + 5).

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The answer of the linear equation for Y=2x+5 is x = (y-5)/2.

What is linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.  The standard form of a linear equation in one variable is of the form Ax + B = 0.  Now in this equation, x is a variable, A is a coefficient, and B is constant.

The given linear equation is,

Y=2x+5

Now, solve this linear equation for x

Take 5 to LHS it will change sign to -ve

y-5 = 2x

Next, take coefficient of x below to LHS

(y-5)/2 = x

Now, swap the sides

x = (y-5)/2

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SOLUTION:

Step 1:

In this question, we are given the following:

The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 800 cubic centimeters when the pressure is 450 millimeters of mercury​ (mm Hg), find the volume when the pressure is 200 mm Hg.

Step 2:

This is an application of Boyle's law which states that:

Boyle’s law is a gas law that states that the pressure exerted by a gas (of a given mass, kept at a constant temperature) is inversely proportional to the volume occupied by it. In other words, the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of gas are kept constant.

Next:

CONCLUSION:

The volume when the pressure is 200 mm Hg is:

By solving  ( 3 / x - 4) = (x - 5) / x equation we get ,

x = 10 and x = 2 .

Given ( 3 / x - 4) = (x - 5) / x,

3x = (x - 5) (x - 4)

By solving this equation,

3x = x( x - 5 ) - 4( x- 5)

3x = x² - 5x - 4( x - 5)

3x = x² - 5x  - 4x + 20

3x = x² - 9x + 20 = 0

3x - x² + 9x -20 = 0

12x - x² - 20 = 0

-x² + 12x -20 = 0

-1(x(x - 2 ) - 10( x - 2 )) = 0

-1( x - 10) ( x - 2) = 0

x - 10 = 0

x - 2 = 0

∴  x = 10

    x = 2

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