math is not fun please help

Math Is Not Fun Please Help

Answers

Answer 1

Answer:

∠ RST = 22°

Step-by-step explanation:

since ∠ RSU = 91°

and ∠ TSU = 69°

so ∠ RST = 22°

HOW:

given that;

∠ RSU = 91°

and

∠ TSU = 69°

we would subtract 69° from 91°

91°-69°= 22°


Related Questions

X=
////////////////////////

Answers

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

Step-by-step explanation:

Using the alternate exterior angles theorem,

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

Marty graphs the hyperbola (y+2)2/36−(x+5)2/64=1 .


How does he proceed?


Drag a value, phrase, equation, or coordinates in the boxes to correctly complete the statements.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.


Marty first identifies the center of the hyperbola as Response area, and that the hyperbola opens Response area. Since a = Response area, the coordinates of the vertices are Response area.


The slopes of the asymptotes of this parabola are ± Response area, and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are Response area.


Once this information is gathered, the asymptotes are graphed as dashed lines, and the hyperbola is drawn through the vertices, approaching the asymptotes.

Answers

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

Marty first identifies the center of the hyperbola as (-5,2), and that the hyperbola opens up and down. Since a = 6, the coordinates of the vertices are (-5, -4) and (-5, 8).The slopes of the asymptotes of this parabola are a = ± 3/4, and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are y - 2 = ± 3/4(x + 5).

Equation of an hyperbola

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:

(-5, 2 - 6) = (-5,-4).(-5, 2 + 6) = (-5,8).

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

±a/b.

Hence:

a/b = 6/8 = 3/4.-a/b = -6/8 = -3/4.

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

y - 2 = ± 3/4(x + 5).

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Please help!
Write an equation that represents the function graphed in blue by using transformations from y = |x| , which is graphed in green.

Answers

Answer:

-1/4*|X-1|

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;

Finding b:

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

0= -a*|1+b|      

|1+b| = 0/-a

|1+b| = 0

1+b = 0

b = -1

and y becomes:

y = -a*|X-1|

Finding a:

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

a = 1/4The general equation for blue, B:y = -1/4*|X-1|

Blaise M.

What is Y=2x+5 solved

Answers

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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SAMANTHA HAS $27 TO RENT A BIKE FROM CYCLES RUS. SHE
HAS TO PAY A $IO FEE PLUS $2 FOR EVERY HOUR SHE HAS THE
BIKE. WRITE AND SOLVE AN INEQUALITY TO FIND THE
MAXIMUM NUMBER OF HOURS SAMANTHA CAN RENT THE BIKE.

Answers

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.

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.

Answers

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.

[tex]\begin{gathered} Mathematically,\text{ we have that:} \\ V\text{ }\propto\text{ }\frac{1}{P} \\ Then,\text{ we have that:} \\ V\text{ =}\frac{k}{P}\text{ \lparen where k is a constant \rparen} \end{gathered}[/tex][tex]when\text{ V = 800 cubic centimetres , then P = 450 mm Hg}[/tex][tex]\begin{gathered} 800\text{ =}\frac{k}{450} \\ cross-multiply,\text{ we have that:} \\ \text{k = 800 x 450 = 360,000} \end{gathered}[/tex]

[tex]\begin{gathered} Then,\text{ the equation connecting V and P =} \\ \text{ V }=\frac{360,000}{P} \end{gathered}[/tex]

Next:

[tex]when\text{ P = 200 mm Hg, we have that:}[/tex][tex]\begin{gathered} V\text{ = }\frac{360,000}{200} \\ \text{V = 1800 cubic centimetres } \end{gathered}[/tex]

CONCLUSION:

The volume when the pressure is 200 mm Hg is:

[tex]V\text{ = 1800 cubic centimetres}[/tex]

which two county libraries charge the same penalty per week

Answers

Answer:

where's the rest of the question⁉️

PLEASE HELP ASAP! What is the rate of change (slope) and the initial value (y-axis) for this table?

Answers

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

Hello I just need help with A and B on my homework I was able to complete C

Answers

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:

[tex]44,49,53,54,58,74,74,74,80[/tex]

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:

[tex]\bar{x}=\frac{44+49+53+54+58+74+74+74+80}{9}=\frac{560}{9}=62.2222\ldots[/tex]

Rounded to one decimal place, the mean is 62.2

A man is lying on the beach, flying a kite. he holds the end of the kite string at ground level and estimates the angle of elevation of the kite to be 50

Answers

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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1. What is the slope of a line Parallel to y=-2/3x - 7*3/2-3/2O 2/3-2/3

Answers

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:

[tex]-\frac{2}{3}[/tex]

how to find the inverse of f(x) = 3x - 7​

Answers

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].

First step:

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

[tex]y=3x-7[/tex][tex]y+7=3x[/tex][tex]\frac{y+7}{3}=x[/tex]Last step:

Make lettering according to the rule above.

[tex]\frac{x+7}{3} =f^{-1}(x)[/tex]

we have a coin which, with equal odds, is either weighted so that heads has .75 probability, or weighted so that heads has .25 probability. we flip the coin twice and observe two heads. what is the conditional probability that the coin is weighted toward heads with .75 probability?

Answers

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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In Emily's physics class, she had to solve the equation 9 = 12at2 + ut for u. Each step of her work is shown below.

Use the drop-down menus to explain each step.

Answers

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

How to determine the solution for the equation for u?

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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PLS HELP!!!
The tables show the cat population on two islands over several years. Describe mathematically, as precisely as you can, how the
cat population on each island is changing.
year
01 2 3
number of cats on Meow Island 2 6 18, 54 162
2 3 4
number of cats on Purr Island 2 6 10 14 18
B I
year
Type your response in the space below.
Type here
01
t

Answers

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 ,,,,

What is an expression?

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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TEST SCORES The average test score in a class is 74%. Half of the class scored within 7 points of the average.
One student received a score of x%. Which shows an expression that could be used to determine how far the student's score is from the average?
A. |74-7|
B. |x|-74
C. |x-74|
D. 74-|7|

Answers

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)

What is the justification for the above result?

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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there is an ongoing debate about how many spaces should be placed after a period in typed documents. alana read about a study where 100100100 participants all read the same document typed in courier new font. half of the participants were randomly assigned the document with one space after each period, and the other half were given the document with two spaces after each period. participants who read the document with two spaces after each period were able to finish reading significantly faster than those with one space after each period. alana concluded that using two spaces after each period will help people read all documents faster. why is alana's conclusion not appropriate?

Answers

Alana's conclusion from the study is not appropriate.

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

In this study, there was no attempt made to research the alternative fonts. Alana reads about the study that includes only courier new font and arrives at a conclusion.The study in inconsistent with the standard scientific methods as it is not inclusive of all factors and possibilities and is thus inappropriate.

What is an appropriate study?

The achievement of the research objectives is ensured by an appropriate study design. The important element of appropriate studies known as formulated research are missing from observational studies.Observational studies are in which the outcome is not tried to be altered through analysis unlike appropriate studies.This describes an investigation of a specific phenomenon that meets all requirements and adheres to the scientific method.

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Write an equation and solve.You bought a magazine for $5 and 4 erasers. You spent a total of $25. How much did each eraser cost?

Answers

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

The equation can now be shown as follows;

[tex]\begin{gathered} 25=m+4e \\ 25=5+4e \\ Subtract\text{ 5 from both sides of the equation;} \\ 20=4e \\ \text{Divide both sides of the equation by 4} \\ 5=e \end{gathered}[/tex]

Therefore each eraser cost $5

(a) Find an angle between 0° and 360° that is coterminal with 600°.(b) Find an angle between 0 and 2n that is coterminal withЗп2

Answers

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,

[tex]\text{Coterminal angle = 600 - 360 = 240}\degree[/tex]

The coterminal angle is 240°.

QUESTION B

The angle is given as

[tex]-\frac{3\pi}{2}[/tex]

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

Hence, we have

[tex]\begin{gathered} \text{Coterminal angle = 2}\pi-\frac{3\pi}{2} \\ =\frac{\pi}{2} \end{gathered}[/tex]

The coterminal angle is π/2.

7+[-8-5^2]/(1-4)^3+17

Answers

Answer:

2.6

Explanations:

Given the expression;

[tex]\frac{7+\lbrack-8-5^2\rbrack}{(1-4)^3+17}[/tex]

Simplify the expression in the bracket to have:

[tex]\begin{gathered} =\frac{7+\lbrack-8-25\rbrack}{(-3)^3+17} \\ =\frac{7+(-33)}{(-3\times-3\times-3)+17} \\ =\frac{7+(-33)}{-27+17} \end{gathered}[/tex]

Simplify the result to have;

[tex]\begin{gathered} =\frac{7-33}{-10} \\ =\frac{-26}{-10} \\ =2.6 \end{gathered}[/tex]

Hence the result of the given function on simplification is 2.6

1+2 |x-1| less than or equal to 9

Answers

SOLUTION

The question is

[tex]1+2|x-1|\leq9[/tex]

Now let's solve. This becomes

[tex]\begin{gathered} 1+2|x-1|\leq9 \\ 2|x-1|\leq9-1 \\ 2|x-1|\leq8 \\ \\ \text{dividing both sides by x we have} \\ \\ |x-1|\leq4 \end{gathered}[/tex]

This becomes

[tex]\begin{gathered} x-1\leq4 \\ or \\ x-1\ge4 \end{gathered}[/tex]

So we have our x as

[tex]undefined[/tex]

Make up a word problem to solve for system of equations. Be creative

Answers

Explanation:

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

[tex]x\text{ +y + z = 24}[/tex][tex]4x\text{ + 6y + 10z = 148}[/tex][tex]\frac{1}{2}x\text{ + }\frac{1}{4}y+\frac{1}{3}z\text{ = 9}[/tex]

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

[tex]x\text{ +y + z = 24}[/tex][tex]2x\text{ + 3y + 5z = 74}[/tex][tex]6x\text{ + 3}y+4z\text{ = 108}[/tex]

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

[tex]x\text{ +y + z = 24}[/tex][tex]y+3z\text{ =26}[/tex][tex]6x\text{ + 3}y+4z\text{ = 108}[/tex]

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

[tex]x\text{ +y + z = 24}[/tex][tex]y+3z\text{ =26}[/tex][tex]\text{ -3y -2z = -36}[/tex]

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

[tex]x\text{ +y + z = 24}[/tex][tex]y+3z\text{ =26}[/tex][tex]7z\text{ = 42}[/tex]

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

[tex]x=10[/tex][tex]z=6[/tex]

and

[tex]y=8[/tex]

We can conclude that the correct answer is:

Answer:

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:

[tex]x\text{ +y + z = 24}[/tex][tex]4x\text{ + 6y + 10z = 148}[/tex][tex]\frac{1}{2}x\text{ + }\frac{1}{4}y+\frac{1}{3}z\text{ = 9}[/tex]

Solution for this system of equations:

[tex]x=10[/tex][tex]y=8[/tex]

[tex]z=6[/tex]

3:5:7=....:30:...
help me keeds please

Answers

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 .

3 is 6 5 is 10 and 7 is 14 the reason I already did this
Please

Please help
graph x<2.

Answers

Answer:

Bottom right

Step-by-step explanation

Answer:

first answer is correct

Find all the points having an x coordinate of 1 whose distance from the point (-3,-2) is 5

Answers

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

How to calculate the coordinates of the points?

From the question, we have

Distance = 5 unitsPoints = (-3, -2) and (1, y)

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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6 divided by 396 long divison attatch work !

Answers

6 divided by 396 is 66

The graph shows g(x), which is a transformation of f(x)= 1x1. Write the function rule for
g(x).

Answers

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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a box contains 2828 red balls, 2020 green balls, 1919 yellow balls, 1313 blue balls, 1111 white balls, and 99 black balls. what is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 1515 balls of a single color will be drawn?

Answers

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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2.a statewide real estate sales agency, farm associates, specializes in selling farm property in the state of nebraska. its records indicate that the mean selling time of farm property is 90 days. because of recent drought conditions, the agency believes that the mean selling time is now greater than 90 days. a statewide survey of 100 farms sold recently revealed that the mean selling time was 94 days, with a standard deviation of 22 days. at the .10 significance level, has there been an increase in selling time?

Answers

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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4. Find all values of x that make the statement true.

Answers

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

x = 10 and x = 2 .

Solution:

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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