1. In your own words, describe the following:

a.) Cartesian Coordinate System

b.) The uses of the system

c.) Who developed the system?

d.) Historically, why is the system unique?

2. Use the list below to write the correct term for each definition on the line provided.

axes (of a graph) coordinates coordinate grid intersection number line ordered pair

origin quadrant x-axis

x-coordinate y-axis y-coordinate

a.) the first number of an ordered pair

b.) the second number of an ordered pair

c.) any of four regions formed by the axes in a rectangular coordinate system

d.) the point at which two lines meet

e.) numbers that correspond to points on a graph in the form (x, y)

f.) the intersection of the x-axis and y-axis in a coordinate plane, described by (0,0)

g.) the horizontal and vertical number lines used in a rectangular graph or coordinate grid system as a fixed reference for determining the position of a point

h.) the vertical ( ) axis on a coordinate plane

i.) the horizontal ( ) axis on a coordinate plane

j.) a line on which numbers can be written or visualized

k.) the location of a single point on a rectangular coordinate system where the digits represent the position relative to the x-axis and y-axis Example: (x, y) or (3, 4)

l.) network of evenly spaced, parallel horizontal and vertical lines especially designed for locating points, displaying data, or drawing maps

Answer: To solve -x²-2x=0 by factoring, we can factor out x from the left-hand side:

x(-x-2) = 0

This equation is true if either x = 0 or -x-2 = 0. Solving for x in the second equation:

-x-2 = 0

-x = 2

x = -2

Therefore, the solutions to the equation -x²-2x=0 are x = 0 and x = -2.

To solve x²-4x-8--6x by factoring, we can simplify it first by combining like terms:

x²-10x-8 = 0

To factor this quadratic, we need to find two numbers that multiply to -8 and add to -10. These numbers are -2 and -8, so we can write:

x²-2x-8x-8 = 0

(x²-2x) - (8x+8) = 0

x(x-2) - 8(x+1) = 0

(x-8)(x-2) = 0

Therefore, the solutions to the equation x²-4x-8--6x are x = 8 and x = 2.

To solve 3x² +12=-21x-24 by completing the square, we first need to move all the terms to one side:

3x² + 21x + 36 = 0

Next, we divide both sides by 3 to simplify the coefficient of x²:

x² + 7x + 12 = 0

To complete the square, we need to add and subtract (7/2)² = 49/4 inside the parentheses:

x² + 7x + 49/4 - 49/4 + 12 = 0

(x + 7/2)² = 1/4

Taking the square root of both sides and solving for x, we get:

x + 7/2 = ±1/2

x = -7/2 ± 1/2

Therefore, the solutions to the equation 3x² +12=-21x-24 by completing the square are x = -4 and x = -3.

To solve -x²-3x-13 = -2x² by using the quadratic formula, we first need to move all the terms to one side:

-x² + x - 13 = 0

Next, we identify the coefficients a, b, and c:

a = -1, b = 1, c = -13

Substituting these values into the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

x = (-1 ± sqrt(1² - 4(-1)(-13))) / 2(-1)

x = (-1 ± sqrt(1 + 52)) / (-2)

x = (-1 ± sqrt(53)) / (-2)

Therefore, the solutions to the equation -x²-3x-13 = -2x² by using the quadratic formula are approximately x = -3.25 and x = 4.25.

Step-by-step explanation:

(D) the floor of a classroom is a perfect example of a line segment.

Therefore, (D) the floor of a classroom is a perfect example of a line segment.

Know more about line segments here:

https://brainly.com/question/2437195

#SPJ4

The correct form of the question is given below;
Which is an example of a line segment?

(A) the edge of a book

(B) the corner of a box

(C) a beam of light

(D) the floor of a classroom

a. The probability of drawing a red ball from Box 1 is 30%.

b. If a red ball is drawn from Box 1, the probability of drawing another red ball from Box 2 on the second round is 60%.

c. If the first draw from Box 1 was black, the conditional probability of drawing a red ball from Box 3 on the second draw is 80%.

d. The probability of drawing two red balls at both draws, without any prior information, is 46%.

e. The probability of drawing a red ball at the first draw and a black ball at the second draw, without any prior information, is 21%.

a. The probability of drawing a red ball from Box 1 can be calculated by dividing the number of red balls in Box 1 by the total number of balls in Box 1. Therefore, the probability is 3/(3+7) = 3/10 = 0.3 or 30%.

b. Since a red ball was drawn from Box 1, we only consider the balls in Box 2. The probability of drawing a red ball from Box 2 is 6/(6+4) = 6/10 = 0.6 or 60%. Therefore, the probability of drawing another red ball when the first ball drawn from Box 1 is red is 60%.

c. If the first draw from Box 1 was black, we only consider the balls in Box 3. The probability of drawing a red ball from Box 3 is 8/(8+2) = 8/10 = 0.8 or 80%. Therefore, the conditional probability of drawing a red ball from Box 3 when the first ball drawn from Box 1 was black is 80%.

d. Before any draws, the probability of drawing two red balls at both draws can be calculated by multiplying the probabilities of drawing a red ball from Box 1 and a red ball from Box 2. Therefore, the probability is 0.3 * 0.6 = 0.18 or 18%. However, since there are two possible scenarios (drawing red balls from Box 1 and Box 2, or drawing red balls from Box 2 and Box 1), we double the probability to obtain 36%. Adding the individual probabilities of each scenario gives a total probability of 36% + 10% = 46%.

e. Before any draws, the probability of drawing a red ball at the first draw and a black ball at the second draw can be calculated by multiplying the probability of drawing a red ball from Box 1 and the probability of drawing a black ball from Box 2 or Box 3. The probability of drawing a red ball from Box 1 is 0.3, and the probability of drawing a black ball from Box 2 or Box 3 is (7/10) + (2/10) = 0.9. Therefore, the probability is 0.3 * 0.9 = 0.27 or 27%. However, since there are two possible scenarios (drawing a red ball from Box 1 and a black ball from Box 2 or drawing a red ball from Box 1 and a black ball from Box 3), we double the probability to obtain 54%. Adding the individual probabilities of each scenario gives a total probability of 54% + 10% = 64%.

To learn more about probability click here: brainly.com/question/31828911

#SPJ11

Carl can select red marbles most likely.

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given Carl is going to select 1 marble,

total marbles in bag = 12

number of red marbles = 6

probability of red marbles = 6/12

number of blue marbles = 3

probability of blue marbles = 3/12

number of green marbles = 1

probability of green marbles = 1/12

number of yellow marbles = 2

probability of yellow marbles = 2/12

since the chances of red marble is more as compared than others.

Hence there of chances of selecting red marble.

Learn more about probability;

brainly.com/question/30034780

#SPJ1

the image of bag is attached.

Y >= 2X - 5

Step-by-step explanation:

yeah-ya..... right?

Respuesta:

x = 5.656854249

Explicación paso a paso:

[NOTA: Solo quería disculparme de antemano por cualquier mala gramática, ya que estoy usando un traductor para esto.]

x/Sen30°= 8/Sen45° [Multiplica ambos lados por Sen30°]

x = (8/Sen45°) * Sen30° [Resuelve usando una calculadora]

x = 5.656854249

Answer:

m∠2= 52° (alt. ∠s)

m∠1 +m∠2= 180° (adj. ∠s on a str. line)

m∠1 +52°= 180°

m∠1= 180° -52°

m∠1= 128°

m∠3= 47° (alt. ∠s)

m∠4 +47°= 180°

m∠4= 180° -47°

m∠4= 133°

m∠5 +52° +47°= 180° (adj. ∠s on a str. line)

m∠5 +99°= 180°

m∠5= 180° -99°

m∠5= 81°

☆ The sum of the angles of a straight line is 180°.

Answer:

Step-by-step explanation:

Given equation is 8h + 13 = 45

Where h is number of hour

So 8h=45-13

8h =32

h= 4 hour is the answer

For Fund 1, the expected return is 5% with a standard deviation of 13.42%. For Fund 2, the expected return is 2% with a standard deviation of 24.66%. If risk-averse, Fund 1 is preferred.

To find the expected value and standard deviation of returns for Fund 1, we use the formula

Expected value = Σ(Probability of state of economy × Return for that state)

Standard deviation = sqrt[Σ(Probability of state of economy × (Return for that state - Expected value)^2)]

Expected value of Fund 1 = (0.2 × 20) + (0.5 × 10) + (0.3 × (-10)) = 5%

Standard deviation of Fund 1 = sqrt[(0.2 × (20-5)^2) + (0.5 × (10-5)^2) + (0.3 × (-10-5)^2)] = 13.42%

To find the expected value and standard deviation of returns for Fund 2, we use the same formula

Expected value of Fund 2 = (0.2 × 40) + (0.5 × 20) + (0.3 × (-40)) = 2%

Standard deviation of Fund 2 = sqrt[(0.2 × (40-2)^2) + (0.5 × (20-2)^2) + (0.3 × (-40-2)^2)] = 24.66%

If you are risk-averse, you would prefer a lower-risk investment with a lower standard deviation. Based on the standard deviations calculated above, Fund 1 is the lower-risk option, so you should pick Fund 1.

To know more about standard deviation:

https://brainly.com/question/23907081

#SPJ4

Answer:

2 used 2 new

Step-by-step explanation:

The contractor would have to work for 20 hours on the site to earn $555 total pay

What is total cost function?

Total cost function is the sum of the fixed charge, which is fixed cost to the person paying the contractor when the contractor visits the site and charge per hour multiplied by the number of hours spent working

TC=a+bX

TC=total cost=$555

a=fixed charged=$55

b=charge per hour=variable element of contractor's pay=$25

X=number of hours spent working=unknown

$555=$55+$25X

$555-$55=$25X

$500=$25*X

X=$500/$25

X=20

The contractor needs to work for 20 hours in order to earn a total pay of $555

Find out more about fixed and variable cost on:https://brainly.com/question/9212451

#SPJ4

Answer:

x ≈ 55.6

Step-by-step explanation:

Using the sine ratio in the right triangle

sin20° = \(\frac{opposite}{hypotenuse}\) = \(\frac{19}{x}\) ( multiply both sides by x )

x × sin20° = 19 ( divide both sides by sin20° )

x = \(\frac{19}{sin20}\) ≈ 55.6 ( to the nearest tenth )

The postulate that proves that the two triangles are congruent is A. HL (Hypotenuse-Leg).

The Hypotenuse-Leg Triangle Congruence Theorem can be described as the triangle theorem which is one of the case of congruency that is been seen as two right triangles are congruent.

From the triangle, we can see that the hypotenuse as well as the leg of the right triangle is been seen as being congruent , and it should be noted that congruency implies that both the sides as well as the angles seems equal in their orientation.

Read more about triangles at:

https://brainly.com/question/17335144

#SPJ1

The probability that none of the 4 light bulbs work is 2.56%.

As per the given information, the probability that an individual light bulb works is 0.6.

Therefore, the probability that it does not work (i.e., fails) is:

1 - 0.6 = 0.4

Since each light bulb works independently of the other light bulbs, the probability that none of the 4 light bulbs work is the product of the individual probabilities that each light bulb fails.

Calculated as,

P(none work) = P(first fails) × P(second fails) × P(third fails) × P(fourth fails)

P(none work) = 0.4 × 0.4 × 0.4 × 0.4

P(none work) = 0.0256

Therefore, the probability that none of the 4 light bulbs work is 0.0256 or approximately 2.56%.

For similar questions on limit,

brainly.com/question/282767

#SPJ4

Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

The side measures for the figure in this problem are given as follows:

6 units and 8 units.

To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:

Area = Length x Width.

The dimensions for this problem are given as follows:

x + 3 and x + 5.

As the area is of 48 square units, we have that:

(x + 3)(x + 5) = 48

x² + 8x + 15 = 48

x² + 8x - 33 = 0.

The coefficients are given as follows:

a = 1, b = 8, c = -33.

Using a quadratic function calculator, the positive root is given as follows:

x = 3.

Hence the dimensions are:

More can be learned about the area of a rectangle at brainly.com/question/25292087

#SPJ1

Answer:

No, No, Yes, No, Yes, Yes

Step-by-step explanation:

A graph is a function if it passes the vertical line test (in other words, every vertical line that can be drawn intersects the graph at no more than one point).

This is because for a function, each input must map onto no more than one output.

Complete question is;

Identify the sampling technique used, and discuss potential sources of bias (if any). Explain. After a hurricane, a disaster area is divided into 200 equal grids. Thirty of the grids are selected, and every occupied household in the grid is interviewed to help focus relief efforts on what residents require the most.

Answer:

A) Cluster Sampling

B) Non - response bias.

Step-by-step explanation:

A) There are different sampling techniques such as:

-Convenience Sampling

-Cluster Sampling

-Systematic random Sampling

-Simple random Sampling

-Stratified random Sampling

Now, the most appropriate type used would be Cluster sampling. Cluster sampling is defined as a sampling technique that divides the samples into clusters or non - overlapping sub-groups and some of these clusters will be in the sample.

So from the question, the disaster area has been divided into 200 equal grids. This 200 grids can also be referred to as clusters or non overlapping subgroups. They are also included in the sample being interviewed. Thus, it's clearly a cluster sampling technique that was used.

B) There are different sources of bias such as;

- Undercoverage bias

- Response bias

- Non - response bias.

The most likely potential source of bias will be non response bias. This source of bias arises when the data/results of some people in the sample are not provided.

In the question, it's very possible that some people in the sample may not be willing to provide answers to the interview questions. Thus there is a high possibility of non - response bias.

Answer:

55

Step-by-step explanation:

Answer:

the answer is =

y = \(-\frac{1}{4} x\)

Answer:

$66.35

Step-by-step explanation:

To find this answer with y=mx+b, we should first explain what it is. Y is our output or answer. M is our variable and x is the slope of our variable or how often it occurs. B, is our y intercept, our initial starting amount. Knowing this, we must figure out y. To do this we must multiply his hourly wage by the hours he works which is $12.50x5. This will get us $62.50. Now that we know how much he makes hourly, we add his initial wage of $3.85 to get us $66.35

This means he will make $66.35 if he works a full 5 hour shift.

Answer:

66.35

Step-by-step explanation:

math

The probability of getting more than one success in five trials with a probability of success of 0.05 on each trial is 0.0207. a. To find P(r=0), we use the binomial probability formula: P(r=0) = (n choose r) * p^r * (1-p)^(n-r)

Where n is the number of trials, p is the probability of success on a single trial, and r is the number of successes. We want to find, and (n choose r) is the binomial coefficient which represents the number of ways to choose r items from a set of n items. In this case, n = 5, p = 0.05, and we want to find P(r=0). Using the formula above, we get:

P(r=0) = (5 choose 0) * 0.05^0 * (1-0.05)^(5-0)

= 1 * 1 * 0.9512

= 0.7744

Therefore, the probability of zero successes in five trials with a probability of success of 0.05 on each trial is 0.7744.

b. To find P(r > 1), we use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, we want to find the probability of getting more than one success, so we will find the probability of getting one or fewer successes and subtract that from 1.

P(r > 1) = 1 - P(r ≤ 1)

To find P(r ≤ 1), we can use the binomial probability formula again:

P(r ≤ 1) = P(r=0) + P(r=1)

= (5 choose 0) * 0.05^0 * (1-0.05)^(5-0) + (5 choose 1) * 0.05^1 * (1-0.05)^(5-1)

= 0.7744 + 0.2049

= 0.9793

Therefore, P(r > 1) = 1 - P(r ≤ 1) = 1 - 0.9793 = 0.0207.

The probability of getting more than one success in five trials with a probability of success of 0.05 on each trial is 0.0207.

To learn more about probability, visit here

https://brainly.com/question/11034287

#SPJ4

\(\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{let's use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_3(3^{2x+1})\implies 2x+1\)

Answer:

Step-by-step explanation:

11 x 6.41

= 70.51

or

= 7051/100

or

=70 50/100

If you increase the confidence level, the length of the confidence interval increases.

An area created using fixed-size samples of data from a population (sample space) that follows a particular probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. The likely location of the population parameter is shown by a confidence interval. For instance, the population mean is between 9 and 11, according to the 95% confidence interval of the mean [9 11].

Given,

If you increase the confidence level, the length of the confidence interval

c) increases

If you increase the confidence level, the length of the confidence interval increases.

To learn more about confidence interval, visit:

https://brainly.com/question/24131141

#SPJ4

Answer:

m+10

Step-by-step explanation:

We know that yesterday, eric had m baseball cards. Thus, we can denote that the total number of baseball cards he had yesterday is m.

We know that he got 10 more today. Since he is receiving more, he is adding to his collection. Since he is getting more, we have to add 10 to how many baseball cards he used to have. He used to have m baseball cards, so today he has m+10 baseball cards.

This is the answer as we cannot combine 10 and m. Since m is a variable with no set value as of now, and 10 is a constant number that has no variable, they are not like terms and cannot be added. So the answer is m+10 baseball cards.

I hope this helped.

Please consider giving brainliest if anyone else responds.

Option- 3 is correct that is both a and b are true.

a. The statement is true that is cosx = \(1 - \frac{sinx}{cscx+cotx}\)

b. The statement is true that is sinx = \(1 - \frac{cosx}{secx+tanx}\)

Given that,

a. We have to prove the statement is true or false.

Statement: cosx = \(1 - \frac{sinx}{cscx+cotx}\)

Now, Take the right hand side

= \(1 - \frac{sinx}{cscx+cotx}\)

= \(1 - \frac{sinx}{\frac{1}{sinx} +\frac{cosx}{sinx} }\)

By using LCM

= \(1 - \frac{sinx}{\frac{1+cosx}{sinx} }\)

= \(1 - \frac{sinx\times sinx}{1+cosx} }\)

= \(1 - \frac{sin^2x}{1+cosx} }\)

= \(\frac{1+cosx - sin^2x}{1+cosx} }\)

We know from trigonometric identities 1 - sin²x = cos²x

= \(\frac{cos^2x+cosx }{1+cosx} }\)

= \(\frac{cosx(1+cosx )}{1+cosx} }\)

= cosx

LHS = RHS

Therefore, The statement is true

b. We have to prove the statement is true or false.

Statement: sinx = \(1 - \frac{cosx}{secx+tanx}\)

Now, Take the right hand side

= \(1 - \frac{cosx}{secx+tanx}\)

= \(1 - \frac{cosx}{\frac{1}{cosx} +\frac{sinx}{cosx} }\)

By using LCM

= \(1 - \frac{cosx}{\frac{1+sinx}{cosx} }\)

= \(1 - \frac{cosx\times cosx}{1+sinx} }\)

= \(1 - \frac{cos^2x}{1+sinx} }\)

= \(\frac{1+sinx - cos^2x}{1+sinx} }\)

We know from trigonometric identities 1 - cos²x = sin²x

= \(\frac{sin^2x+sinx }{1+sinx} }\)

= \(\frac{cosx(1+sinx )}{1+sinx} }\)

= sinx

LHS = RHS

Therefore, The statement is true

To know more about trigonometry visit:

https://brainly.com/question/11550042

#SPJ4

The probability that Justen wins is 4/9.

The probability that Justen wins is determined by the likelihood that the highest number rolled on the two dice is a 1, 2, 3, or 4. To find this probability, we can first calculate the probability that the highest number rolled is a 5 or 6, which is what would cause Gaberil to win.

The probability of rolling a 5 or 6 on one die is 2/6, or 1/3. The probability of rolling a 5 or 6 on both dice is (1/3) * (1/3) = 1/9.

However, we also need to account for the possibility that one die rolls a 5 or 6 and the other does not.

This can happen in two ways: either the first die rolls a 5 or 6 and the second does not, or the first die does not roll a 5 or 6 and the second does.

The probability of each of these scenarios is (1/3) * (2/3) = 2/9.

So the total probability of Gaberil winning is 1/9 + 2/9 + 2/9 = 5/9.

Since there are only two possible outcomes (either Gaberil wins or Justen wins), the probability of Justen winning is 1 - the probability of Gaberil winning. So the probability of Justen winning is 1 - 5/9 = 4/9.

Therefore, the probability that Justen wins is 4/9.

Learn more about probability at https://brainly.com/question/2489066

#SPJ11

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\(Division \: \: \: Property\)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

The correct answer is (( A )) .

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️