Which of the following correctly completes the square for the equationbelow?X? + 18x = 0A. (x + 18)2 = 81B. (x + 9)2 = 87C. (x + 3)2 = 9OD. (3)

Answer:

the answer is 2

Step-by-step explanation:

Answer:

\(-\frac{4}{5}\).

Step-by-step explanation:

1. Find the slope of the given equation.

To find this value, we need to solve the equation for y.

\(15x-12y=216\\\\-12y=-15x+216\\\\y=\frac{-15x}{-12} +\frac{216}{-12}\\\\ y=\frac{5x}{4} -18\)

The slope of a linear equation is always the number by which the x in being multiplied when the equation is solved for y. Hence, the value of the slope is \(\frac{5}{4}\) .

2. Find slope of the original line.

The problem gives us information to find the slope of the line perpendicular to \(15x-12y=216\). Since the slope of the given equation is  \(\frac{5}{4}\) , the slope of a perpendicular line is the multiplicative reciprocal with the opposite sign. This is inverting the fraction, and adding the opposite symbol of what the original fraction had, like this:

a. We invert the fraction.

We previously had \(\frac{5}{4}\), now we'll have \(\frac{4}{5}\)

b. Add the opposite sign before the fraction.

  \(\frac{4}{5}\) doesn't have a sign before it, that means that it is positive. Converting it to negative we have   \(-\frac{4}{5}\).

\(-\frac{4}{5}\) is our final answer.

Answer:

12

Step-by-step explanation:

Pythagoras Theorem is clearly used in this question.

To Calculate the Hypotenuse:

C = \(\sqrt{a^2+b^2}\)

The Adjacent angle has already given as 9, so you can factor that into the question.

In Order to calculate the Opposite angle you need to use the following formula.

\(b = \sqrt{c^2-a^2}\)

With the integers we already have for both Hypotenuse and Adjacent factored in this will be your equation:

\(b = \sqrt{15^2-9^2} = 12\)

Therefore you answer is 12, Hope this helps, feel free to make as brainilest.

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ANSWER A

If two events is mutually exclusive, it means that they cannot occur at the same time. Coin tossing is an example of something being mutually exclusive, landing on heads and tails cannot happen at the same time; it's either one or the other! In our case, this is not the case. The pizza having mushrooms on it does not affect the type of crust. The crust type and mushrooms can happen at the same time; you can have both! Therefore, Thick Crust Pizza and Pizza with mushrooms are not mutually exclusive.

ANSWER B

ANSWER 1: We know that there are nine pizzas in the oven. Looking at the chart, we see that three total pizzas have thick crust. One of them has no mushrooms and two of them do have mushrooms. This probability is 3/9, or 1/3.

ANSWER 2: We want to find a pizza that has both mushrooms and a thick crust. As we saw when solving for Answer 1, we have that 2 pizzas have both thick crust and mushrooms. This probability is 2/9.

ANSWER C

A dependent event is one that will depend on the result before it. Thick crust pizza and mushrooms do not affect each other at all; they do not depend on each other. They both do their own thing. We need to justify with things we found in Answer B. Well, when we added the event of mushrooms our probability decreased. If one of the events depended on the other, the probability would have definitely increased.  Therefore, these events are both independent.

I hope that this helps you! Have a wonderful day!

Answer:

Step-by-step explanation:

Hello

Please what’s the explanation to get the answer (2+2) ² (2+3)³

we use PEMDAS

Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

(2 + 2)² + (2 + 3)³ =

4² + 5³ =

16 + 125 =

141

The answer is explained below.

In order to be considered a language, a system of communication must have vocabulary, grammar, syntax, and people who use and understand it. Mathematics meets this definition of a language. Linguists who don't consider math a language cite its use as a written rather than spoken form of communication.

Mathematics is pure language - the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms. In a spoken language, there exist words, like "happiness", that defy definition.

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Answer:

1

Step-by-step explanation:

So,6 to the power of 0 is 0.So the leftover is just one.

Answer:

To convert a ratio into the form of a percentage

Answer:

Answer:

The smaller number in 0.01

Step-by-step explanation:

To find this answer, just take the fraction and find the quotient of both numbers.

1.789/178 = 0.01005056179

Now take the quotient and compare it to 0.05.

Is 0.01 larger or 0.05 - the answer is 0.01.

The volume of the closet space = 207,936 in³

The volume of the one roll of toilet paper = 141.3in³

To calculate the volume of the closet, the formula that should be used is the formula for the volume of a rectangle = length×width×height.

Where;

length = 57 in

width = 57

height = 64

volume = 57×57×64 = 207,936 in³

The volume of the toilet paper with the shape of a cylinder would be = πr²h

where;

radius = diameter/2= 6/2=3in

height = 5 in

volume of cylinder = 3.14×3×3×5 =141.3in³

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The value of the S & P 500 before the open on June 22nd, 2010 is 1,113.20 points.

The percent change points is -1.61%/

The value of the S & P 500 before the open would be higher than the value at the close of June 22nd, 2010. This was because the index declined over the day.

Value before the open of June 22nd, 2010 = value at the close + change

17.89 + 1095.31 = 1,113.20 points

Percentage change = (change in points / points before open) x 100

(-17.89 /1,113.20) x 100 = -1.61%

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The time it will take the ball to reach a height of 90feet is 1.2 and 4.4secs

Given the height h (in feet) of the ball t seconds after being kicked expressed as:

h = –16t2 + 90t + 4.

If the ball is at a height of 90feet, hence:

90 = –16t2 + 90t + 4

–16t2 + 90t + 4 - 90 = 0

16t^2  -90t  + 86= 0

8t^2  -45t  + 43= 0

Factorizing the result to get the values of t:

\(t=\frac{45 \pm \sqrt{45^2-4(43)(8)} }{16} \\t=\frac{45 \pm \sqrt{2,025-1376} }{16} \\t=\frac{45 \pm {25.47}}{16} \\t=4.4s \ and\ 1.22secs\)

Hence the time it will take the ball to reach a height of 90feet is 1.2 and 4.4secs

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Answer:

198.25cm³

Solution

V=ABh=30.5·6.5=198.25cm³

Answer:

Conclusion is that there is sufficient evidence to reject the claim that the proportion of people who favor the use of oxygenated fuels year around to reduce air pollution is 60%.

Step-by-step explanation:

We are given;

Population proportion; p = 60% = 0.6

Sample mean: x¯ = 315

Sample size; n = 500

Significance level = 0.09

Defining the hypothesis, we have;

Null Hypothesis; H0: p = 0.6

Alternative hypothesis; Ha: p > 0.6

z-score formula in this case is;

z = (x¯ - np)/√(np(1 - p))

Plugging in the relevant values;

z = (315 - (500 × 0.6))/√(500 × 0.6(1 - 0.6))

z = 1.72

From z-distribution table, the p-value at z = 1.72 is;

1 - P(Z ≤ z-score)

This gives:

p-value = 1 - 0.95728 = 0.04272

Thus p-value is less than the significance level of 0.09, thus we will reject the null hypothesis and conclude that there is sufficient evidence to reject the claim that the proportion of people who favor the use of oxygenated fuels year around to reduce air pollution is 60%.

Answer:

y = -10x -6

Step-by-step explanation:

The probability that the third largest observation in the sample is less than 0.7 is  0.2401 =  24.01%.

The sample size n = 5,

Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.

Probability that X₃ is less than 0.7:

Since X₃ is the third largest observation =  (X₁ and X₂) < 0.7.

The probability that X₃ is less than 0.7 is (0.7)² = 0.49.

.

The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.

We then get the product of both cases:

Probability = 0.49 * 0.49 = 0.2401

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It should be noted that the wind speed is 70km per hour and the plane speed is 490km per hour.

Based on the information given, the following an be illustrated.

Let P = speed of plane

Let w = speed of wind

The appropriate equation will be:

(P + W) (3/2) = 840 ....... i

(P - W) × 2 = (840 / 2) ...... ii

P + W = 560 .....i

P - W = 420 ......ii

Subtract the equations

2P = 980

P = 980 / 2 = 490

P + W = 560

490 + W = 560

W = 560 - 490

W = 70

Therefore, the wind speed is 70km per hour and the plane speed is 490km per hour.

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The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.

To write the equation of a line in slope-intercept form, we use the formula:y = mx + b

where:

- y represents the dependent variable (the vertical axis)

- x represents the independent variable (the horizontal axis)

- m represents the slope of the line

- b represents the y-intercept, the point where the line intersects the y-axis.

In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:

y = (3/5)x + 2

This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).

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Answer:

-------------------------

Apply the Triangle Inequality Theorem.

It states that:

We'll take the sum of two shortest sides and compare with the longest:

It confirms the theorem, without testing the other two sides (which is obvious) so the answer is yes.

The matching answer choice is e).

Step-by-step explanation:

slope = rise/run = (y2-y1)/(x2-x1)

= (3-2)/(0-3)

=(1)/(-3)=-1/3

The intercept is given in one of the points, (0.3).

y=mx+b

y=(-1/3)x+3

I can't tell if this is one of your options bc I think the copy paste didn't quite come through correctly.

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

6.507

I think that this is correct.

Answer:

Confidence Interval = (1.41, 1.59)

Step-by-step explanation:

To construct a confidence interval for the population mean, we can use the following formula:

Confidence Interval = sample mean ± (margin of error * standard error)

where the standard error is equal to the standard deviation divided by the square root of the sample size.

Given the information provided, we can calculate the standard error as:

standard error = 2.16 / sqrt(1370) = 0.058

Then, we can calculate the margin of error as 0.12.

Substituting these values into the formula, we get:

Confidence Interval = 1.5 ± (0.12 * 0.058)

Confidence Interval = (1.41, 1.59)

Therefore, we can interpret the 95% confidence interval as follows: we are 95% confident that the true population mean of the number of days that people feel lonely in the past 7 days is between 1.41 and 1.59. This means that if we were to take many samples of 1370 subjects and compute the confidence intervals for each sample using the same method, we would expect about 95% of the intervals to contain the true population mean.

The values of the variables in number 3, in simplest radical form, are:

f = 6;  o = 3.

The simplest radical form, also known as simplified radical form or simplified surd, refers to expressing a square root (√) or other roots in the simplest possible way without any perfect square factors in the root. In other words, it involves reducing the radical expression to its simplest form.

Solving problem 3, we would apply the necessary Trigonometric ratios to find the variables:

sin 60 = opp/hyp

sin 60 = 9√3 / f

f = 9√3 / sin 60

f = 9√3 / √3/2 [sin 60 = √3/2]

f = 9√3 * 2/√3

f = 18/3

f = 6

tan 60 = opp/adj

tan 60 = 9√3 / o

o = 9√3 / tan 60

o = 9√3 / √3 [sin 60 = √3]

o = 9√3 * 1 / √3

o = 9/3

o = 3

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Answer:

o = 9

f = 18

Step-by-step explanation:

Triangle #3 is a right triangle with two of its interior angles measuring 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, this triangle is a special 30-60-90 triangle.

The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.

In triangle #3, the longest leg is 9√3 units.

As "a√3" is the shortest leg, the scale factor "a" is 9.

The side labelled "o" is the shortest leg opposite the 30° angle. Therefore:

\(o = a=9\)

The side labelled "f" is the hypotenuse of the triangle. Therefore:

\(f= 2a = 2 \cdot 9=18\)

Therefore:

Answer:

7x - 8

Step-by-step explanation:

eight less than product of seven and X

seven and x = 7x

eight less than = - 8

put it all together = 7x - 8

Answer:

7x - 8

Step-by-step explanation:

product of seven and X

7 X x = 7x

8 less than it

7X - 8

This is because we're looking for something that is smaller than 7X by 8

Answer:

9x+7=3

Have a great day!

Answer:

neither

Step-by-step explanation:

Experimental and theoretical probabilities do not match; Field Trip B is the most popular with 32% relative frequency.

What is frequency?

Frequency refers to the number of times an event or observation occurs within a given period, sample size, or population. In the context of data analysis, frequency is often used to describe how often a particular value or category appears in a dataset or sample. It can be expressed as an absolute frequency (the actual number of times an event occurred) or a relative frequency (the proportion or percentage of times an event occurred compared to the total number of observations).

The experimental probability of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins. For example, the experimental probability of selecting Field Trip A is 8/50 = 0.16 or 16%, the experimental probability of selecting Field Trip B is 16/50 = 0.32 or 32%, and so on.

The theoretical probability of selecting each field trip is 1/5 or 0.2 or 20%. This is because the spinner has 5 equal sections, and each section represents a different trip.

The experimental and theoretical probabilities do not match exactly. For example, the experimental  of selecting Field Trip B is 0.32 or 32%, while the theoretical probability is only 0.2 or 20%. This could be due to chance or random variation, as the teacher only spun the spinner 50 times. With a larger sample size, the experimental and theoretical probabilities should converge closer to each other.

The relative frequency of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins, and then multiplying by 100 to express it as a percentage. For example, the relative frequency of selecting Field Trip A is (8/50) x 100 = 16%, the relative frequency of selecting Field Trip B is (16/50) x 100 = 32%, and so on.

Based on the data, Field Trip B appears to be the most popular, as it was selected the most number of times (16 times out of 50 spins).

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Commplete Question:

A science teacher uses a fair spinner to simulate choosing one of five different field trips for her classes. The spinner has 5 equal sections, each representing a different trip. The teacher spins the spinner 50 times and records the results in the table below:

Field Trip Number of times selected

A                8

B                16

C               9

D                12

E                5

Apply math models to analyze the data and answer the following questions:

What is the experimental probability of selecting each field trip?

What is the theoretical probability of selecting each field trip?

Do the experimental and theoretical probabilities match? If not, what could be the reason for the difference?

What is the relative frequency of selecting each field trip?

Based on the data, which field trip appears to be the most popular?

Answer:

y=x+2

Step-by-step explanation:

So, our line has the same y intercept as the equation is y=-2+x, and parallel to 3x+3y=6

We want to write the equation in y=mx+b form, where m is the slope and b is the y intercept

The y intercept of y=-2+x is -2, (we can rearrange it to be y=x-2) so that's the y intercept of our line

so far, here's our line:

y=mx-2

First, let's put 3x+3y=6 into slope-intercept form

subtract 3x from both sides

3y=-3x+6

divide by 3

y=-x+2

Perpendicular lines are negative and reciprocal; if you multiply their slopes together, the result is -1.

The slope for y=-x+2 is -1.

To find the slope of the new line:

-1m=-1

divide by -1

m=1

The slope of our line is 1

here's our line:

y=x+2

hope this helps!