A 6-sided die is rolled. What is the probability of rolling a number that is even and a 3?.

Answer:

\(-2x^2+x+3=0\)

\(-x^2+x+5=0\)

Step-by-step explanation:

Algebraic Manipulation

Consists of applying basic rules of algebra to simplify or transform algebraic expressions into others.

We are required to rewrite two expressions as quadratics in standard form.

Question 1:

\(\displaystyle \frac{x}{2} = x^2 - \frac{3}{2}\)

To get rid of the denominators, multiply by 2:

\(x=2x^2-3\)

Move all the terms to the left side:

\(x-2x^2+3=0\)

Order by degree:

\(\boxed{-2x^2+x+3=0}\)

Question 2:

\(\displaystyle \frac{5}{x} + 1 = x\)

Multiply by x (x must be different from 0):

\(5+x=x^2\)

Move all the terms to the left side:

\(5+x-x^2=0\)

Order by degree:

\(\boxed{-x^2+x+5=0}\)

Answer:

43

Step-by-step explanation:

2 significant figures means we keep the first 2 and round the 1 place

42.598 we round to 43 since next to the 2 is a 5 so we round up

And 43 are 2 significant figures since none of them are zero

Hopes this helps please mark brainliest

Answer:

A vertical reflection is given by the equation y=−f(x) y = − f ( x ) and results in the curve being “reflected” across the x-axis. A horizontal reflection is given by the equation y=f(−x) y = f ( − x ) and results in the curve being “reflected” across the y-axis.

If your observed Z or t statistic falls in the "critical region," it means that the probability of obtaining a value as extreme or more extreme than the observed statistic is very low, assuming the null hypothesis is true.

The critical region is a range of values of a test statistic, such as Z or t, that indicate the rejection of the null hypothesis. In hypothesis testing, the null hypothesis is a statement that there is no significant difference between two groups or that there is no effect of an intervention. The alternative hypothesis is the opposite of the null hypothesis, and it suggests that there is a significant difference or an effect of the intervention.

The critical region is determined by the level of significance, which is a pre-specified threshold that is usually set at 0.05 or 0.01. If the observed test statistic falls within the critical region, it means that the probability of obtaining a value as extreme or more extreme than the observed statistic is very low, assuming the null hypothesis is true. This probability is called the p-value. Therefore, you would reject the null hypothesis and conclude that there is a significant difference or relationship between the variables being studied.

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West Moreland is -157 ( below sea level would be a negative value)

Dallas is 430 above

-157 to sea level is 157 feet

Sea level to 430 is 430 feet

Total distance = 157 + 430 = 587 feet.

Answer:

587 feet

Westmoreland is 157 feet below the sea level.

This is a negative number, so add 157 to get to 0.

Dallas is 430 above sea level.

Add 430 and 157. You get 587.

Hope it helps!

Answer:let

Length =L

Width =W

L=5W

Perimeter(p)=2L+2W

P=10W+2W

84=12W

Divide both sides by 12

W=7m

L=5*7=35m

Hence, the length and width are 35m and 7m respectively

Step-by-step explanation:

ANSWER

(7, -2)

EXPLANATION

We want to know the image point after a translation.

A translation is basically a shift in the position of the object.

The object point is (5, -5) and it translates 2 units right and 3 units up.

That means there is a shift +2 units on the x axis and +3 units on the y axis.

Therefore, the image point is:

(5 + 2, -5 + 3)

= (7, -2)

That is the image point.

Answer:

105/88

Step-by-step explanation:

Answer:

39/88

Step-by-step explanation:

Check image for explanation.

Answer:

52mm

Step-by-step explanation:

(4x3)2+(4x4)+4x3= 52mm

triangle sides+square sides+bottom square side= answer

Hope this helps :)

Let's denote the initial illumination from the lamp as I1, the initial distance between the book and the lamp as d1, the final illumination as I2, and the final distance as d2.

According to the inverse square law, the illumination is inversely proportional to the square of the distance. Mathematically, this can be expressed as:

I1 ∝ 1/d1^2

I2 ∝ 1/d2^2

We are given that the initial distance (d1) is 9 cm, and we want to find the distance (d2) at which the book receives one-third (1/3) of the initial illumination.

Let's express this relationship using the equation:

I2 = (1/3) * I1

Since the illumination is inversely proportional to the square of the distance, we can write:

(1/3) * I1 = 1/d2^2

To find the distance (d2), we can rearrange the equation as follows:

d2^2 = (1/3) * d1^2

d2^2 = (1/3) * 9^2

d2^2 = (1/3) * 81

d2^2 = 27

Taking the square root of both sides:

d2 = √27

d2 ≈ 5.2 cm

Therefore, the book needs to be moved approximately 5.2 cm further from the lamp so that it receives one-third as much light.

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The measure of ∠E will be equal to 38°.

Given,

m∠BFE = 118° and m∠C = 86°

And BF bisects ∠ABD

From the Property of Linear Pair,

∠AFB + ∠BFE = 180°

=> ∠AFB + 118° = 180°

=> ∠AFB = 62°

Now, we can see that ∠AFB and ∠FBD are equal because they are alternate angles.

And ∠FBD and ∠ABF are equal because BF bisects ∠ABD.

So, In ∆ABF,

∠AFB + ∠ABF + ∠BAF = 180° (because of the angle sum property of a triangle)

=>62° + 62° + ∠BAF = 180°

=>∠BAF = 180° - 124°

=> ∠BAF = 56°

Similarly, in ∆ABE,

∠A +∠C  +∠E = 180°

=> 56° + 86° + ∠E = 180°

=> ∠E = 38°

Therefore, m∠E = 38°.

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Answer:

429

Step-by-step explanation:

Answer:

the answer is -3 because -++ in the high eat number so the -7 is the bigest

Step-by-step explanation:

Cog, KY tj, kyzkysiyso6doydi6wkyx co70 kysu5, 5i

The given system of equations to have a Unique solution, the value of k must be any real number except 1 (k ≠ 1).

The value of k for which the given system of equations has a unique solution, we can use the concept of determinants. The system of equations is as follows:

kx + 2y = 3   -- (1)

3x + 6y = 10  -- (2)

To have a unique solution, the determinant of the coefficients of x and y must not be zero.

The determinant of the coefficient matrix for the system is:

D = | k   2 |

       | 3   6 |

By calculating the determinant, we have:

D = (k * 6) - (2 * 3)

D = 6k - 6

For the system to have a unique solution, the determinant D must not equal zero.

6k - 6 ≠ 0

Simplifying the inequality:

6k ≠ 6

Dividing both sides by 6:

k ≠ 1

Therefore, for the given system of equations to have a unique solution, the value of k must be any real number except 1 (k ≠ 1).

In other words, if k is not equal to 1, the system of equations will have a unique solution. If k is equal to 1, the system will either have infinitely many solutions or no solution.

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Answer: 225 units

Regular pentagons have 5 sides of equal length and 5 angles of equal measure. so if you have one side you can solve the rest. We have y so 5 times y equals 5 times 9=45 units per side. Multiply by the number of sides (5) and you get 225 units.

The first model of inequality satisfy the problem i.e 2w + 2* 4w ≤ 106

A rectangle is a four-sided, two-dimensional flat shape. The opposite sides of a rectangle's four sides are parallel and equal to one another. It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees. A particular kind of parallelogram that has all of its angles equal is the rectangle. A square is a rectangle with four equally sized sides. Let's now explore the characteristics of the rectangle in this essay.

Rectangles' essential characteristics are as follows:

A rectangle is a parallelogram.

The Perimeter of the rectangle is 2a + 2b where a and b are the two sides

Now , if w is the width of the rectangle then, the length is 4w given in problem.

Perimeter,

2w + 2* 4w

As it is given in the problem

2w + 2* 4w ≤ 106

The first model of inequality satisfy the problem.

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Answer:

Step-by-step explanation:

138° - 80° = 58°

0.3193 is the probability of your 73% surity that at least seven of these people can read and write ( are not illiterate ).

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. A probability is a number between 0 and 1, where 1 indicates certainty and 0 indicates impossibility of the event.

p = 0.73

q = 1 - p = 1 - 0.73 = 0.27

n = 8

Using binomial probability formula ,

P(X = x) = (n C x) * px * (1 - p)n - x

P(X > 7) = (8 C 7) * 0.737 * (0.37)8-7  +(8 C 8) * 0.738 * (0.37)8-8

              =  0.238624 + 0.080646

Probability = 0.3193  

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Answer:

10 apples

Step-by-step explanation:

141-11 is 130. it says there are 11 loose apples on display. in total, there are 130 apples in the bag

we know that there are 13 bags of apples. so 130/13 is 10. there are 10 apples in each bag

The equation of the line through \((1,2)\) which make equal intercepts on the axis \(x+y=3\)

The equation of the line through (1,2) makes an equal intercept on the axis

The formula of the intercept form is

\(\frac{x}{a} +\frac{y}{b} =1\)

If they make an equal intercept

\(a=b\\\frac{x}{a} +\frac{y}{a} =1\\x+y=a\)

Put the value of the point in the axis, and we get.

\(1+2=a\\a=3\)

Put the value in the equation, and we get.

\(x+y=3\)

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Answer:

\(2y^2-7y+6=0\)

Step-by-step explanation:

We are given that \(\alpha\) and \(\beta\) are the zeroes of the polynomial \(6y^2-7y+2\)

\(y^2-\frac{7}{6}y+\frac{1}{3}\)

We have to find a quadratic polynomial whose zeroes are \(1/\alpha\) and \(1/\beta\).

General quadratic equation

\(x^2-(sum\;of\;zeroes)x+ product\;of\;zeroes\)

We get

\(\alpha+\beta=\frac{7}{6}\)

\(\alpha \beta=\frac{1}{3}\)

\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha \beta}\)

\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7/6}{1/3}\)

\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7}{6}\times 3=7/2\)

\(\frac{1}{\alpha}\times \frac{1}{\beta}=\frac{1}{\alpha \beta}\)

\(\frac{1}{\alpha}\times \frac{1}{\beta}=\frac{1}{1/3}=3\)

Substitute the values

\(y^2-(7/2)y+3=0\)

\(2y^2-7y+6=0\)

Hence, the quadratic polynomial whose zeroes are \(1/\alpha\) and \(1/\beta\) is given by

\(2y^2-7y+6=0\)

You probably forgot to mention the options. After a little research, I was able to get the complete question with the mentioned options you should have mentioned. The potential complete question is:

Ellen plans to leave an 18 percent tip with her $23.75 lunch bill. Which of these expressions could she use to determine her total bill?

Check all that apply.

(1.18)(23.75) 23.75 – [(0.18)(23.75)] 23.75 + [(0.18)(23.75)] (0.18)(23.75)

Answer:

The expression \(23.75\:+\:\left[\left(0.18\right)\left(23.75\right)\right]\) will determine her total bill.

Step-by-step explanation:

Total lunch bill = $23.75

As he pans to 18% tip of the total bill, so the expression will be:

\(=23.75\:+\:\left(\:18\%\:\:of\:\:23.75\:\right)\)

\(=23.75\:+\:\left(\:\frac{18}{100}\:\times \:23.75\:\right)\)

\(=23.75\:+\:\left(\:0.18\times \:23.75\:\right)\)

or

\(=23.75\:+\:\left[\left(0.18\right)\left(23.75\right)\right]\)

Therefore, the expression \(23.75\:+\:\left[\left(0.18\right)\left(23.75\right)\right]\) will determine her total bill.

Answer:

(1.18)(23.75)

23.75 + [(0.18)(23.75)]

Step-by-step explanation:

ur welcome

Answer:

$1,300

Step-by-step explanation:

commission on the first $10,000

= 4/100 * 10000

= $400

remaining amount

= $28,000 - $10,000

= $18,000

commission on remaining $18,000

= 5/100 * 18000

= $900

total commission

= $400 + $900

= $1,300

It seems like you're looking for guidance on choosing a topic and collecting data for a statistics project. Here are some steps you can follow:

1. Choose a Topic: Consider your interests and areas that you find intriguing. As mentioned, sports, real estate, and crime statistics are popular choices. Think about specific aspects within these domains that you would like to explore further.

2. Refine Your Research Question: Once you have chosen a general topic, narrow down your focus by formulating a specific research question. For example, if you're interested in sports, you could investigate the relationship between player performance and team success.

3. Determine Data Collection Method: Decide how you will gather data to answer your research question. Depending on your topic, you can collect data through surveys, observations, controlled experiments, or by analyzing existing datasets available from reputable sources. Ensure that the data you collect aligns with the statistical tools and techniques covered in your course.

4. Collect Data: Implement your chosen data collection method. Ensure that your data collection process is reliable, consistent, and representative of the population or phenomenon you are studying. Maintain proper documentation of your data sources and collection procedures.

5. Organize and Clean Data: Once you have collected your data, organize it in a structured manner, and ensure it is free from errors and inconsistencies. This step is crucial to ensure the accuracy of your analysis.

6. Analyze Data: Apply appropriate statistical techniques to analyze your data and answer your research question. This may involve calculating descriptive statistics, performing hypothesis tests, or conducting regression analyses, depending on the nature of your data and research question.

7. Draw Conclusions: Interpret your results and draw meaningful conclusions based on your data analysis. Discuss any patterns, trends, or relationships that you have observed. Consider the limitations of your study and any potential sources of bias.

8. Communicate Your Findings: Present your findings in a clear and concise manner, using appropriate visualizations such as graphs, mean, charts, or tables. Prepare a report or presentation that effectively communicates your research question, methodology, results, and conclusions.

Remember to consult with your instructor to ensure that your chosen topic and data collection method align with the requirements of your course. They can provide guidance and offer suggestions to help you successfully complete your statistics project.

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The height of the office building casting a shadow of 107ft is approximately 124.83 ft.

A ratio is simply the relation between two amounts showing how many times a value is contained within another value.

Given the data in the question;

Ratio of height of office building and its height = x / 107

Ratio of height of post and its height = 7 / 6

Equate the two to get the height of the office building.

x / 107 = 7 / 6

Solve for x

x × 6 = 7 × 107

6x = 749

x = 746 / 6

x = 124.83 ft

Therefore, the height of the building is 124.83 ft.

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