Please Help! A bag contains four green marbles and five yellow marbles. You randomly select three marbles. What is the probability that all three marbles are green when (a) you replace each marble before selecting the next marble, and (b) you do not replace each marble before selecting the next marble? Write each probability as a decimal rounded to the nearest thousandth. Then compare the probabilities.

The the value of the length AC =10.7 cm.

ABCD is a kite,  AC⊥DB and DE=EB

From the given triangle AED, length of BD is 10 cm , so lengh of DE will be 5 cm.

The three sides of a right triangle are connected by the geometry theorem known as the Pythagorean theorem. According to this rule, the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.

Now, using the pythagoras theorem and solving further for the ΔAED, we get,

AD^2=AE^2+DE^2

6^2=AE^2+5^2

36=AE^2+25

AE=3.3

Similarily, using the pythagoras theorem and solving further for the ΔCED

CD^2=CE^2+DE^2

9^2=CE^2+5^2

CE^2=81-25

CE=7.4cm

As from the figure,AC=AE+EC , so we can write as follows,

AC=3.3+7.4

AC=10.7cm

To learn more about Pythagoras' theorem​ refer the link:

https://brainly.com/question/26689586

#SPJ9

Explanation

The Hypotenuse leg theorem states that if the hypotenuse and leg of a triangle are congruent to the hypotenuse and leg of another rigth triangle then the two triangles are congruent

therefore, to prove the triangles are congruent we need to know that

also, the legs must be congruent, so

therefore, the answer is

I hope this helps you

Area of the pond is 86.625 m²

Given data :

Diameter of the pond = 14m

Radius of the inner circle (pond), r = 7 m

Width of the concrete path = 1.75m

Radius of outer circle (Including pond + Path), R = 7 + 1.75 = 8.75 m

Area of the path = Area of the outer circle − Area of the inner circle.

= πR² - πr²

= 22 / 7 x ( 8.75 + 7) ( 8.75 − 7 )

= 86.625 m²

Learn more about circle's area refer to :

https://brainly.com/question/14068861

#SPJ4

Answer:

338

Step-by-step explanation:

ok

The angle of Sonny's line of sight to both Sam and Sal, we can use the Law of Cosines. The angle of Sonny's line of sight to both Sam and Sal is approximately 77 degrees (rounded to the nearest degree).

Let's consider the triangle formed by Sam, Sonny, and Sal. Let's label the sides of the triangle:

The side opposite Sam as side a (distance between Sonny and Sal)

The side opposite Sonny as side b (distance between Sam and Sal)

The side opposite Sal as side c (distance between Sam and Sonny)

According to the Law of Cosines, we have the formula:

c^2 = a^2 + b^2 - 2ab * cos(C)

Where C is the angle opposite side c.

We want to find angle C, which is the angle of Sonny's line of sight to both Sam and Sal.

Plugging in the given distances:

c = 175 ft

a = 201 ft

b = 153 ft

Using the Law of Cosines:

175^2 = 201^2 + 153^2 - 2 * 201 * 153 * cos(C)

Simplifying and solving for cos(C):

cos(C) = (201^2 + 153^2 - 175^2) / (2 * 201 * 153)

cos(C) = 0.228

To find the angle C, we can take the inverse cosine (cos^-1) of 0.228:

C ≈ cos^-1(0.228) ≈ 77.08 degrees

Therefore, the angle of Sonny's line of sight to both Sam and Sal is approximately 77 degrees (rounded to the nearest degree).

Learn more about Cosines here

https://brainly.com/question/23720007

#SPJ11

Answer:

128.5 thousand dollars

Step-by-step explanation:

The number of DVDs the company can sell to maximize the profit is 85

What is differentiation?

In mathematics, differentiation is the process of determining the derivative, or rate of change, of a function. Differentiation is a technique for determining a function's derivative. Differentiation is a mathematical procedure that determines the instantaneous rate of change of a function based on one of its variables. The process of finding the derivative of dependent variable in an implicit function by differentiating each term separately

Given data ,

Let the profit P for producing n DVD copies be P ( n )

where P ( n ) = −0.02n² + 3.40n − 16

Now , to find the maximum number of DVDs to produce in order to maximize the profit is calculated by finding the derivative of P ( n ) with respect to n

And , dP (n) / dn = 0

So , the equation will be

P ( n ) = −0.02n² + 3.40n − 16

dP (n) / dn = -0.04n + 3.4

When dP (n) / dn = 0 , we can find the value for n

So ,

-0.04n + 3.4 = 0

Adding 0.04n on both sides , we get

0.04n = 3.4

Divide by 0.04 on both sides , we get

n = 85

Hence , The number of DVDs the company can sell to maximize the profit is 85

To learn more about differentiation click :

https://brainly.com/question/20319481

#SPJ2

The the type ii error is D: "There is insufficient evidence to conclude that the capacity of her car's gas tank is not 10 gallons when, in fact, it is 10 gallons."

Type II error occurs when the null hypothesis is not rejected even though it is false. In this case, the null hypothesis is that the capacity of Anna's car gas tank is 10 gallons, and the alternative hypothesis is that it is not 10 gallons. The correct answer indicates that there is insufficient evidence to reject the null hypothesis, which means that Anna believes the capacity of her car's gas tank is not 10 gallons, but in reality, it is 10 gallons. Therefore, the correct answer is option D.

You can learn more about type ii error  at

https://brainly.com/question/28166129

#SPJ11

The probability to answer 5 questions correctly from 14 true or false questions is 0.1222

The given situation represents a binomial experiment, where there are only two possible outcomes for each trial: success (answering correctly) and failure (answering incorrectly). To find the probability of a particular number of successes, we use the binomial probability formula:

P(x)= nCx × p^x × q^(n-x)

Where, n is the total number of trials, p is the probability of success on each trial, q is the probability of failure on each trial (1-p), and x is the number of successes desired.

n = 14 (total number of questions)

p = 1/2 (probability of answering correctly when guessing randomly), and q = 1/2 (probability of answering incorrectly when guessing randomly).

To find P(5), we substitute these values in the formula

P(5) = 14C5 * (1/2)^5 * (1/2)^9= 2002 * (1/32) * (1/512)= 2002 / 16384≈ 0.1222

Therefore, the answer is option D, 0.1222.

To learn more about Binomial experiment:https://brainly.com/question/9325204

#SPJ11

Answer:

It is true

Step-by-step explanation:

20/-7 is ~2.56

-2.8 (8 repeating) is -2.8......

So it is true

Hope this helps!

Answer:

True

Step-by-step explanation:

Answer:

y= -1x + 3

Step-by-step explanation:

Declan's reasoning does make sense. This is because 3/4 and 1/2 have the same denominator, and 3/4 is a larger fraction than 1/2.

Therefore, it is reasonable to assume that 3/4 is greater than 6/12 because 6/12 simplifies to 1/2. Simplifying fractions means dividing the numerator and denominator by the same number, in this case, 6 is divisible by 2, so we can reduce the fraction to 1/2.

So, Declan is correct in his reasoning that 3/4 is greater than 6/12. It is important to understand the relationship between fractions and their denominators to make such comparisons accurately.

3/4 = 9/12

1/2 = 6/12

6/12 = 6/12

Since 9/12 (which is equivalent to 3/4) is greater than 6/12 (which is equivalent to 1/2), we can say that 3/4 is indeed greater than 6/12.

Therefore, Declan's reasoning is correct.

Learn more about Fractions:

https://brainly.com/question/78672

#SPJ4

The zeros of the cubic equation f(x) = x³ - 3 · x² - 5 · x + 15 are 3, √5 and - √5, respectively.

Herein we find the definition of a cubic equation, in which we must determine all its zeros. According to fundamental theorem of algebra, cubic equation have three zeros, there are two possibilities:

A value of x is a zero of the cubic equation p(x), when p(x) = 0. An approach consists in evaluating the function at all values of each choice. If we know that r₁ = 3, r₂ = √5, r₃ = - √5, then the results of the function are, respectively:

r₁ = 3

f(3) = 3³ - 3 · 3² - 5 · 3 + 15

f(3) = 27 - 27 - 15 + 15

f(3) = 0

r₂ = √5

f(√5) = (√5)³ - 3 · (√5)² - 5 · (√5) + 15

f(√5) = √125 - 15 - √125 + 15

f(√5) = 0

r₃ = - √5

f(- √5) = (- √5)³ - 3 · (- √5)² - 5 · (- √5) + 15

f(- √5) = - √125 - 15 + √125 + 15

f(- √5) = 0

To learn more on zeros of polynomials: https://brainly.com/question/29445765

#SPJ1

a) 3 - 8 + 2i - (-5i) = -5 + 2i +5i = -5 + 7i

b) 4 - 20i - 2i + 10i² = 4 - 22i + 10(\(\sqrt{-1}\))² = 4 - 22i + 10(-1) = 4 - 10 -22i

= -6 -22i

c) Multiply both numerator and denominator by i

\(\frac{i(-2-4i)}{i^{2} }\) = \(\frac{-2i - 4i^{2} }{i^{2} }\) = \(\frac{-2i - 4(\sqrt{-1})^{2} }{(\sqrt{-1})^{2}}\) = \(\frac{-2i - 4(-1)}{-1}\) = \(\frac{-2i+4}{-1}\) = 2i - 4 = -4 + 2i

d) Multiply both numerator and denominator by (3+6i)

\(\frac{(3+6i)(-3+2i)}{(3+6i)(3-6i)}\) = \(\frac{-9+6i-18i+12i^{2} }{9-36i^{2} }\) = \(\frac{-9-12i+12(\sqrt{-1} )^{2} }{9-36(\sqrt{-1} )^{2} }\) = \(\frac{-9-12i+12(-1)}{9-36(-1)}\) = \(\frac{-9-12-12i}{9+36}\)

= \(\frac{-21-12i}{45}\) = \(-\frac{21}{45} - \frac{12}{45}i\)

The inequality that represents the cost c per 14 squares for a new carpet with a budget of $700 is: c ≤ 700/14 = 50 Therefore, the answer is:

The inequality is c ≤ 50.

Assuming that the price of the carpet is constant per square foot, we can write the following inequality to represent the cost c per 14 squares:

c/14 ≤ 700

This inequality states that the cost per 14 square feet (c/14) cannot exceed $700, which is the total amount of money available to purchase the carpet.

To write an inequality representing the cost of a new carpet per 14 square feet, we need to first define the cost per square foot. Let's say the cost per square foot is $x. Then, the cost of the carpet for 14 square feet would be 14x.

Since we have a budget of $700, we can write the inequality:

14x ≤ 700

This inequality represents that the cost of the carpet for 14 square feet should be less than or equal to $700. We can solve for x by dividing both sides by 14:

x ≤ 50

This means that the cost per square foot of the carpet should be less than or equal to $50 for it to fit within the budget of $700.

To learn more about inequality Click here:

brainly.com/question/30231190

#SPJ4

Answer: 36, 37, 38

Step-by-step explanation:

x + (x + 1) + (x - 1) = 111

x + x + 1 + x - 1 = 111

3x = 111

x = 37

Answer:

The test statistic is Z = 1.157

Step-by-step explanation:

Given that:

The sample size n = 1200

The sample proportion of those that will vote for the Republican candidate is represented by \(\hat p = \dfrac{x}{n}\)

\(\hat p = \dfrac{620}{1200}\)

\(\hat p =0.5167\)

The null and the alternative hypothesis can be computed as:

\(H_o: P=0.50 \\ \\ H_a :P>0.50\)

The formula for the one-sample Z-test for the population proportion can be expressed as:

\(Z = \dfrac{\hat p - P_o}{\sqrt{\dfrac{P_o(1-P_o)}{n}}}\)

\(Z = \dfrac{0.5167 - 0.5}{\sqrt{\dfrac{0.5(1-0.5)}{1200}}}\)

\(Z = \dfrac{0.0167}{\sqrt{\dfrac{0.5(0.5)}{1200}}}\)

\(Z = \dfrac{0.0167}{\sqrt{\dfrac{0.25}{1200}}}\)

\(Z = \dfrac{0.0167}{\sqrt{2.08333333\times10^{-4}}}\)

Z = 1.157

Testing the hypothesis, from the information given, it is found that the test statistic is z = 1.157.

The null hypothesis is:

\(H_0: p = 0.5\)

The alternative hypothesis is:

\(H_1: p > 0.5\)

The test statistic is given by:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

For this problem, the parameters are: \(p = 0.5, n = 1200, \overline{p} = \frac{620}{1200} = 0.5167\)

Hence, the value of the test statistic is:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.5167 - 0.5}{\sqrt{\frac{0.5(0.5)}{1200}}}\)

\(z = 1.157\)

The test statistic is z = 1.157.

A similar problem is given at https://brainly.com/question/24166849

Answer:

  (b)  Yes, they are congruent

Step-by-step explanation:

Given two triangles with a side length marked as 5 units, you want to know whether they are congruent. One triangle has marked angles 65° and 67° with the angle opposite the marked side being unmarked. The other triangle has angles marked 65° and 48°, with the latter being opposite the marked side.

In each case, the sum of angles is 180°, so the measure of the third angle is the value that makes that be the sum of all angles.

Triangle 1:

The third angle is 180° -65° -67° = 48°.

Triangle 2:

The third angle is 180° -65° -48° = 67°.

The measures of the angles in each triangle are 48°, 65°, and 67°. Since the angles are the same, the triangles are similar.

In each case, the marked side is opposite the smallest angle. This means we can claim congruence using either the ASA or AAS postulates.

Yes, they are congruent.

Answer: They have lost 9 games

Step-by-step explanation:

25 percent is 1/4 and do 36 divided by 4=9

By making the subintervals smaller, increasing the number of subintervals, and making the curve more linear, the error of a left Riemann sum can be decreased.

The error of a left Riemann sum is determined by the size of the subintervals, the shape of the curve, and the number of subintervals. If the subintervals are made smaller, the error will decrease because the left Riemann sum estimates the area under the curve below the left endpoints of the subintervals. In addition, if the number of subintervals is increased, the error will decrease because more slices of the curve will be taken into account. The shape of the curve also affects the error of the left Riemann sum. If the curve is more linear, the error will be lower because the left endpoint of each subinterval will be closer to the actual area below the curve. The formula for calculating the error of a left Riemann sum is:

Error = (b-a) × max[f(x)] - [f(a) + f(b) + 2f(c) + ... + 2f(n-1)]

Where a and b are the endpoints of the interval being considered, f(x) is the function being integrated, and c, d, e, and n are the intermediate points. By making the subintervals smaller, increasing the number of subintervals, and making the curve more linear, the error of a left Riemann sum can be decreased.

Learn more about left Riemann sum here:

https://brainly.com/question/30184175

#SPJ4

In order to determine the probability of a random selected student to be a men, we need to divide the number of men by the number of all the students in the class. We have:

The probability of a random student being a man is approximately 67%.

The speed of the cyclist in miles per hour is 16 miles per hour

The speed of an object is the rate of change of the object's distance over time

From the question, we have the following parameters that can be used in our computation:

A cyclist rides 8 miles in 30 minutes.

The parameters in the above statement can be further expressed as

Distance = 8 miles

Time = 30 minutes

This means that the distance is 8 miles and the time taken to cover the distance is 30 minutes

Convert the minutes to hour

So, we have

Time = 0.5 hour

The speed of the cyclist in miles per hour is then calculated as

speed = 8 miles/0.5 hour

Evaluate the quotient

speed = 16 miles/hour

Hence, the cyclist' speed is 16 miles/hour

Read more about speed at

https://brainly.com/question/14335655

#SPJ1

Answer:

D

\(r - p \leqslant 150\)

Now we add and subtract this value to the expression to create a perfect square: x² + 6x + 9 - 9 = (x + 3)² - 9S

implifying this expression, we get: (x + 3)² - 9

Therefore, the value that completes the square for x² + 6x is 9.

The value that completes the square for x² + 6x is 9. The process of completing the square involves finding a constant term that can be added to an expression in order to make it a perfect square. Here's how it works in this case:

We have the expression x² + 6x. First, we need to factor out any common factor from the x² and 6x terms:

x² + 6x = x(x + 6)

Now we take half the coefficient of the x-term (6) and square it:

(6/2)² = 9.

Now we add and subtract this value to the expression to create a perfect square: x² + 6x + 9 - 9 = (x + 3)² - 9S

implifying this expression, we get: (x + 3)² - 9Therefore, the value that completes the square for x² + 6x is 9.

To know more about common factor visit:

brainly.com/question/30961988

#SPJ11

Answer:

24

Step-by-step explanation:

140-20= 120

120 divided by 5= 24

To check do 24 times 5 and add the 20 from day 1.

The highest level of detailed information about social scientific findings can typically be found in academic journals. These journals publish peer-reviewed research articles written by experts in the field, ensuring a rigorous review process and a high level of quality and accuracy.

Academic journals provide detailed information about the methodology, data analysis, and results of social scientific studies. They often include statistical analyses, charts, and graphs to support the findings. Additionally, these journals may also provide in-depth discussions of the implications and limitations of the research, as well as suggestions for future studies.

Accessing academic journals can sometimes require a subscription or payment, but many universities, libraries, and research institutions provide access to these resources. Some journals also offer open access options, allowing anyone to read and download their articles free of charge.

It's important to note that when using information about social scientific findings from academic journals, it is crucial to properly cite and reference the original source to avoid plagiarism. Academic integrity is a fundamental principle in research and scholarly writing.

To know more about social scientific findings , visit :

https://brainly.com/question/32574546

#SPJ11

Answer:

1.4 people out of 10

Step-by-step explanation:

Just divide it by 10

Answer:

only 4 people

The confidence interval is defined as the range in which the true population parameter value is anticipated to lie with a certain level of confidence. When constructing a confidence interval for the population median using observed data, the following formula is used: Median = X[n+1/2]

Step by step answer

Given the sample size of n=10 and a 90% confidence interval:\(α = 0.10/2\)

= 0.05.

Using a standard normal distribution, the z-value can be obtained: \(z_α/2\)= 1.645.
Calculate the median from the sample data, \(X: X[n+1/2] = X[10+1/2]\)= \(X[5.5] = 1.61.\)
The sample size is even, so the median is the average of the middle two numbers.
Calculate the standard error as follows: \(SE = 1.2533 / sqrt(10)\)

= 0.3964.
Calculate the interval as follows:\((1.61 - 1.645 x 0.3964, 1.61 + 1.645 x 0.3964) = (1.23, 1.99).\)
Therefore, the 90% confidence interval is (1.23, 1.99).

To know more about median visit :

https://brainly.com/question/11237736

#SPJ11

2.) No correlation

3.) Negative correlation

Step-by-step explanation:

Answer: C

Step-by-step explanation: all other statements are true because of CPCTC theorem. Therefore, we can conclude that C is the correct answer

Answer:

C

Step-by-step explanation:

The present data set includes data from the years 2010-2012. The dimensions of the data frame are 624 rows and 8 columns. The variable or column names are "year", "month", "day", "date", "dow", "time", "size", and "price".

To find the years included in the data set, we can use the unique() function on the "year" column:

```R
unique(present$year)
```

This will return the unique values in the "year" column, which are 2010, 2011, and 2012.

To find the dimensions of the data frame, we can use the dim() function:

```R
dim(present)
```

This will return the number of rows and columns in the data frame, which are 624 and 8, respectively.

To find the variable or column names, we can use the names() function:

```R
names(present)
```

This will return the names of the columns in the data frame, which are "year", "month", "day", "date", "dow", "time", "size", and "price".

Learn more about dimensions

brainly.com/question/28688567

#SPJ11