Question is in the picture:

Answer:

140 degrees

Step-by-step explanation:

Let's say the angle right next to P is called a and the angle right next to S, not including y, is b. Next, the angle inside the quadrilateral but part of x is c and the angle inside the quadrilateral but part of the triangle is called d, as shown in the picture.

We are mainly interested in c, d, and y.

For quadrilateral QPTS:

- It is a quadrilateral, so all angles add up to 360 degrees

- Every vertex is on the circle's circumference, so it forms a cyclic quadrilateral, where opposite angles add up to 180 degrees

Given these, we can say that:

a + b + c + 130 = 360

a + b = 180

130 + c = 180

We are looking for c, so subtract 130 from both sides

c = 50

Triangle QRS:

- is a triangle, so the angles add up to 180 degrees

d + y + 90 = 180

subtract 90 from both sides to isolate d/y

d + y = 90

We know that c = 50, and d+c=x, so we can add c to both sides to get

d + c + y = 90 + 50 = 140

x + y = 140

Answer:

Step-by-step explanation:

Given:

The equation is y = 2x.

The objective is to find which of the table values match the with a given graphs.

The general equation of straight line is,

Here, m represents the slope and b represents the y intercept.

Consider the graph A and find the slope of the equation.

Take two coordinates from the graph as,

The formula to find the slope of the equation is,

Fro mthe graph A, the value of y intercept is 0.

Substitute the obtained values in the equation of straight line.

Thus, the given equation, coordinates of the table A matches with the graph A.

Hence, option (D) is the correct ant

Answer:

31 yards

Step-by-step explanation:

25 yard + 6 yards = 31 yards

Based on the given information, counting 140 blinks in one hour would be considered a reasonable number as it falls within one standard deviation of the average blink rate.

The study conducted on 50 men found that the average number of times they blinked in one hour was 150, with a standard deviation of 25. A standard deviation is a measure of how spread out the data is from the mean. In this case, the standard deviation of 25 indicates that most of the men fell within one standard deviation above or below the average.

To determine if 140 blinks in one hour is a reasonable number, we can use the concept of standard deviation. Since one standard deviation from the mean is 25, a reasonable range would be from 150 - 25 = 125 to 150 + 25 = 175 blinks. As 140 falls within this range, it can be considered a reasonable number.

It's important to note that this analysis assumes a normal distribution of blink rates among men and that the sample size of 50 is representative of the population. If these assumptions hold, counting 140 blinks in one hour would be considered within the expected range.

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Answer:Solve for x 2x-4=10 2x − 4 = 10 2 x - 4 = 10 Move all terms not containing x x to the right side of the equation. Tap for more steps... 2x = 14 2 x = 14 Divide each term in

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Do 300,000/3 and count 0 to find answer

The correct answer is

H₀ : μh - μc = 0

H₀ : μh - μc ≠ 0

Given that,

Regarding the subsequent 3 inquiries: A study collected information on how much time 28 randomly chosen high school students and 31 randomly chosen college students spent each day on their cellphones. The researcher is interested in learning whether there is proof that students use their phones for varying amounts of time in high school and college.

Because the samples of college and high school students are independent, the independent samples t-test should be utilized.

The study's research (Claim) aims to ascertain whether students' cell phone usage patterns alter between high school and college.

For the independent samples t-test and the stated claim, the proper null and alternate hypotheses are,

H₀ : μh - μc = 0

H₀ : μh - μc ≠ 0

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The proper null and alternative hypotheses are

\(H_{0}\) : μh = μc

\(H_{A}\) : μh - μc

The study's research wants to ascertain whether difference between the time spent by high school students and college students.

The actual test begins by considering two hypothesis i.e. null hypothesis and alternative hypothesis.

Let, H= time spent on the phone by high school students;

C= Time spent on the phone by college students; and

d=H−C

For the independent samples t-test and the stated claim, the proper null and alternate hypotheses are,

\(H_{0} :\) μh = μc  (time spent by high school students is equal to college students)

\(H_{A} :\) μh - μc  (difference between the time spent by high school students and college students)

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Answer:

Molecules in both the metal and the surrounding air will start moving at lower speeds?

Step-by-step explanation:

I'm not sure this is the right answer, because i thought that the air and the metal would be in equilibrium.

So sorry if this is wrong, chemistry isn't my strongest subject.

Answer:

The air molecules that are surrounding the metal will speed up, and the molecules in the metal will slow down.

Step-by-step explanation:

We have determined that the mean of the discrete random variable x is 2, and the variance is 5. This was achieved by solving the equations representing the mean and variance using the probabilities p(x) and the given expected values.

The mean of a discrete random variable x is given by the formula:

\(E(X) = \mu = \sum{x \cdot p(x)}.\)

Both E(X) and \(\mu\) represent the mean of the variable.

The probability p(x) represents the likelihood of x taking the value x. In this case, the expected value for E(X) is 2, so we can express it as:

\(2 = \sum{x \cdot p(x)}\) (1)

Similarly, the variance is defined as:

\(\Var(X) = E(X^2) - [E(X)]^2\).

Here, \(E(X^{2})\) represents the expected value of\(X^{2}\), and E(X) represents the mean of X.

The given expected value for \(E(X^{2})\) is 9, so we can write:

\(9 = \sum{x^2 \cdot p(x)}\)(2)

Now, we have two equations (1) and (2) with two unknowns, p(x and x, which we can solve.

Let's start with equation (1):

\(2 = \sum{x \cdot p(x)}\)

\(= 1 \cdot p_1 + 2 \cdot p_2 + 3 \cdot p_3 + \dots + 6 \cdot p_6\)

\(= p_1 + 2p_2 + 3p_3 + \dots + 6p_6 (3)\)

Next, let's consider equation (2):

\(9 = \sum{x^2 \cdot p(x)}\)

\(= 1^2 \cdot p_1 + 2^2 \cdot p_2 + 3^2 \cdot p_3 + \dots + 6^2 \cdot p_6\)

\(= p_1 + 4p_2 + 9p_3 + \dots + 36p_6\) (4)

We have equations (3) and (4) with two unknowns, p(x) and x.

We can solve them using simultaneous equations.

From equation (3), we have:

\(2 = p_1 + 2p_2 + 3p_3 + 4p_4 + 5p_5 + 6p_6\)

We can express \(p_1\) in terms of\(p_2\) as follows:

\(p_1 = 2 - 2p_2 - 3p_3 - 4p_4 - 5p_5 - 6p_6\)

Substituting this in equation (4), we get:

\(9 = (2 - 2p_2 - 3p_3 - 4p_4 - 5p_5 - 6p_6) + 4p_2 + 9p_3 + 16p_4 + 25p_5 + 36p_6\)

\(= 2 - 2p_2 + 6p_3 + 12p_4 + 20p_5 + 30p_6\)

\(= 7 - 2p_2 + 6p_3 + 12p_4 + 20p_5 + 30p_6\)

We can express \(p_2\) in terms of \(p_3\) as follows:

\(p_2 = \frac{7 - 6p_3 - 12p_4 - 20p_5 - 30p_6}{-2}\)

\(p_2 = -\frac{7}{2} + 3p_3 + 6p_4 + 10p_5 + 15p_6\)

Now, we substitute this value of \(p_2\)in equation (3) to get:

\(2 = p_1 + 2(-\frac{7}{2} + 3p_3 + 6p_4 + 10p_5 + 15p_6) + 3p_3 + 4p_4 + 5p_5 + 6p_6\)

\(= -7 + 8p_3 + 16p_4 + 27p_5 + 45p_6\)

Therefore, we obtain the values of the probabilities as follows:

\(p_3 = \frac{5}{18}$, $p_4 = \frac{1}{6}$, $p_5 = \frac{2}{9}$, $p_6 = \frac{1}{6}$, $p_2 = \frac{1}{9}$, and $p_1 = \frac{1}{18}.\)

Substituting these values into equation (3), we find:

\(2 = \frac{1}{18} + \frac{1}{9} + \frac{5}{18} + \frac{1}{6} + \frac{2}{9} + \frac{1}{6}\)

2 = 2

Thus, the mean of the discrete random variable x is indeed 2.

In the next step, let's calculate the variance of the discrete random variable x. Substituting the values of p(x) in the variance formula, we have:

\(\Var(X) = E(X^{2}) - [E(X)]^{2}\)

\(= 9 - 2^{2}\)

= 5

Therefore, the variance of the discrete random variable x is 5.

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The first runner covers 30 yards in 4 seconds, a speed of 5 yards per second. The second runner covers a distance of 20 yards in 4 seconds but starts 10 yards ahead. Both runners have a speed of 5 yards per second.

The first runner maintains a constant speed of 5 yards per second and covers a distance of 30 yards in 4 seconds. The second runner also has a speed of 5 yards per second but starts 10 yards ahead. Therefore, the second runner covers a shorter distance of 20 yards in the same 4 seconds.

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Answer:

1. A

2. C

Step-by-step explanation:

If they are corresponding, so their angle measures are the same. Hope this helps. :)

Answer:

1) 1 and 6

2) 110. these are corresponding angles so they are congruent

Step-by-step explanation:

Answer:

1)

\( \frac{19}{12} \: or \: 1\frac{7}{12} \)

2)

\( \frac{5}{21} \)

Answer:

Step-by-step explanation:

The graph answer is in the image below

Answer:

33.9

Step-by-step explanation:

What function uses the OPPOSITE and the ADJACENT?

tanR=  

adjacent /opposite

​  

=  

70/ 47

tanR=  

70 /47

R=tan  

−1

(  70 /47  )

​  

​

Answer:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x/4-(28/1)=0

Step by step solution :

STEP

1

:

28

Simplify ——

1

Equation at the end of step

1

:

x

— - 28 = 0

4

STEP

2

:

x

Simplify —

4

Equation at the end of step

2

:

x

— - 28 = 0

4

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 4 as the denominator :

28 28 • 4

28 = —— = ——————

1 4

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x - (28 • 4) x - 112

———————————— = ———————

4 4

Equation at the end of step

3

:

x - 112

——————— = 0

4

STEP

4

:

When a fraction equals zero

4.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

x-112

————— • 4 = 0 • 4

4

Now, on the left hand side, the 4 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

x-112 = 0

Solving a Single Variable Equation:

4.2 Solve : x-112 = 0

Add 112 to both sides of the equation :

x = 112

One solution was found :

x = 112

Step-by-step explanation:

make me as brain liest

Answer:

25,36,49,64,81,100

................................

Answer:

Your answer is 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Step-by-step explanation:

1 - 4  

+ 3

4 - 9

+ 5

9 - 16

+ 7

+9, +11, +13, +15, +17, +19...

Answer:

Step-by-step explanation:

t is the number of hours

12.24+0.11t = 12.74-0.15t

0.11t + 0.15t = 12.74 - 12.24

0.26t = 0.5

t= 0.5/0.26

t= 1.92 hours

approx to 2 hours

Value at Risk (VaR) is a popular measure of financial risk that quantifies the maximum potential loss a portfolio could incur over a specified time period with a given level of confidence. VaR is based on statistical modeling that considers historical returns and market volatility to estimate the worst-case scenario loss that could occur under normal market conditions.

However, VaR has several shortcomings. Firstly, VaR assumes that asset returns are normally distributed, which is not always the case. Secondly, VaR does not account for extreme events or tail risks that could result in catastrophic losses. Thirdly, VaR is a static measure and does not adjust to changes in market conditions.

To overcome these limitations, other risk measures have been developed, such as Expected Shortfall (ES) or Conditional Value at Risk (CVaR). These measures take into account the potential losses beyond the VaR threshold and the distribution of returns in the tail region. ES measures the expected loss in the tail region, while CVaR calculates the average loss in the worst-case scenarios.

In conclusion, while VaR is a popular risk measure, it has limitations that can lead to inaccurate risk assessments. Other risk measures, such as ES and CVaR, provide a more comprehensive and realistic assessment of financial risk, particularly in extreme market conditions.

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The optimal solution for this LP model is x = 2 and y = 2, with a maximum objective function value of 10

To graph the constraints, we can rewrite each inequality in slope-intercept form:

2x + 2y < 8

y < -x + 4

3x + 2y < 12

y < -1.5x + 6

x + 0.5y < 3

y < -2x + 6

Now we can plot these three lines on a coordinate plane and shade the regions that satisfy each inequality. The feasible region is the region that satisfies all three inequalities.

To find the optimal solution, we need to evaluate the objective function at each corner point of the feasible region and choose the point that maximizes the objective function.

The corner points of the feasible region are (0,0), (0,3), (1.5,3), and (2,2).

Objective function at (0,0): 3(0) + 2(0) = 0

Objective function at (0,3): 3(0) + 2(3) = 6

Objective function at (1.5,3): 3(1.5) + 2(3) = 9

Objective function at (2,2): 3(2) + 2(2) = 10

Therefore, the optimal solution is at (2,2), which gives a maximum value of 3(2) + 2(2) = 10.

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The inverse of the statement is "If a number does not have exactly two distinct factors, then the number is not prime." Thus Option 2 is the answer.

   When a conditional statement is reversed, the hypothesis and conclusion are both negated. The hypothesis in the original statement is "a number with exactly two distinct factors," while the conclusion is "is prime."

  To make the inverse, we negate both sections. "A number does not have exactly two distinct factors" is the antonym of "A number that has exactly two distinct factors." "Is not prime" is the opposite of "is prime."

    As a result, the inverse statement is "If a number does not have exactly two distinct factors, then the number is not prime."

     It's crucial to remember that a statement's inverse could or might not be accurate. In this instance, the inverse is true since the definition of a prime number is incompatible with the fact that a number has more than two components if it has more than exactly two different factors.

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Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Based on the information provided, it is difficult to determine whether this school's giving rate should be greater than or less than 8%.

The factors mentioned, such as the graduation rate, student-to-faculty ratio, class sizes, and freshman retention rate, provide some insight into the school's characteristics but do not directly indicate the giving rate. The giving rate refers to the percentage of alumni or donors who contribute financially to the school.

To assess whether the giving rate should be greater than or less than 8%, additional information related to the school's fundraising efforts, alumni engagement, and past giving patterns would be necessary. Factors such as alumni participation rates, donation campaigns, and fundraising initiatives play a significant role in determining the giving rate.

Therefore, without specific data on the school's fundraising efforts and historical giving patterns, it is not possible to conclusively determine whether the giving rate should be greater than or less than 8%. Further analysis and information are needed to make an accurate assessment.

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After  solving the equation 5(X - C)  = D , for the given matrices , we get , the unknown matrix X is = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\) .

In the question ,

it is given that , the matrices are

A = \(\left[\begin{array}{ccc}7&3\\4&3\end{array}\right]\)   B = \(\left[\begin{array}{ccc}7&2\\7&2\end{array}\right]\)   C = \(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\)   and D = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) .

and the equation is given as 5(X - C)  = D ,

and we have to find the value of unknown matrix X .

let the matrix X be = \(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\)

Substituting , the given matrices A , B , C and D in the equation 5(X - C)  = D ,

we get ,

5(X - C)  = D ,

5X - 5C = D ,

5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) - 5\(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\) = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\)

5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) - \(\left[\begin{array}{ccc}15&15\\20&0\\0&40\end{array}\right]\)

Simplifying further ,

we get ,

5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}25&45\\50&30\\30&40\end{array}\right]\)

Dividing both sides by 5 ,

we get ,

X = \(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\)

Therefore , the matrix X is = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\) .

The given question is incomplete , the complete question is

Solve the matrix equation for the unknown matrix X.

A = \(\left[\begin{array}{ccc}7&3\\4&3\end{array}\right]\)   B = \(\left[\begin{array}{ccc}7&2\\7&2\end{array}\right]\)   C = \(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\)   and D = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) . the equation is

5(X - C)  = D .

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Step-by-step explanation:

1.) Combine multiplied terms into a single fraction

−1/2

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

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

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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Therefore, the cost of white washing the walls will be Rs 5 × 588.72 = Rs 2943.60.

The total surface area of the four walls can be calculated by multiplying the perimeter of the room (2 × (length + width)) by the height of the room. In this case, the total surface area of the four walls is 2 × (16 + 14) × 10 = 600 square meters.

Next, we need to subtract the areas of the windows and doors from the total surface area of the walls. There are four windows with dimensions of 1.3 meters in height and 1.4 meters in width, so the total area of the windows is 4 × (1.3 × 1.4) = 7.28 square meters. There are also two doors with dimensions of 2 meters in height and 1 meter in width, so the total area of the doors is 2 × (2 × 1) = 4 square meters.

Subtracting the areas of the windows and doors from the total surface area of the walls, we get 600 square meters - (7.28 square meters + 4 square meters) = 588.72 square meters.

Finally, we can calculate the cost of white washing the walls by multiplying the rate per square meter (Rs 5) by the total surface area of the walls (588.72 square meters). Therefore, the cost of white washing the walls will be Rs 5 × 588.72 = Rs 2943.60.

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a. The probability that the fifth draw gives the first white ball is 0.01.

b. The probability that 2 of the 5 drawn balls are white is 0.3456.

c. The probability that it takes more than 5 draws to get a white ball is 0.32768.

a. The probability that the first white ball is drawn on the fifth draw can be calculated using the geometric distribution. Let W denote the event that a white ball is drawn and R denote the event that a red ball is drawn. The probability of getting a white ball on the first draw is 6/10, and the probability of getting a red ball is 4/10. Since the balls are replaced after each draw, the probability of getting a white ball on the fifth draw is

P(W on the 5th draw) = P(R, R, R, R, W) = (4/10)^4 × (6/10) = 0.01

b. To calculate the probability that 2 of the 5 drawn balls are white, we can use the binomial distribution. Let X denote the number of white balls drawn out of 5. Then, the probability of drawing 2 white balls out of 5 is:

P(X = 2) = (5 choose 2) × (6/10)^2 × (4/10)^3 = 0.3456

c. The probability that it takes more than 5 draws to get a white ball is the complement of the probability that a white ball is drawn within the first 5 draws. This can also be calculated using the geometric distribution

P(more than 5 draws to get a white ball) = 1 - P(W on or before 5th draw)

= 1 - P(R, R, R, R, W) - P(R, R, R, W) - P(R, R, W) - P(R, W) - P(W)

= 1 - (4/10)^4×(6/10) - (4/10)^3×(6/10) - (4/10)^2×(6/10) - (4/10)×(6/10) - (6/10)

= 0.32768

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Answer:

A

Step-by-step explanation:

When you distribute values, 'a' while be multiplied by everything. since there is a plus sign in front of the 'b' then that will not be distributed. so an 'ab' will add the an 'ac' but an 'ad' is still going to subtract away from the equation.