2. In a class of 45 students, 15 are in the Math Club and 10 are in the Art Club. If a student is selected at random, what is the probability that the selected student is:
a) in the Math club? _____
b) in the Art club? _____​

The amount of the payment is $2,705.88.

The payment amount is rounded to the nearest penny, and it is specified to use dollar signs and commas where needed. The total payment is $2,705.88, which indicates the monetary value of the transaction. The precision of the payment amount is provided, ensuring that it is accurate up to the nearest penny. The formatting guidelines for using dollar signs and commas are followed, adding clarity to the monetary value presented.

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The probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur, is 3/5.

The symbol "∩" represents the intersection of two events.

For example, "a ∩ d" means the event where both "a" and "d" occur together.

The symbol "~" means "not" or "complement." So, "~ (a ∩ d)" means the event where "a ∩ d" does NOT occur, or in other words, where "a" OR "d" does not occur.

Now, onto the question.

We are given that p(a ∩ d) = 2/5, which means that the probability of both events "a" and "d" occurring together is 2/5.

We want to find the probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur.

To find this probability, we need to use some basic probability rules.

One of these rules is that the probability of an event happening (let's call it "E") is equal to 1 minus the probability of the complement of that event not happening (~E).

In other words, p(E) = 1 - p(~E).

So, if we apply this rule to the event "~ (a ∩ d)", we get:
p(~ (a ∩ d)) = 1 - p(a ∩ d)

Now we can substitute in the value we were given for p(a ∩ d):
p(~ (a ∩ d)) = 1 - 2/5

Simplifying this gives:
p(~ (a ∩ d)) = 3/5

Therefore, the probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur, is 3/5.

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The student's height is 145cm and the average water depth in the pond is 110cm. Since the student is taller than the average water depth, they would not be at significant risk in the pond, as the water level would likely be below their head. However, it's always important to exercise caution and follow safety guidelines when around water, regardless of depth.

It is difficult to determine if the student is at risk in the pond. Height alone does not necessarily indicate swimming ability or water safety knowledge. However, if the student is not a strong swimmer or lacks knowledge of water safety, they may be at risk in any body of water, including one with an average depth of 110cm. It is important for all individuals to take precautions when swimming, such as wearing a life jacket and staying within their comfort and skill level in the water.

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To determine if the student has a risk in the pond based on their height, we need to consider the relationship between the student's height and the water depth.

In this scenario, the student's height is 145 cm, while the average water depth in the pond is 110 cm.

If the water depth is lower than the student's height, it means that the student's head will remain above the water surface, and there is no immediate risk of drowning due to water submersion. In this case, the student's height of 145 cm is greater than the water depth of 110 cm, indicating that the student's head would be above the water, and they would not face an immediate risk in terms of being submerged.

However, it is important to note that other factors could pose a risk in a pond or any body of water, such as the presence of strong currents, slippery surfaces, or the individual's swimming ability. It is crucial to consider these additional factors and exercise caution when in or near bodies of water, regardless of height.

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Answer:

0?

Step-by-step explanation:

the line is fully horizontal meaning there isn't a slope

A total of 549 of people at the convention are bored by the cable news

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

Not bored = 122

Bored = 9/11 of the people

This means that

Not bored = 1 - Bored

So, we have

Not bored = 1 - 9/11

Evaluate

Not bored = 2/11

Recall that Not bored = 122

So, we have

2/11 * x = 122

Where x = the number of people

This gives

x = 122 * 11/2

Evaluate

x = 671

Recall that

Bored = 9/11 of the people

So, we have

Bored = 9/11 * 671

Evaluate

Bored = 549

Hence, the number of people at the convention that are bored is 549

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Answer: 7/8 hours

Step-by-step explanation:

Answer:

153.86 mm²

Step-by-step explanation:

Radius of circle = diameter/2 = 14/2 = 7mm

Area of circle = πr² = (3.14)(7mm)²

= 3.14 x 49 mm²

= 153.86 mm²

I do not know that that is hard

Answer: Why does this guy need so much soda? And my brain isn't working for math right now. Sorry sweetheart.

Step-by-step explanation: Have a nice day!

The set A defined as a multiple of 3 that are less than 20 is given as:

A = {3,6,9,12,15,18}

A set is a collection of elements in a defined order

The universal set U which contains natural number of at most 25 is given as

U = {1,2,3,4,5,6,7,8,9,10,...,25}

The set A defined as a multiple of 3 that are less than 20 is given as

A = {3,6,9,12,15,18}

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Answer:

11

Step-by-step explanation:

Answer:

f(-2) = 11

Step-by-step explanation:

Given the function, f(x) = -3x + 5:

We can evaluate f(-2) by substituting -2 as the input (or x-value) for the function:

f(-2) = -3x + 5

f(-2) = -3(-2) + 5

f(-2) = 6 + 5

f(-2) = 11

Therefore, f(-2) = 11.

<Mop=<Qon

<moq=<pon

are vertically opposite angle..

Answer:

17,200

Step-by-step explanation:

Answer:

17200

Step-by-step explanation:

10^4=10000

so you do 1.72×10000=17200

Answer:

y = 3x + 4

Step-by-step explanation:

slope is 9/3 simplified to 3

y intercept is 4

The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

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Answer: \(6+2log_{2} 6\)

Step-by-step explanation:

\(S=s_{1} +s_{2} +s_{3} = 2(h_{1} +h_{2} +h_{3} )\)

\(h_{1} = log_{2}2=1\)

\(h_{2} = log_{2}4=2\)

\(h_{3} = log_{2}6\)

\(S = 2(1+2+log_{2}6) = 6+2log_{2}6\)

Answer:

-5x=-50

x=-10

Step-by-step explanation:

the probability that a tomato grown in the special soil will be a winner is approximately 0.0228 or 2.28%.

To find the probability that a tomato grown in the special soil will be a winner, we need to determine the probability that its diameter is greater than 4 inches.

Let's denote the mean diameter as μ and the standard deviation as σ.

Given:

Mean diameter (μ) = 3.2 in.

Standard deviation (σ) = 0.4 in.

To calculate the probability, we need to standardize the value 4 inches using the standard normal distribution.

The standardized value (z-score) can be calculated using the formula:

z = (x - μ) / σ

Substituting the values into the formula:

z = (4 - 3.2) / 0.4

z = 0.8 / 0.4

z = 2

Now, we need to find the probability of a z-score greater than 2. This can be determined using a standard normal distribution table or a calculator.

Looking up the z-score of 2 in a standard normal distribution table, we find that the probability associated with it is approximately 0.9772.

However, since we are interested in the probability of the tomato's diameter being greater than 4 inches, which corresponds to the right tail of the distribution, we subtract this probability from 1 to obtain the desired probability:

P(diameter > 4) = 1 - 0.9772 ≈ 0.0228

Therefore, the probability that a tomato grown in the special soil will be a winner is approximately 0.0228 or 2.28%.

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99% Confidence Interval for the Population Percentage of Defective Disks = (0.1004, 0.1196).

Rules for Decimals. Align up the decimal points. To ensure that every one of the values have the same number of places following the decimal, add 0s. Add the same way you would with complete numbers.

Step 1:

Sample Size: n=7002

Number of non-defective disks =6232

Number of defective disks: x = 7002-6232=770

Sample proportion \(\widehat{p}\) = x/n = 770/ 7002 = 0.110

Estimated proportion of disks which are defective: Sample proportion: \(\widehat{p}\) = 0.110

Step 2:

Range of confidence for the population proportion:

\(=\widehat{p}\pm z_{\alpha /2}\sqrt{(\widehat{p}(1-\widehat{p}))/n}\)

\(\alpha = (100-99)/100 = 0.01; \alpha/2 = 0.005\)

99% Confidence interval =

\(=\widehat{p}\pm z_{0.005}\sqrt{(\widehat{p}(1-\widehat{p}))/n}\)

from standard normal tables z0.005 = 2.58

99% Confidence Level for the Population Percentage of Defective Disks =

\(=\widehat{p}\pm z_{0.005}\sqrt{(\widehat{p}(1-\widehat{p}))/n}\)

\(=0.11\pm 2.58\sqrt{(0.11(1-0.11))/7002}\)

\(=0.11\pm 2.58\sqrt{(0.110\times 0.89)/7002}=0.11\pm 2.58\sqrt{\frac{0.0979}{7002}}\)

\(=0.11\pm 2.58\times 0.0037 = 0.11\pm 0.0096 =(0.1004, 0.1196)\)

99% Confidence interval for population proportion of disks which are defective= (0.1004, 0.1196).

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The constants A, B, C, and D are determined by satisfying the boundary conditions, we find the solution to the given IVP y" - y = ex, with initial conditions y(0) = 1 and y'(0) = 1.

To solve the given initial value problem (IVP) using Green's function, we follow the steps below:

Step 1: Find the Green's function.

The Green's function G(x, ξ) satisfies the homogeneous differential equation y" - y = δ(x - ξ), where δ(x - ξ) is the Dirac delta function. In this case, the homogeneous equation is y" - y = 0.

The general solution to the homogeneous equation is y_h(x) = c1e^x + c2e^(-x), where c1 and c2 are constants.

To find the Green's function, we need to consider two cases: x < ξ and x > ξ. We denote the Green's function as G_1(x, ξ) for x < ξ and G_2(x, ξ) for x > ξ.

For x < ξ:

In this case, the Green's function satisfies the equation G_1" - G_1 = 0. The general solution is G_1(x, ξ) = Ae^x + Be^(-x), where A and B are constants.

For x > ξ:

In this case, the Green's function satisfies the equation G_2" - G_2 = 0. The general solution is G_2(x, ξ) = Ce^x + De^(-x), where C and D are constants.

Step 2: Apply the boundary conditions to find the constants.

We are given the boundary conditions y(0) = 1 and y'(0) = 1. Substituting these values into the Green's function expression and its derivative, we can set up a system of equations to solve for the constants.

For x < ξ:

Using the boundary conditions, we have:

G_1(0, ξ) = A + B = 1,

G_1'(0, ξ) = A - B = 1.

Solving these equations, we get A = 1 and B = 0.

For x > ξ:

Using the boundary conditions, we have:

G_2(0, ξ) = C + D = 1,

G_2'(0, ξ) = C - D = 1.

Solving these equations, we get C = D = 1/2.

Step 3: Combine the Green's functions and the solution.

The solution to the IVP is given by the convolution of the Green's functions with the forcing term ex. We obtain the following expression for the solution:

y(x) = ∫[G_1(x, ξ)ex] dξ + ∫[G_2(x, ξ)ex] dξ.

Using the values of the Green's functions we found earlier, we can evaluate the integrals and simplify the expression for the solution.

In summary, by applying Green's function method, we find the solution to the given IVP y" - y = ex, with initial conditions y(0) = 1 and y'(0) = 1.

The solution is given by the convolution of the Green's functions G_1(x, ξ) and G_2(x, ξ) with the forcing term ex. The constants A, B, C, and D are determined by satisfying the boundary conditions.

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Answer:

Point D

8 3/5 = 40+3= 43

43÷5 = 8,6

........

Answer:

y=-4x-24

Step-by-step explanation:

The equation of a line is always in the form y=mx+c. By subbing in the values given by the two points, we get:

0=-6m+c

-24=c

∴0=-6m-24

6m=-24

m=-4

∴the equation is: y=-4x-24

Answer:20

Step-by-step explanation:

If 9 x 2=18 then 10 x 2=20 should be the answer.

Evaluating the algebraic expression 8ab2bc gives 48

Information made available in the question include

8ab2bc

a = 3,

b=1/2 ,  

c = 4

The expression given is an algebra that consist of 4 terms

Evaluating the expression

8 * a * b * 2 * b * c

substituting the terms a, b, and c

= 8 * 3 * 1/2 * 2 * 1/2 * 4

= 8 * 3 * ( 1/2 * 2 ) * ( 1/2 * 4 )

= 8 * 3 * ( 1 ) * ( 2 )

= 8 * 3 * 2

= 8 * 6

= 48

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Answer:

(- 4, - 12 ) , (4, 12 )

Step-by-step explanation:

Given the 2 equations

y = 3x → (1)

y = x² + 3x - 16 → (2)

Substitute y = x² + 3x - 16 into (1)

x² + 3x - 16 = 3x ( subtract 3x from both sides )

x² - 16 = 0 ( add 16 to both sides )

x² = 16 ( take the square root of both sides )

x = ± \(\sqrt{16}\) = ± 4

Substitute these values into (1) for corresponding values of y

x = - 4 : y = 3 × - 4 = - 12 ⇒ (- 4, - 12 )

x = 4 : y = 3 × 4 = 12 ⇒ (4, 12 )

The  equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)

The given diagram shows two intersecting lines tangential to a circle at points A and C.

Using the theorem that states, the measure of the angle at the vertex is equal to the half of the difference of the measure of the intercepted arcs.

Mathematically;

<B = 1/2(arcADC - arcAC)

58 = 1/2(238 -x)

Hence the  equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)

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we know that

If y varies inversely as the square of x,

then

the equation that represent this situation is equal to

we have

y=9 when x=12

Find the value of the constant of proportionality k

substitute the value of x and the value of y in the equation above

Find the value of y when the value of x=15

substitute in the equation

therefore

the answer is

y=5.76

Answer:

10,000

Step-by-step explanation:

100/0.01 is 10k

we have

6x+7y=4x+4y

we figure out that

the solution is ----> (x,-4)

substitute the value of y=-4 in the equation

6x+7*(-4)=4x+4*(-4)

6x-28=4x-16

Combine like terms

6x-4x=28-16

2x=12

x=12/2

x=6

So the the missing value is x=6.