Suppose a jar contains 12 red marbles and 21 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

Answer:

The  result of the verification is : The indicated function is an explicit solution of the given differential equation

Step-by-step explanation:

From the question we are told that

The  given differential equation is  9y' + y = 0

  The  indicate solution is \(y = e^{-\frac{x}{9} }\)

Generally \(y' =  -\frac{1}{9} e^{-\frac{x}{9} }\)

So

    \(9( -\frac{1}{9} e^{-\frac{x}{9} }) + e^{-\frac{x}{9} } =0\)

For the  indicated function to be explicit solution of the given differential equation then the RHS and LHS of the above equation must be that same

      \(- e^{-\frac{x}{9} } + e^{-\frac{x}{9} } =0\)

      \(0=0\)

Thus result of the verification is : The indicated function is an explicit solution of the given differential equation

The area of the Region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

To find the area of the region bounded by y = √x, y = 2-x², and y = -√2x, we need to graph the equations and determine the points of intersection. Then we can integrate to find the area.

Firstly, we'll graph the equations and find the points of intersection:

y = √xy = 2-x²y = -√2xGraph of y = √x, y = 2-x², and y = -√2xWe need to solve for the points of intersection, so we'll set the equations equal to each other and solve for x:√x = 2-x²√x + x² - 2 = 0Let's substitute u = x² + 1:√x + u - 3 = 0√x = 3 - u

(Note: Since we squared both sides, we have to check if the solution is valid.)u = -2x²u + x² + 1 = 0 (substituting back in for u

)Factoring gives us:u = (1, -2)We can then solve for x and y:x = ±1, y = 1y = 2 - 1 = 1, x = 0y = -√2x = -√2, x = 2y = 0, x = 0Graph of y = √x, y = 2-x², and y = -√2x with points of intersection to find the area, we need to integrate.

The area is bounded by the x-values -1 to 2, so we'll integrate with respect to x:$$\int_{-1}^0 (2 - x^2) - \sqrt{x} \ dx + \int_0^1 \sqrt{x} - \sqrt{2x} \ dx$$

We can then simplify and integrate:$$\left[\frac{2x^3}{3} - \frac{2x^{5/2}}{5/2} + \frac{4}{3}x^{3/2}\right]_{-1}^0 + \left[\frac{2x^{3/2}}{3} - \frac{4x^{3/2}}{3}\right]_0^1$$$$= \frac{4}{3} + \frac{4}{3} - \frac{4}{15} + \frac{4}{3} - \frac{4}{3}$$$$= \frac{32}{15}$$

Therefore, the area of the region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

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Answer:

m ≈ 3

Step-by-step explanation:

3.53631284916 x 10^3 ≈ 3 x 10^3

Answer: -8

Step-by-step explanation: So we after simplification we get

[(2/5) - (1/2) + (3/5)+ (7/2)] - [(3/5)/(1/4) - (1/5)]

After this I suppose it's just addition & subtraction, and can be easily done to get -8.

Answer:

B

Step-by-step explanation:

using the recursive rule \(a_{n}\) = 3\(a_{n-1}\) and a₁ = 10, then

a₁ = 10

a₂ = 3a₁ = 3 × 10 = 30

a₃ = 3a₂ = 3 × 30 = 90

the first 3 terms are 10 , 30 , 90

3.75 ft and 1.25 ft

Explanation

Step 1

Diagram

Step 2

set the equations

let x represents the longest piece

lety represents the smaller piece

so

a)A carpenter cuts a 5-ft board in two pieces, hence

b)One piece must be three times as long as the other,then

Step 3

finally, solve the equations:

a) replace the x value from equation (2) into equation(1)

b) now, replace the y value into equation (2) to find x

therefore, the lengths of the pieces are

3.75 ft and 1.25 ft

I hope this helps you

Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

Answer:

The correct answer is B.

Approximately 200 students received a test score between 70.5 and 80.

Answer:

Set your calculator to Degree mode.

55^2 = 90^2 + 50^2 - 2(90)(50)cos(C)

3,025 = 10,600 - 9,000cos(C)

-7,575 = -9,000cos(C)

cos(C) = 101/120

C = cos^-1 (101/120) = 32.7°

Answer:

A.

slippery slope

Step-by-step explanation:

Just did it

This sentence does not contain any kind of fallacious reasoning. It is simply a statement indicating that the speaker is about to provide some important information to avoid any misunderstandings or false rumors about them.

Arguments or statements that appear to be logically sound but are in fact defective or untrue are referred to as fallacious reasoning. It happens when an argument's justification is founded on false premises, scant evidence, or fallacious reasoning.

The given phrase is:

One more thing, which I should definitely mention because if I don't, they'll probably be saying the same thing about me.

There aren't any glaring instances of erroneous thinking in this sentence. Instead, it's a declaration made by the speaker in order to preemptively address any prospective criticism or rumors that might be circulated about them by others.

On the other hand, illogical or incorrect ideas or cognitive processes are referred to as fallacious reasoning.

A few typical examples include ad hominem attacks, where an individual's character or personal traits are attacked instead of their argument, slippery slope arguments, where a chain reaction of events is assumed to occur based on a single initial event, hasty generalizations, where a conclusion is drawn based on insufficient evidence and loaded language, where emotionally charged language is used to manipulate an audience's response.

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Hey there!

If you are solving for x, then your final solutions are \(x=\sqrt{-y},-\sqrt{-y}\).

Hope this helps!

Answer:

Its B

Step-by-step explanation:

Linear funtions need 1 x value for every y value so its B

The question requires us to use the sine rule to solve the problem.

The value of f(7) for y = f(x) is y = 7

Function is a term used to refer to expression with variables. the variables consists of independent variable and dependent variable

Given data

y = f(x)

f(7)

hence y = f(7)

y = 7

f(x) = 7

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The circled portion in the confidence interval formula p ± z represents the Margin of Error, which plays a crucial role in interpreting the range of plausible values for the population parameter.

In the confidence interval formula p ± z, the circled portion represents the Margin of Error.

The Margin of Error is a critical component of a confidence interval and quantifies the level of uncertainty in the estimate.

It indicates the range within which the true population parameter is likely to fall based on the sample data.

The Margin of Error is calculated by multiplying the critical value (z) by the standard deviation of the sampling distribution.

The critical value is determined based on the desired level of confidence, often denoted as (1 - α), where α is the significance level or the probability of making a Type I error.

The Margin of Error accounts for the variability in the sample and provides a measure of the precision of the estimate.

It reflects the trade-off between the desired level of confidence and the width of the interval.

A larger Margin of Error indicates a wider confidence interval, implying less precision and more uncertainty in the estimate.

Conversely, a smaller Margin of Error leads to a narrower confidence interval, indicating higher precision and greater certainty in the estimate.

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Just add the powers while it is multiply

-1+(-3)

= -1 - 3

= -4

So it is \(2^{-4}\)

Answer:

The percentage increase in \(T\) is 20 %.

Step-by-step explanation:

Let be \(T = \frac{k\cdot x}{y}\), whose initial parameters are \(k = k_{o}\), \(x = x_{o}\) and \(y = y_{o}\). If these three parameters are increased by 20 %, then initial and final values of \(T\) are, respectively:

Initial value

\(T_{i} = \frac{k_{o}\cdot x_{o}}{y_{o}}\) (1)

Final value

\(T_{ii} = \frac{(1.2\cdot k_{o})\cdot (1.2\cdot x_{o})}{1.2\cdot y_{o}}\)

\(T_{ii} = \frac{1.2\cdot k_{o}\cdot x_{o}}{y_{o}}\) (2)

(1) in (2):

\(T_{ii} = 1.2\cdot T_{i}\)

And the percentage increase in T is:

\(\%T = \frac{T_{ii}-T_{i}}{T_{i}}\times 100\,\%\) (3)

\(\%T = \frac{1.2\cdot T_{i}-T_{i}}{T_{i}}\times 100\,\%\)

\(\%T = 20\,\%\)

The percentage increase in \(T\) is 20 %.

Answer:

Step-by-step explanation:

Lets subsitute k, x and y as  100 to make it easier for us

So k = 100, x = 100, y = 100

Step 1 :-   T = kx/y

- T = 100 * 100 / 100 = 100

Step 2 :- Increase by 20% = 100 * 20% = 20,    100 + 20 = 120

Step 3 :- Percentage Increase = Increased value OVER original calue          MULTIPLIED by 100%

SO = ( 120 - 100 ) ,,,,   20/100 * 100% = 0.2* 100 = 20%

Answer: -1

Step-by-step explanation:

Order of Operations, 5 to the power of 2 is 25 24-25 is -1 Hope this helps!

Answer:

-1

Step-by-step explanation:

24 - 5^2

24-25

=25-24

= -1

The probability that someone who tests positive for opium use actually uses opium is  0.854  .

In the question ,

it is given that , the false positivity rate is 2% .

Let the sample size be of  100 .

11% of the people actually use opium = 100*0.11 = 11.

People who do not use opium = 100 - 11 = 89.

the test for opium has a 2% false positive , that is

= 2% of 89 = 89*0.02 = 1.78

So , the True negative = 89-1.78 = 87.22

the test for opium has a 5% false negative , that is

= 5% of 11 = 11*0.05 = 0.55

So , the True positive = 11-0.55 = 10.45

Probability is calculated by favorable/total.

Total (positive) = true + false = 10.45 + 1.78 = 12.23  .

Favorable (true) = 10.45

Probability is = 10.45/12.23 = 0.854

Therefore , the required probability is 0.854    .

The given question is incomplete , the complete question is

Suppose that a test for opium use has a 2% false positive rate and a 5% false negative rate. that is, 2% of people who do not use opium test positive for opium and 5% of opium users test negative for opium. furthermore, suppose that 11% of people actually use opium.

Find the probability that someone who tests positive for opium use actually uses opium.

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To know the answer, we have to build the following relation:

Where x is the number of slices she will need in 7 pizzas. Solving for x:

Answer: 140 slices of pepperoni

The probability 1000, 1600, and 1776 were leap years according to the calendar used before the time of pope gregory, but 1492 was not.

The calendar used before the time of Pope Gregory was the Julian Calendar, which was introduced by Julius Caesar in 46 BC. This calendar used a system of leap years, where an extra day was added to the month of February every four years. This was to account for the fact that a solar year is slightly longer than 365 days. For a year to be a leap year under this system, it must be divisible by 4. Therefore, 1000, 1600, and 1776 were leap years according to the Julian Calendar, but 1492 was not since it is not divisible by 4. This calendar was replaced by the Gregorian Calendar in 1582, which uses a slightly modified leap year system. Under this system, a year is only a leap year if it is divisible by 4, but not if it is divisible by 100, unless it is also divisible by 400. Therefore, 1600 would still be a leap year under the Gregorian Calendar, but 1700, 1800, and 1900 would not be.

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To find the function that produce the table usong the general form line:

The maximum home value that can be financed is approximately $35,365.85.

Let's represent the maximum home value that can be financed by H.

If the minimum down payment is 18%, the amount financed is 100% - 18% = 82%.

Therefore, we have:

H × 82% = $29,000

Multiplying both sides by (1/82%), we get:

H = $29,000 / 82%

= $35,365.85

Hence, the maximum home value that can be financed is approximately $35,365.85.

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The constant of proportionality in the relationship is 3/2

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

X Y

2 3

6 9

The above represents the table of values

Since the data on the table of values represents a proportional relationship, then the constant of proportionality is

Constant of proportionality = Y/X

So, we have

Constant of proportionality = 3/2

Hence, the constant of proportionality is 3/2

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There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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Solution:

The given equation is:

We can write it as:

Rearrange the terms, we get:

This can be written as:

Now wrt Standard form of a quadratic equation:

we have:

and

We know that product of zeroes :

then

then

so that,

Sum of roots :

then

then

then

solving for p, we get:

so that, we can conclude that the correct answer is:

and

Answer:

2/3

Step-by-step explanation:

\(2 \frac{1}{4} : \frac{1}{2}\) = \(\frac{9}{4} : \frac{1}{2}\)

\(\frac{\frac{9}{4} }{\frac{1}{2} }\) = \(\frac{3}{x}\)

3 * 1/2 = 9/4x

3/2 = 9/4 x

x = 3/2 ÷ 9/4 = 3/2 * 4/9 = 12/18 = 6/9 = 2/3

Answer:

102, 78

Step-by-step explanation:

angle 1= x

angle 2= x-24

x+x-24=180

x=102

x-24=78

102+78=180

The measure of the angles are 102 and 78 degrees

If the difference of two supplementary angles is 24 degrees, then;

x - y = 24

y = x - 24

Taking the sum of the angles and equating to 180 degrees since they are supplementary

x + y = 180

x + x - 24 = 180

2x = 180 + 24

2x = 204

x = 102

Since y = 180 - x

y = 180 - 102

y = 78 degrees

Hence the measure of the angles are 102 and 78 degrees

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Answer:

Lorrie and karrie

Step-by-step explanation: