A circle with radius four has a sector with a central angle of 8/5 pi radians. what is area of the sector

Answer:

Check the explanation

Step-by-step explanation:

Let

  \(W(t) = W_1 + W_2 + ... + W_n\)  

where W_i denotes the individual fare of the customer.

All W_i are independent of each other.

By formula for random sums,

E(W(t)) = E(Wi) * E(n)

  \(E(Wi) = \mu_G\)  

Mean inter arrival time =    \(\mu_F\)  

Therefore, mean number of customers per unit time =    \(1 / \mu_F\)  

=> mean number of customers in t time =    \(t / \mu_F\)  

=>    \(E(n) = t / \mu_F\)  

Answer:

It will take 41.3 minutes for the element to decay to 40 grams

Step-by-step explanation:

The amount of element after t minute is given by the following equation:

[tex]x(t) = x(0)e^{-rt}[/tex]

In which x(0) is the initial amount and r is the rate that it decreases.

Element X decays radioactively with a half life of 9 minutes.

This means that [tex]x(9) = 0.5x(0)[/tex]. We use this to find r. So

[tex]x(t) = x(0)e^{-rt}[/tex]

[tex]0.5x(0) = x(0)e^{-9r}[/tex]

[tex]e^{-9r} = 0.5[/tex]

[tex]\ln{e^{-9r}} = \ln{0.5}[/tex]

[tex]-9r = \ln{0.5}[/tex]

[tex]9r = -\ln{0.5}[/tex]

[tex]r = -\frac{\ln{0.5}}{9}[/tex]

[tex]r = 0.077[/tex]

So

[tex]x(t) = x(0)e^{-0.077t}[/tex]

There are 960 grams of Element X

This means that [tex]x(0) = 960[/tex]

[tex]x(t) = 960e^{-0.077t}[/tex]

How long, to the nearest tenth of a minute, would it take the element to decay to 40 grams?

This is t when [tex]x(t) = 40[/tex]. So

[tex]x(t) = 960e^{-0.077t}[/tex]

[tex]40 = 960e^{-0.077t}[/tex]

[tex]e^{-0.077t} = \frac{40}{960}[/tex]

[tex]\ln{e^{-0.077t}} = \ln{\frac{40}{960}}[/tex]

[tex]-0.077t = \ln{\frac{40}{960}}[/tex]

[tex]0.077t = -\ln{\frac{40}{960}}[/tex]

[tex]t = -\frac{\ln{\frac{40}{960}}}{0.077}[/tex]

[tex]t = 41.3[/tex]

It will take 41.3 minutes for the element to decay to 40 grams

Answer:

crosses and touches is %100 RIGHT

Step-by-step explanation:

For the single roots -1 and 2,the graph crosses the x-axis at the intercepts

For the double root 3 the graph touches at the intercepts

"These are the point at which the graph of the function intersects the x-axis or Y-axis"

"These are the values for which the function equals zero."

For given question,

We have been given a function f(x) = (x + 1)(x - 2)(x - 3)²

To find the roots of function f(x)

⇒ f(x) = 0

⇒ (x + 1)(x - 2)(x - 3)² = 0

⇒ x + 1 = 0        or         x - 2 = 0      or      (x - 3)²=0

⇒ x = -1      or    x = 2   or x = 3

This means x = -1, 2, 3 are the roots of the function f(x)

From the graph of the function we can observe that the for the single roots -1 and 2,the graph of the function f(x)  crosses the x-axis at the intercepts x = -1 and x = 2 respectively.

And for the double root 3 the graph of the function f(x) touches at the intercept x = 3.

Therefore, For the single roots -1 and 2,the graph crosses the x-axis at the intercepts.

For the double root 3 the graph touches at the intercepts.

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Answer:

Where's the triangle?

Step-by-step explanation:

Answer: the resale value would be $791 after 4 years

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

y = b(1 - r)^x

Where

y represents the value of the laptop computer after x years.

x represents the number of years.

b represents the initial value of the laptop computer.

r represents rate of decay.

From the information given,

P = $2500

x = 4

r = 25% = 25/100 = 0.25

Therefore,

y = 2500(1 - 0.25)^4

y = 2500(0.75)^4

y = $791

Answer: its 4. Look at the graph, x is horizontal and y is vertical (first go sideways then go up.) if coordinates are x,y then first go sideways when looking for x. they give you x. 7. then we go up. the graph intersects 7 at 4, therefore the coords are 7, 4 and your y coordinate is 4.

Step-by-step explanation:

Answer:

38

Step-by-step explanation:

An inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords.

Inscribed Angle =1/2 Intercepted Arc

We know the intercepted are is 76 degrees

<c = 1/2 (76) = 38

The inscribed angle = 38

Answer:

38

Step-by-step explanation:

Its definetly under 90 degrees. And it is also under 76 degress, so thatmeans it is 38 degrees

Step-by-step explanation:

The bacteria is always doubled because in the sequence we multiply the number by 2

3 x 2 = 6 x 2 = 12 x 2 = 24 x 2 = 48 x 2 = 96

Answer: Stocks will have the highest liquidity and convertability to cash

Answer:

1.25

Step-by-step explanation:

Answer:

  12,765

Step-by-step explanation:

The exponential formula for the population can be written as ...

  population = (initial population)(1 -decay rate)^t

where t is in years, and the decay rate is the loss per year.

The given numbers make this ...

  population = 100,000(0.9918^t)

In 250 years, the population will be about ...

  population = 100,000(0.9918^250) ≈ 12,765.15

There will be about 12,765 butterflies in 250 years.

In 250 years, there will be approximately 12,765 butterflies in the population.

This figure is obtained by applying the exponential decay formula with a 0.82% decrease rate per year from an initial population of 100,000 butterflies.

To determine the butterfly population in 250 years given a yearly decrease rate of 0.82%, we utilize the exponential decay formula:

[tex]\[ P(t) = P_0 \times (1 - r)^t \][/tex]

where:

- (P(t)) represents the population after (t) years,

- (P_0) is the initial population, which is 100,000,

- (r) is the annual decrease rate in decimal form, which is 0.82% or 0.0082,

- (t) is the time in years, here 250 years.

By substituting the given values into the formula:

[tex]\[ P(250) = 100,000 \times (1 - 0.0082)^{250} \][/tex]

Upon calculation, the population after 250 years is found to be approximately 12,765, rounding to the nearest whole number for practical purposes. This result is based on the principle of exponential decay, reflecting how a consistent percentage decrease affects the population over a prolonged period.

The average number of people per car visiting the national park is approximately 2.91.

In order to find the average number of people per car, you would first multiply the number of cars by the number of people in each.

Therefore, 57 cars had 4 people (57*4=228), 61 cars had 2 people (61*2=122), 9 cars had 1 person (9*1=9), and 5 cars had 5 people (5*5=25). After this, add all the results (228+122+9+25 = 384).

The total number of cars is the sum of all cars, which is (57+61+9+5 = 132).

Now, to find the average number of people per car, you would divide the total number of people, which is 384 by the total number of cars, which is 132. Therefore, the average number of people per car is 384 / 132 = about 2.91 people per car.

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Answer:

Given:

P=950

r=0.07

t=8

F=950(1.07)^8

= 1632.28 (total amount)

Interest = total amount - principal

=1632.28 - 950

=682.28

Step-by-step explanation:

The formula is:

Future value = accumulated amount, F = P(1+r)^t

P=principal

r=annual interest rate [compounded annually]

t=number of years of loan

Answer:

0.5

Step-by-step explanation:

Answer:

7

3.5

Step-by-step explanation:

Answer:

The radius of the circle is [tex]\(7 \, \text{cm}\)[/tex], and the diameter is [tex]\(14 \, \text{cm}\)[/tex].

Explanation:

The radius [tex](\(r\))[/tex] of a circle is half of its diameter ([tex]\(d\)[/tex]), and the diameter ([tex]\(d\)[/tex]) is twice the radius ([tex]\(r\)[/tex]). So, we can find the radius and diameter of the circle with a given radius of 7 cm.

Given:

Radius ([tex]\(r\)[/tex]) = 7 cm

To find the diameter ([tex]\(d\)[/tex]), we use the relationship:

[tex]\[d = 2r\][/tex]

Substituting the given value of the radius:

[tex]\[d = 2 \times 7\][/tex]

[tex]\[d = 14\][/tex]

So, the diameter of the circle is [tex]\(14 \, \text{cm}\)[/tex].

Therefore, the radius of the circle is [tex]\(7 \, \text{cm}\)[/tex], and the diameter is [tex]\(14 \, \text{cm}\).[/tex]

Question:

What is the diameter of a circle whose radius is 7 cm?

Answer: x = 3

Step-by-step explanation

This is a simultaneous equation. So to find x , we solve to ascertained the coordinate or point of intersection of the too lines.

y = 4x + 2, and 6x - y = 4

To solve , we need to rearrange first

y = 4x + 2 will be

4x - y = -2 -------------------------1

Equation 2 is in order

6x - y = 4 -------------------------- 2

Now solve the two equation for x by using any methods you are familiar with.

4x - y = -2

6x - y = 4, now subtract equation 2 from 1 in order to eliminate y,

we now have

-2x = -6, now divide through by 2

x = 3.

Hence y could be find by substitution for x in any of the equation above and now check.

4x - y = -2

4(3) - y = -2

12 - y = = -2

y = 12 + 2

y = 14.

Now let check

6x - y = 4

6(3) - 14

18 - 14

= 4.

Therefore, the value of x is 3

The opposite of a coordinate in mathematics is obtained by changing the sign of the given number. Without the specific coordinate for point D, the opposite cannot be determined from the provided options.

The question seems to refer to the notion of opposite coordinates in a coordinate system. In mathematics, particularly in the context of a coordinate plane, the opposite of a coordinate is simply the same number with its sign changed. If the original coordinate for point D is not given in the question, it's impossible to determine the correct opposite coordinate from the options provided.

Answer:

A = πr²

Step-by-step explanation:

Answer:

The answer is x=5, −9

Answer:

The mean women's shoe size in U.S. units is 8.73.

The standard deviation in U.S. units is  1.40.

Step-by-step explanation:

For the women, the mean size was 38.73 with a standard deviation of 1.75.  This size is expressed in European units.

If we want to convert to US units, we have to use the equation:

[tex]US\, size=EuroSize*0.7987-22.2[/tex]

If we use the properties of the expected value, then the mean expressed in US units is:

[tex]Property: E(y)=E(ax+b)=aE(x)+b\\\\\\E(y)=0.7987E(x)-22.2\\\\E(y)=0.7987*38.73-22.2\\\\E(y)=8.73[/tex]

To calculate the standard deviation, we use the properties of variance:

[tex]Property: V(y)=V(ax+b)=a^2V(x)\\\\\sigma_y=\sqrt{a^2V(x)}=a\sigma_x\\\\\sigma_y=0.7987*1.75=1.40[/tex]

Answer:

B. The mean amount of [tex]CO_2[/tex] emitted by the new fuel is actually lower than 89 kg but they fall to conclude it is lower than 89 kg

Step-by-step explanation:

A Type II error is the failure to reject a false null hypothesis.

Given the null and alternate hypothesis of a fuel company which wants to test a new type of gasoline designed to have lower [tex]CO_2[/tex] emissions.:

[tex]H_0: \mu = 8.9 kg\\H_a: \mu < 8.9 kg \\\text{ (where \mu is the mean amount of CO_2 emitted by burning one gallon of this new gasoline)}[/tex]

where [tex]\mu[/tex] is the mean amount of [tex]CO_2[/tex] emitted by burning one gallon of this new gasoline.

If the null hypothesis is false, then:

[tex]H_a: \mu < 8.9 kg[/tex]

A rejection of the alternate hypothesis above will be a Type II error.

Therefore:

The Type II error is: (B) The mean amount of [tex]CO_2[/tex]  emitted by the new fuel is actually lower than 89 kg but they fall to conclude it is lower than 89 kg.

You can use the definition of type 2 error to find out which of the given option describes the type 2 error.

The Option which indicates Type II error is:

Option B. The mean amount of CO2 emitted by the new fuel is actually lower than 89 kg but they fall to conclude it is lower than 89 kg.

Firstly the whole story starts from hypotheses. The null hypothesis is tried to reject and we try to accept the alternate hypothesis.

The negative is just like the doctor's test getting negative means no disease. Similarly, if we conclude null hypothesis negative means it is accepted. If it is accepted wrongly means the negative test result was false, thus called false negative. This error is called type II error.

Since the null hypothesis here is [tex]H_0: \text{typically emitted } {\rm CO_2} = 8.9 \: \rm kg[/tex],

Thus the type II error would be when we fail to reject that CO2 emission is 8.9 kg (or say  we accept that CO2 emission is 8.9 kg generally) but the actual amount was lower than 8.9 kg(the alternate hypothesis was true)

Thus,

The Option which indicates Type II error is:

Option B. The mean amount of CO2 emitted by the new fuel is actually lower than 89 kg but they fall to conclude it is lower than 89 kg.

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Step-by-step explanation:

For the charges that have same sign of charges will repel each other while for the charges that have different charges will attract each other. So, we can say that like charges repel and unlike charges attract each other.

The Coulomb's law of attraction of repulsion states that force between charges is directly proportion to the product of charges and inversely proportional to the square of distance between them. Mathematically, it is given by :

[tex]F=\dfrac{kq_1q_2}{r^2}[/tex]

Hence, all the given statements are true.

Answer:

9

Step-by-step explanation:

6+x, when x = 3

6+(3)

6+3=9

Answer:

9

Step-by-step explanation:

6 + x, when x = 3

So, 6 + 3 = answer

So, 6 + 3 = 9

Stay Safe, Stay at Home!! Lots of Love <3 <3 =) :3

Please consider the graph of the sphere.

We know that the volume of sphere is equal to [tex]\frac{4}{3}\pi r^3[/tex], where r represents radius of sphere.

We can see that diameter of sphere is 30 inches. We know that radius is half the diameter, so radius of the given sphere would be half of 30 inches that is [tex]\frac{30}{2}=15[/tex] inches.

[tex]V=\frac{4}{3}\pi r^3[/tex]

[tex]V=\frac{4}{3}\pi (15\text{ in})^3[/tex]

[tex]V=\frac{4}{3}\pi \times 3375\text{ in}^3[/tex]

[tex]V=4\times 1125\pi \text{ in}^3[/tex]

[tex]V=4500\pi \text{ in}^3[/tex]

Therefore, the volume of the given sphere is [tex]4500\pi\text{ in}^3[/tex] and option B is the correct choice.

Answer:

The mean of the sampling distribution(SRS 49) of the sample mean is 420 and the standard deviation is 3.

The mean of the sampling distribution(SRS 576) of the sample mean is 420 and the standard deviation is 0.875.

By the Central Limit Theorem, the sample size does not influence the sample mean, but it does decrease the standard deviation of the sample

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Population

mean = 420, standard deviation = 21.

Sample of 49

Mean = 420, standard deviation [tex]s = \frac{21}{\sqrt{49}} = 3[/tex]

The mean of the sampling distribution of the sample mean is 420 and the standard deviation is 3.

Sample of 49

Mean = 420, standard deviation [tex]s = \frac{21}{\sqrt{576}} = 0.875[/tex]

The mean of the sampling distribution of the sample mean is 420 and the standard deviation is 0.875.

Increasing the sample size from 49 to 576 in a simple random sample from a population with a mean of 420 and a standard deviation of 21 keeps the mean of the sampling distribution the same but decreases the standard deviation.

When taking a simple random sample (SRS) from a population where the mean (μ) is 420 and the standard deviation (σ) is 21, and using a sample size (n) of 49, the sampling distribution of the sample mean will have:

When the sample size increases to 576, the sampling distribution of the sample mean will still have a mean of 420, but the standard deviation will decrease because it is inversely proportional to the square root of the sample size. The new standard deviation will be 21/√576 = 21/24 = 0.875.

The effect of increasing the sample size is that while the mean of the sampling distribution remains the same, the standard deviation decreases, leading to a more narrow distribution. This indicates that there is less variability in the sample means, and they will be closer to the population mean, which is in accordance with the Central Limit Theorem.

Answer:

A is correct, "All numbers bigger than -3 and smaller than 3"

Step-by-step explanation:

The open circle means greater than, if it was filled in, it would be greater than or equal to. And the black line connecting each shows its more than -3 and less than 3. Hope this helps! Please rate brainliest if it does :)

Answer:

The probability of  the student will pass the quiz = .0546

Step-by-step explanation:

Given -

Total no of question = 10

If the student guesses on each question there are two outcomes true of false

the probability  of guesses  question correctly =  [tex]\frac{1}{2}[/tex]

the probability  of success is (p) =  [tex]\frac{1}{2}[/tex]

the probability  of guesses  question incorrectly = [tex]\frac{1}{2}[/tex]

the probability  of failure is (q) = 1- p = [tex]\frac{1}{2}[/tex]

If the student guesses on each question he must answered at least 8 question correctly

the probability of  the student will pass the quiz = [tex]P(X\geq8 )[/tex]

= P(X = 8 ) + P(X = 9) + P(X = 10 )

= [tex]\binom{10}{8}(p)^{8}(q)^{10 - 8} + \binom{10}{9}(p)^{9}(q)^{10 - 9} + \binom{10}{10}(p)^{10}(q)^{10 - 10}[/tex]

= [tex]\frac{10!}{(2!)(8!)}(\frac{1}{2})^{8}(\frac{1}{2})^{10 - 8} +\frac{10!}{(1!)(9!)} (\frac{1}{2})^{9}(\frac{1}{2})^{10 - 9} + \frac{10!}{(0!)(10!)}(\frac{1}{2})^{10}(\frac{1}{2})^{10 - 10}[/tex]

= [tex]45\times\frac{1}{2^{10}} + 10\times\frac{1}{2^{10}} + 1\times\frac{1}{2^{10}}[/tex]

= [tex]\frac{56}{2^{10}}[/tex]

= .0546

Final answer:

The probability of a student passing the true or false quiz by guessing and getting at least 8 out of 10 questions correct is 7/128. This is calculated by finding the binomial probabilities for 8, 9, and 10 correct guesses and summing them.

Explanation:

To determine the probability that the student passes the quiz by guessing, we need to calculate the chances of them getting at least 8 out of 10 true or false questions correct. Since each question can only be true or false, there's a 1/2 chance of guessing each question correctly, and therefore, a 1/2 chance of guessing incorrectly.

The scenarios in which a student can pass are by getting 8, 9, or 10 questions correct. We will use the binomial probability formula, which is P(X=k) = (n choose k) * (p)^k * (1-p)^(n-k), where 'n' is the number of trials (questions), 'k' is the number of successes (correct answers), and 'p' is the probability of success on an individual trial (1/2 for true/false questions).

The probability of getting exactly 8 questions right is (10 choose 8) * (1/2)^8 * (1/2)^(10-8).

The probability of getting exactly 9 questions right is (10 choose 9) * (1/2)^9 * (1/2)^(10-9).

The probability of getting all 10 questions right is (10 choose 10) * (1/2)^10 * (1/2)^(10-10).

We add these individual probabilities together to find the total probability of passing the quiz.

Using a calculator or the binomial coefficients, we find:

P(getting 8 right) = 45 * (1/2)^10,

P(getting 9 right) = 10 * (1/2)^10,

P(getting 10 right) = 1 * (1/2)^10.

Adding these together gives us the total probability:
P(8 or more correct) = [45 + 10 + 1] * (1/2)^10 = 56 * (1/2)^10

After simplifying, we find that the probability of passing the quiz with at least 8 correct answers is thus 56/1024, which can be reduced to 7/128.

Answer:

The Laplace transform of f(t) = 1 is given by

F(s) = (1/s) for all s>0

Step-by-step explanation:

Laplace transform of a function f(t) is given as

F(s) = ∫∞₀ f(t) e⁻ˢᵗ dt

Find the Laplace transform for when f(t) = 1

F(s) = ∫∞₀ 1.e⁻ˢᵗ dt

F(s) = ∫∞₀ e⁻ˢᵗ dt = (1/s) [-e⁻ˢᵗ]∞₀

= -(1/s) [1/eˢᵗ]∞₀

Note that e^(∞) = ∞

F(s) = -(1/s) [(1/∞) - (1/e⁰)]

Note that (1/∞) = 0

F(s) = -(1/s) [0 - 1] = -(1/s) (-1) = (1/s)

Hope this Helps!!!

In this exercise we have to use the knowledge of the Laplace transform to calculate the total value of the given function, thus we will find that:

[tex]F(s) = (1/s) \\for \ all\ s>0[/tex]

So we have that the Laplace transform can be recognized as:

[tex]F(s) = \int\limits^\infty _0 { f(t) e^{-st} \, dt[/tex]

Find the Laplace transform for when f(t) = 1, we have that:

[tex]F(s) = \int\limits^\infty _0 { f(t) e^{-st} \, dt \\\\ F(s) = \int\limits^\infty _0 { 1 e^{-st} \, dt[/tex]

[tex]F(s) = \int\limits^\infty _0 { e^{-st} \, dt = (1/s) [-e^{-st}] \\[/tex]

[tex]F(s) = -(1/s) [(1/\infty ) - (1/e^0)] \\F(s) = -(1/s) [0 - 1] = -(1/s) (-1) = (1/s)[/tex]

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Answer:

Yes

Step-by-step explanation:

Answer:

$38 + 15% off

Step-by-step explanation:

to do this, multiply each original price by the coupon percentage, (38 being .15, and 44 being .4,) and subtract the answers. when this is done and you compare, you will see that the $38 sweatshirt is less money by $2.90.

The cost of the sweatshirt both in-store and online after applying the respective discounts shows that it is better to buy the sweatshirt online, saving Nathan $2.90.

This problem relates to the mathematics field of percentage or discount calculations. To solve this problem, we need to calculate the cost of the sweatshirt after applying the discounts both in-store and online.

First, let's calculate the amount of the 20% discount for the in-store purchase. To find the discount, we multiply the cost of the sweatshirt by the discount rate: $44 * 20% = $8.80. So the total cost for the sweatshirt in-store after the discount would be $44 - $8.80 = $35.20.

Secondly, let's calculate the online price with a 15% discount. The discount on the online price would be calculated as: $38 * 15% = $5.70. Therefore, the cost of the sweatshirt online after the discount is $38 - $5.70 = $32.30.

Based on these calculations, buying online is the better deal by $35.20 - $32.30 = $2.90.

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