Select all the correct answers. What is 221,000,000,000,000,000,000 expressed in scientific notation? 2. 21 × 1021 2. 21E20 2. 21E21 2. 21E-20 2. 21 × 10-21 2. 21 × 10-20 2. 21 × 1020 2. 2.10E-20.

Answer:

SA=72

Step-by-step explanation:

18+18=36

12+12=24

6+6=12

36+24+12=72

Answer:

true

Step-by-step explanation:

-7=4*-3+5

-7=-12+5

To find where the line crosses the x-axis, we need to find the value of x the line crosses the x-axis at the point   \((-5/3, 0).\)

a) The gradient of a line is the coefficient of the x term in its equation in the form y = mx + c, where m is the gradient. Therefore, the gradient of the line with equation \(y = 3x + i is 3\)  .

b) Since the line passes through the point (2, 11), we can substitute these values into the equation  \(y = 3x + i\) to find the value of i:

\(11 = 3(2) + i\)

\(11 = 6 + i\)

\(i = 11 - 6\)

\(i = 5\)

Therefore, the equation of the line can be written as   \(y = 3x + 5.\)

c) The value of k in the equation   \(11 = 6 + k\) is simply the y-intercept of the line. From the equation \(y = 3x + 5\)  , we can see that the y-intercept is 5. Therefore, k = 5, and the equation of the line is \(y = 3x + 5.\)

d) To find where the line crosses the x-axis, we need to find the value of x when y = 0. Substituting y = 0 into the equation \(y = 3x + 5\)  , we get:

\(0 = 3x + 5\)

\(x = -5/3\)

Therefore, the line crosses the x-axis at the point  \((-5/3, 0).\)

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a) The gradient of the line is 3.

c) The Value of k is 6.

d) The line crosses the y-axis at (0, 5).

The line's equation is y = 3x + k,

a) Compare this with the standard equation of line y = mx + c

where 3 is the coefficient of x.

The slope or gradient of a line is represented by the coefficient of x in its equation.

As a result, the gradient of the line y = 3x + k is 3.

b) We now know that the line goes through the point. (2, 11). Using the equation y = 3x + k, we can find the value of the y-intercept (k) at this moment. When we substitute x = 2 and y = 11 into the equation, we get:

11 = 3(2) + k

When we simplify the right side, we get:

11 = 6 + k

c) When we subtract 6 from both sides, we get:

k = 11 - 6 = 5

As a result, the equation of the line is as follows:

y = 3x + 5.

d) So, the y-intercept value is 5, indicating that the line crosses the y-axis at the location. (0, 5).

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In a simple linear regression model, the coefficient of the independent variable (x) in the estimated sample regression equation indicates the change in the predicted value of the dependent variable (y) when x increases by one unit. This coefficient is also known as the slope of the regression line. Therefore, to calculate the predicted value of y, we multiply the coefficient by the value of x and add the intercept.

In a simple linear regression model, the coefficient that indicates the change in the predicted value of y when x increases by one unit is the "slope coefficient" or the "regression coefficient" (usually denoted as b1). This coefficient represents the relationship between the independent variable x and the dependent variable y.

The linear regression equation is given as:

y = b0 + b1 * x

Where:
- y is the predicted value of the dependent variable
- b0 is the intercept coefficient (where the line intersects the y-axis)
- b1 is the slope coefficient (the change in y when x increases by one unit)
- x is the independent variable

In this equation, b1 indicates the change in the predicted value of y when x increases by one unit.

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In the current year, with an increased prevalence of yellow fever due to an outbreak in the region, the positive predictive value (PPV) of the screening test for yellow fever is expected to increase.

Positive predictive value (PPV) is the proportion of positive test results that are true positives. It is influenced by the prevalence of the condition in the population being tested. In this case, the prevalence of yellow fever has increased due to the outbreak, which means there are more true positives in the population.

Given that the sensitivity and specificity of the screening test remain the same, an increase in the prevalence of yellow fever would result in a higher PPV. This is because the probability of a positive test result correctly indicating the presence of yellow fever is higher when there are more cases of the disease in the population.

It's important to note that PPV is affected by both sensitivity and specificity, as well as the prevalence of the condition. In this scenario, the increase in prevalence outweighs the impact of the test's sensitivity and specificity, leading to an expected increase in the positive predictive value of the screening test for yellow fever during the outbreak.

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Answer:

Step-by-step explanation:

The speed of a wave can be calculated by multiplying the wavelength by the frequency or dividing the distance traveled by the time it takes. In this case, the speed (celerity) is given as 1 m/s, and the period is given as 5 seconds.

To find the wavelength, we can use the formula:

Wavelength = Speed / Frequency

Since the speed is 1 m/s and the period (T) is the reciprocal of the frequency (f), we can substitute T = 5 seconds as the period and solve for the frequency:

f = 1 / T = 1 / 5 = 0.2 Hz

Now we can calculate the wavelength:

Wavelength = Speed / Frequency = 1 m/s / 0.2 Hz = 5 meters

Therefore, the correct answer is c. 5 meters.

The wavelength of a wave is the distance between two consecutive crests or troughs. The celerity of a wave is the speed at which the wave travels.The wavelength of a wave is 0.2 meters.

The period of a wave is the time it takes for one complete wave to pass a point.We can use the following equation to calculate the wavelength of a wave:

Wavelength = Celerity / Period

In this case, the celerity is 1 m/s and the period is 5 seconds. Therefore, the wavelength is:

Wavelength = 1 m/s / 5 seconds = 0.2 meters

Therefore, the answer is e. 0.2 meters.

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Answer:

f(x) = x + 3

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments ;)

And if you find this answer helpful, then consider marking it Brainliest

Answer:

its f(x) = x + 3

Step-by-step explanation:

i got a 100 on the quiz

Answer:

x^2+27x+180

Step-by-step explanation:

okay so -12 and 15 are the only solutions

work backward

add 12 and add 15 from x

(x+12)(x+15)

then solve this

x*x=x^2

x*+15=15x

12*x=12x

12*15=180

now put it all together

x^2+15x+12x+180

then simplify

x2+27x+180

(x+12)(x+15)

Then solve again to try it.

x+12=0

x+15=0

x=-12

x=-15

Hope this helps.

Answer:

Math: the science and study of quality, structure, space, and change.

Probability that the person selected at random from the sport centre of 125 people is a fraction of 1/4 or 0.25.

The probability of an event is the fraction of the required number of outcome divided by the number of possible outcomes.

We shall determine the answer to the question as follows;

People in the sport centre = 125

People who used the 3 facilities = 6

People who accessed only gym = 59 - (6 + 11 + 19) = 26

People who accessed only track event = 55 - (6 + 11 + 24) = 14

People who accessed only swimming pool event = 70 - (6 + 19 + 24) = 21

People who accessed only gym and swimming pool events = 29 - 6 = 19

People who accessed only gym and track events = 17 - 6 = 11

People who accessed only swimming pool and track events = 30 - 6 = 24

Total number of people who accessed at least any one of the facilities = 121

The number of people who did not access any of the facility = 125 - 121 = 4, which is the number of possible outcomes for our required outcome.

Therefore, the probability that the person selected doesn't use any facility = 1/4

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A checking account is used for daily basis transaction and a debt and is usually associated with it.Saving accounts is just used for saving money.It has a time limit then you can withdraw your money.It is not on daily basis.

A bank account that allow the user to withdraw the money ,pay bill,transfer money to other person or make a purchase anything by writing checks.Check accounts typically don't earn interest.By checking accounts we can easily deposit and withdraw money for daily transaction.

Saving accounts are intended for storing your money which you don't plan to use daily.saving accounts earns interest at your money.saving account is designed for the accumulation of money in a safe place for future use.saving accounts offer easy access to your money in any emergency.so keeping your money in a saving account means that your money is safe for your future use.

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The probability that the first child selected will be a girl is 0.5 or 50%.

The probability of a child being a boy or a girl is equal, as long as the parents are healthy and have no genetic conditions that affect the gender of the child. In general, the chance of having a boy or a girl is about 50-50.

However, it is important to understand that each individual birth is a random event and that the probability of having a boy or a girl is calculated over a large number of births.

This means that even though the overall probability of having a boy or a girl is equal, it is possible to have a run of several boys or several girls in a row.

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The probability that exactly two of the three people selected also travel by train is 4/9

The probability of an event occurring is specified by the ratio of the number of  required outcomes to the number of possible outcomes.

The number of people that travelled from London to Manchester for the conference = 30

Number of people that traveled by train = 15

Number of people that travelled by plane = 9

Number of people that did not travel by travel by either train or plane = 12

Number of people chosen from those that traveled by plane = 3

The probability that two of those selected also traveled by train can be found as follows;

The number of people that traveled by either train of plane = 30 - 12 = 18

The number of people that traveled by plane and train = 15 + 9 - 18 = 6

The binomial probability distribution formula that can be used to find the probability of an event, p, occurring exactly r times is as follows;

P(p) = \(_nC_r\cdot p^r\cdot q^{n-r}\)

Where;

n = Number of people chosen = 3

r = Number of people chosen that also traveled by train = 2

p = Probability that a person chosen also traveled by train = 6/9 = 2/3

q = Probability that a person chosen did not travel by train = 3/9 = 1/3

Therefore;

\(P = _3C_2\times \left(\dfrac{2}{3}\right) ^2\times \left(\dfrac{1}{3} \right)^{3-2} = \dfrac{4}{9}\)

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Answer:

y = -x - 4

Step-by-step explanation:

y = mx + b is slope intercept form,

where m is the slope, and b is the y-intercept.

As we can see from the picture, the line has a negative slope of 1 (we can also just say -1). We know this is the slope because it has a rise of -1 and a run of -1. (I hope that made sense lol :/)

[Side note, we use x instead of 1.]

The y-intercept is -4 since we can see the line passes through the y-axis at -4.

Therefore, the equation can be written as y = -x - 4

Answer:

∠ 1 = 36°

Step-by-step explanation:

Supplementary angles sum to 180° then

∠ 2 + ∠ 3 = 180° , that is

∠ 2 + 126° = 180° ( subtract 126° from both sides )

∠ 2 = 54°

Complementary angles sum to 90° , then

∠ 1 + ∠ 2 = 90° , that is

∠ 1 + 54° = 90° ( subtract 54° from both sides )

∠ 1 = 36°

your Answers are:

1. 0

2. 128

Answer:

32% or just 32

Step-by-step explanation:

Considering the mean of a discrete distribution, you are expected to earn $0.13 by the end of the game.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

Since 71% of your rolls are successful and 29% of your rolls are unsuccessful, the distribution of your earnings is:

Hence the expected value is:

E(X) = 1 x 0.71 - 2 x 0.29 = 0.71 - 0.58 = 0.13

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The monthly payment the student needs to make is approximately R9,299.91.

To determine the monthly payment the student needs to make, we can use the concept of present value.

The student plans to make monthly payments starting in 4 years' time and continuing until 3 years prior to retirement, which is a total of 44 - 3 - 4 = 37 years of payments.

The insurance company charges a fee of 8% of each payment for the first 15 years and 5% of each payment thereafter. The interest rates guaranteed by the company are 18% per annum during the payment period and 14% per annum during the final 3 years.

PV = P * (1 - (1 + r)^(-n)) / r

For the first 15 years:

PV1 = (P * (1 - (1 + 0.18/12)^(-15*12))) / (0.18/12)

For the remaining 22 years:

PV2 = (P * (1 - (1 + 0.18/12)^(-22*12))) / (0.18/12) * (1 - 0.08)

For the final 3 years:

PV3 = (P * (1 - (1 + 0.14/12)^(-3*12))) / (0.14/12) * (1 - 0.05)

The total present value of the payments should be equal to the desired lump sum of R7,000,000 at retirement.

PV1 + PV2 + PV3 = R7,000,000

By substituting the values and solving the equation, we find that the monthly payment is approximately R9,299.91.

The monthly payment the student needs to make to accumulate R7,000,000 at retirement is approximately R9,299.91.

(b) At age 62, the student plans to use the lump sum to purchase an annuity of R50,000 per month payable until his 70th birthday, and then double the monthly payment until the money runs out. We need to find the age at which he will receive the last full double monthly payment.

The student will receive the last full double monthly payment at the age of 82 years and 11 months.

To determine the age at which the student will receive the last full double monthly payment, we need to calculate the duration of the annuity based on the given conditions.

The annuity provides R50,000 per month until the student's 70th birthday, and then the monthly payment doubles until the money runs out. The interest rate used to calculate the annuity is 9% per annum compounded monthly.

n = log((P * (1 - (1 + r)^(-m))) / (r * A)) / log(1 + r)

Where n is the number of months, P is the monthly payment, r is the monthly interest rate, m is the number of months until the student's 70th birthday, and A is the accumulated lump sum at retirement.

n = log((50,000 * (1 - (1 + 0.09/12)^(-12 * (70 - 62)))) / (0.09/12)) / log(1 + 0.09/12)

Therefore, the annuity will last for approximately 103.74 months, which is equivalent to 8 years and 7.74 months.

To find the age at which the student will receive the last full double monthly payment, we add 70 years and 8 years to the student's current age of 62 years:

70 + 8 = 78 years.

Since the student will receive the last full double monthly payment after 8 years and 7.74 months, we can round up the months to the next full month:

The student will receive the last full double monthly payment at the age of 78 years and 8 months.

(c) An alternative the student considers is to not have the monthly annuity payment double after the age of 70 but instead remain level at R50,000 per month. We need to determine at what age the annuity payments will cease.

If the annuity payments remain level at R50,000 per month, the annuity payments will cease at the age of 94 years and 4 months.

To find the age at which the annuity payments will cease if they remain level at R50,000 per month, we need to calculate the duration of the annuity based on the given conditions.

Using the same formula as in part (b) to calculate the number of months the annuity will last, we can substitute the values:

n = log((50,000 * (1 - (1 + 0.09/12)^(-12 * (70 - 62)))) / (0.09/12)) / log(1 + 0.09/12)

To find the age at which the annuity payments will cease, we add 70 years and 8 years to the student's current age of 62 years:

70 + 8 = 78 years.

Since the annuity will last for 8 years and 7.74 months, we can round up the months to the next full month:

However, in this alternative scenario, the annuity payments will not double after the age of 70. Therefore, the annuity payments will continue at R50,000 per month until the money runs out.

To calculate the remaining duration of the annuity, we subtract 8 years and 7.74 months from the duration of the annuity:

103.74 months - 103.74 months = 0 months.

If the annuity payments remain level at R50,000 per month, the annuity payments will cease at the age of 78 years and 8 months.

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To find the slope of the tangent line to the polar curve r = 2 + 3sin(θ) at the point (2, π), we need to convert the polar equation to Cartesian coordinates and then find the derivative.

The conversion from polar to Cartesian coordinates is given by:

x = rcos(θ)

y = rsin(θ)

Using the given polar equation r = 2 + 3sin(θ), we can substitute the values of x and y in terms of r and θ:

x = (2 + 3sin(θ))cos(θ)

y = (2 + 3sin(θ))sin(θ)

Differentiating both x and y with respect to θ using the chain rule:

dx/dθ = [(2 + 3sin(θ))cos(θ)]' = [-3sin(θ)cos(θ) + (2 + 3sin(θ))(-sin(θ))] = -3sin^2(θ)

dy/dθ = [(2 + 3sin(θ))sin(θ)]' = [3sin^2(θ) + (2 + 3sin(θ))(cos(θ))] = 3cos^2(θ) + 2cos(θ) + 3sin(θ)cos(θ)

To find the slope of the tangent line at (2, π), we substitute θ = π into the derivatives:

dx/dθ = -3sin^2(π) = 0

dy/dθ = 3cos^2(π) + 2cos(π) + 3sin(π)cos(π) = 3cos(π) = -3

Now we need to find dx/dy by taking the ratio of dx/dθ to dy/dθ:

dx/dy = (dx/dθ)/(dy/dθ) = 0 / (-3) = 0

Therefore, the slope of the tangent line to the polar curve at (2, π) is 0

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Answer:

I'm pretty sure it's only B and D

Answer:

7

Step-by-step explanation:

The answer is 7 because 6 times 7 is 42.

42-4 is equal to 38.

x = a number

6x - 4 = 38. Add 4 to both sides.

6x = 42. Divide 6 from both sides.

x = 7.

A quadratic equation is a polynomial equation of degree 2, which means the highest power of the variable is 2. It is generally written in the form: ax^2 + bx + c = 0. Option (d) x = -8, x = 8 is the correct answer.

The given equation is 15x^2 - 56 = 88 - 6x^2.

We need to find the values of x that are solutions to the given equation.

Solution: We are given an equation 15x² - 56 = 88 - 6x².

Rearrange the equation to form a quadratic equation in standard form as follows: 15x² + 6x² = 88 + 56  21x² = 144  

x² = 144/21 = 48/7

Therefore x = ±sqrt(48/7) = ±(4/7)*sqrt(21).

The values of x that are solutions to the given equation are x = -4/7 sqrt(21) and x = 4/7 sqrt(21).

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The given equation is 15x² - 56 = 88 - 6x². Values of x are solutions to the equation below 15x² - 56 = 88 - 6x² are x = -2.62, 2.62 or x ≈ -2.62, 2.62.

Firstly, let's add 6x² to both sides of the equation as shown below.

15x² - 56 + 6x² = 88

15x² + 6x² - 56 = 88

Simplify as shown below.

21x² = 88 + 56

21x² = 144

Now let's divide both sides by 21 as shown below.

x² = 144/21

x² = 6.86

Now we need to solve for x.

To solve for x we need to take the square root of both sides.

Therefore, x = ±√(6.86).

Therefore, the values of x are solutions to the equation below are x = -2.62, 2.62 or x ≈ -2.62, 2.62.

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Answer:

\(6 \frac{2}{3} \)

Step-by-step explanation:

\(5 \div \frac{3}{4} = 6 \frac{2}{3} \)

Answer:

it'll take her approximately 6.5 - 7 hours to run 5 miles.

Step-by-step explanation:

A random lighting scheme, where the lights are turned on and off in a non-predictable manner, would be the most suitable choice for Greg to create an impression of activity in the building.

To create an impression of activity, Greg should use a random lighting scheme where the lights are turned on and off randomly.

Now let's delve into the explanation. A random lighting scheme involves varying the on-off pattern of the lights in a way that does not follow a predictable sequence or pattern. This randomness creates an impression of activity by simulating the natural fluctuations of lighting that would occur in a busy environment.

By randomly turning the lights on and off, Greg can mimic the dynamic lighting conditions that would be observed in a building with people moving around and engaging in various activities. This can enhance the overall ambiance and perception of liveliness within the space.

Random lighting schemes also have practical benefits, as they can help conserve energy by avoiding the constant illumination of areas that are not in use. By randomly cycling the lights, Greg can achieve a balance between creating the desired impression of activity and ensuring efficient energy usage.

In summary, a random lighting scheme, where the lights are turned on and off in a non-predictable manner, would be the most suitable choice for Greg to create an impression of activity in the building.

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Points:

Im sorry but imma yoink your points and not answer the question

Hol up:

There is no question here so it's ok

Step-by-step explanation:

√(20+5²)=√{20+25}=√45=3√5

Answer:

the number of tomatoes he gathered for 3 days = 3 × x = 3x  

Step-by-step explanation:

According to the question Stan gathered x number of tomatoes every single day for three days. The total number of tomatoes she gathered altogether can be calculated below.

The number of tomatoes she gathered daily = x

The number of tomatoes she gathered for 3 days will be the product of the daily number of tomatoes she gathered(x) and the number of days she gathered it(3).

Therefore,

the number of tomatoes he gathered for 3 days = 3 × x = 3x  .

Or you could calculate the number of tomatoes she gathered for that 3 days by summing the number of tomatoes she had daily for that 3 days .

The firs day she gathered x number of tomatoes , the second day another x number and finally the last day another x number of tomatoes. Therefore,

x + x + x = 3x

9514 1404 393

Answer:

Step-by-step explanation:

Apparently, you are supposed to assume that ...

  y = g(x)

  y = 4 - x

For the one given value of x, the corresponding y value is ...

  y = 4 - 3 = 1

So, for that x-value, the table entry is (x, y) = (3, 1).

__

To find the missing x-values, you can solve the equation for x.

  y = 4 - x

  x + y = 4 . . . . add x

  x = 4 - y . . . .  subtract y

Now, for the given y-values, we can find the corresponding x:

  x = 4 -(-1) = 5   ⇒   (x, y) = (5, -1)

  x = 4 -(4) = 0   ⇒   (x, y) = (0, 4)

So, your table will be ...