Amita, Monica and Rita are three sisters.
Monica is x years old.
Amita is 3 years older than Monica.
Rita is twice the age of Amita.
If the mean age of the three sisters is 15, how old is Amita?

Answer:

1=58⁰....... 2=32⁰

Step-by-step explanation:

90⁰+32⁰=122⁰

180⁰-122⁰=58⁰

1=58⁰

Angle W and Y are equal

2=32⁰

Answer:

M<1 is 58

m<2 is 32

Step-by-step explanation:

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

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The change in the temperature is 11°.

Temperature is the physical quantity which describes, how much hot is something? Or we can say it is the quantity which measures the hotness and coldness of something. There are two main quantity values to measure the temperature which are Celsius and Fahrenheit.

Mathematically we can write :

1° Celsius = 32 Fahrenheit

Suppose if we have temperature of two difference time space then we can easily find the difference between the two by simply subtracting them.

For the given question,

last year temperature = 82 degree

temperature today = 71 degree

therefore the change in the temperature in one year is :

82 - 71 = 11 degree.

Thus , the change in temperature is 11 degree.

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the scientist needs to take a sample of at least 41 measurements of the river's depth to estimate the average depth with a 99% confidence level and a margin of error of 2 feet. We can use the following formula to determine the sample size needed:

n = \((z*σ / E)^{2}\)

Where:

n is the sample size

z is the z-score associated with the desired level of confidence (in this case, 2.576 for a 99% confidence interval)

σ is the standard deviation of the population

E is the margin of error (in this case, 2 feet)

Substituting the given values, we get:

n = \((2.576 * 4.33 / 2)^{2}\)

n = 40.22

Since we cannot have a fractional sample size, we need to round up to the nearest whole number:

n = 41

Therefore, the scientist needs to take a sample of at least 41 measurements of the river's depth to estimate the average depth with a 99% confidence level and a margin of error of 2 feet.

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Answer: The correct formula would be the 3rd option .5s + 4a = 15

Hope this helps!

’

Answer:

y = 3x = 1

Step-by-step explanation:

Answer:

y = 3x - 1

Step-by-step explanation:

Check. Plug in the given x, and see if the result is the given y:

y = 3x - 1

When: (x = 8 , y = 23)

23 = 3(8) - 1

23 = (3 * 8) - 1

23 = (24) - 1

23 = 23 (True).

When: (x = 2 , y = 5)

5 = 3(2) - 1

5 = (3 * 2) - 1

5 = 6 - 1

5 = 5 (True)

When: (x = -3 , y = -10)

-10 = 3(-3) - 1

-10 = (3 * -3) - 1

-10 = (-9) - 1

-10 = -10 (True).

When (x = 9 , y = 26)

26 = 3(9) - 1

26 = (3 * 9) - 1

26 = (27) - 1

26 = 26 (True).

When you graph, simply graph the given points (bolded) onto the graph.

The expected activity time for the given statement is = 5.33

The average amount of time required for an activity when it is repeatedly performed is known as the expected time. The weighted average of the three estimated times, i.e., the optimistic time, the most probable time, and the pessimistic time, is used in project management analysis to determine the expected time of activity.

A network model called the Program Evaluation and Review Technique (PERT) allows for randomness in the timing of activity completion. PERT was created in the late 1950s again for a massively labor-intensive Polaris project for the US Navy. It might shorten a lot of time and cost needed to finish a project.

optimistic = 2

most likely = 5

pessimistic = 10.

We will use the following formula to calculate the anticipated time for each activity in order to solve this problem:

Expected Time = (Optimistic Time + (4 x Most likely) + Pessimistic Time) / 6

Putting the values into formula:

= (2 + (4 x 5) + 10)/ 6

= (2 + 20 + 10) / 6

= 5.33

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For n independent Bernoulli's trial , with probability of success as "p" then , the

(a) probability of no failure is ⇒ pⁿ ,

(b) at least one failure is ⇒ 1 - pⁿ  ,

(c) at most one failure is ⇒ pⁿ + ⁿCₙ₋₁.pⁿ⁻¹(1-p) ,

(d) at least two failure is ⇒ 1 - [ pⁿ + ⁿCₙ₋₁.pⁿ⁻¹(1-p) ]  .

In the question ,

it is given that ,

number of Bernoulli's trials is = "n"  ;

the probability of success is ⇒ p ;

Part (a)

the probability of No Failure is equivalent to probability of all success .

= pⁿ .

Part(b)

The probability of at least one failure can be written as

= 1 - (probability of all success)

= 1 - pⁿ

Part(c)

the required probability of at most one failure is =

= probability of "No Failure" \(+\) probability of "One Failure"

= ⁿCₙpⁿ(1-p)⁰ + ⁿCₙ₋₁.pⁿ⁻¹(1-p)¹

= pⁿ + ⁿCₙ₋₁.pⁿ⁻¹(1-p)

Part(d)

the probability of at least two failure is =

= 1 - probability of "at most one failure"     ...substituting from part(c)  

= 1 - [ ⁿCₙpⁿ(1-p)⁰ + ⁿCₙ₋₁.pⁿ⁻¹(1-p)¹ ]

= 1 - [ pⁿ + ⁿCₙ₋₁.pⁿ⁻¹(1-p) ]

Therefore , the required probabilities are (a) pⁿ  ,

(b) 1 - pⁿ  ,

(c) pⁿ + ⁿCₙ₋₁.pⁿ⁻¹(1-p)  and  

(d) 1 - [ pⁿ + ⁿCₙ₋₁.pⁿ⁻¹(1-p) ]   .

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(a). The solution to the given equation is z = (9/2) + (23/2)i.

(b).  The value of complex numbers α is α = ± (1/√2)(1 + i).

(c).  No complex numbers `β` such that `β⁴ = −1`.

(a). Solving the equation z − 3z* = 28i − 18 in the set of complex numbers. Given the equation,

z − 3z* = 28i − 18,

let's put z = x + iy and solve for `x` and `y`. Therefore,

x + iy − 3x − 3iy = 28i − 18

Simplifying, we get

−2x − 2iy = 28i − 18 or -x - iy = -14i + 9.

Multiplying by `-i` on both sides, we have

x - iy = 14 + 9i.

Adding the above equation to -x - iy = -14i + 9, we get

2y = 23i − 5.

Therefore, y = (23/2)i − (5/2)

Substituting the value of `y` in the above equation, we get x = 9/2.

Therefore, the solution is z = (9/2) + (23/2)i.

(b) Find all complex numbers `α` such that `α² = i`.

To find all complex numbers `α` such that `α² = i`, we need to find the square roots of `i`.

Let's write `i` in polar form.

i = cos(π/2) + i sin(π/2)

 = e^(iπ/2).

Therefore, the two square roots of `i` are given by α = ± e^(iπ/4).

So, all complex numbers `α` such that `α^2 = i` are given by

α = ± (1/√2)(1 + i).

(c). Are there complex numbers `β` such that `β⁴ = −1`? Explain your answer.

Let's write `-1` in polar form.

-1 = cos(π) + i sin(π)

  = e^(iπ).

Therefore, the four roots of `-1` are given by

β = e^(iπ/4 + kπ/2) where `k = 0, 1, 2, 3`.

Substituting `k = 4`, we get

β = e^(iπ/4 + 2π)

  = e^(iπ/4).

Therefore, there are no complex numbers `β` such that `β⁴ = −1`.

Hence, the answer is "No".

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Answer:

\( {x ^{2} = \frac{25}{64} } \\ x = \sqrt{ \frac{25}{64} } \\ x = \frac{5}{8} \: \: x = - \frac{5}{8} \)

Answer:

\(48m^2-72mn\)

Step-by-step explanation:

We need to solve \((8m-3n)^2 - (4m+3n)^2\)

We know that,

\((a+b)^2=a^2+b^2+2ab\\\\(a-b)^2=a^2+b^2-2ab\)

Using the above formula,

\((8m-3n)^2 - (4m+3n)^2=(8m)^2+(3n)^2-2(8m)(3n)-[(4m)^2+(3n)^2+2(4m)(3n)]\\\\=64m^2+9n^2-48mn-(16m^2+9n^2+24mn)\\\\=64m^2+9n^2-48mn-16m^2-9n^2-24mn\\\\=48m^2-48mn-24mn\\\\=48m^2-72mn\)

So, the final answer is \(48m^2-72mn\).

Answer:

\(a_{n} =n-4\)

Step-by-step explanation:

With every number following, you just keep subtracting 4 from the previous number

Based on the information provided, the archaeological sample's estimated age is = 0.214136  years

Half life given is 5730

t₆.₅ = Ln2/k

k= ln 2/ 5730

The rate constant ,

k = 0.00012 year⁻¹

Given that 23 % of the 14C remains

then |A1|/|A2|  = 0.23

As we know ,

|A1|/|A2| = e ⁻₍kt₎

Hence, on solving the equation we get ,

ln(0.23)= -1.46967

t = -0.31471/ --1.46967

= 0.214136 years

The amount of time needed for a quantity (of substance) to decrease to half of its initial value is known as the half-life (symbol t12). In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long stable atoms last. The phrase is also used more broadly to describe any kind of exponential decay (or, very infrequently, nonexponential decay).

The biological half-life of medications and other compounds in the human body, for instance, is a term used in the medical sciences. Half-opposite life's in exponential growth is time's doubling.

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Answer:1200

Step-by-step explanation: hope this helps

Answer:

The price is 1,200 per foot

Solution:

540,000 ÷ 450 = 1,200

Message:

I hope this helps

Answer:

The area of the trapezoid:

A = (base1 + base2) x height/2

  = (6 + 12) x 8/2

  = 18 x 4

  = 72

Hope this helps!

:)

Answer:

53°

Step-by-step explanation:

the angles are oriented along the same point on the line crossing through a set of parallel lines so the angles will measure the same

(b) 734.0 ft-lbs of work is done.

To find the work done by the force, we need to use the formula:

Work = force x distance x cos(θ)

where:

force = 56 pounds (the given constant force)

distance = 16 feet (the distance the door is being pulled)

θ = 35 degrees (the angle between the force and the displacement of the door)

We need to convert the angle to radians to use it in the formula:

theta = 35 degrees x (pi/180) = 0.6109 radians

Now we can substitute the values into the formula:

Work = 56 pounds x 16 feet x cos(0.6109 radians)

Work = 734.0 ft-lbs (rounded to one decimal place)

Therefore, the answer is (b) 734.0 ft-lbs.

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Answer:

It would take 14 months for the center to reach its goal, and the line should be discrete because there cannot be partial members.

Step-by-step explanation:

At x = 14 months, the members will become 500 in number.

The general equation of a straight line is -

Other possible equations of line are -

We have the fitness center already has 150 members and adds an average of 25 members per month. The function f(x) = 150 + 25x represents the membership after [x] months.

We have the function as -

f(x) = 150 + 25x

Now, it can be seen from the graph that at x = 14 months, the members will become 500 in number.

Therefore, at x = 14 months, the members will become 500 in number.

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Answer:

Multiply to -63

and add to -2

Step-by-step explanation:

I'm a genius.

Answer:

(x - 9)(x + 7)

Step-by-step explanation:

Given

x² - 2x - 63

Consider the factors of the constant term (- 63) which sum to give the coefficient of the x- term, that is

numbers that multiply to give - 63 and add to give - 2

The factors are - 9 and + 7 , since

- 9 × 7 = - 63 and - 9 + 7 = - 2 , then

x² - 2x - 63 = (x - 9)(x + 7) ← in factored form

It can be deduced that the p-value is less than the level of significance.

It should be noted that the level of significance simply means the measure of the strength of the evidence that's is present in a sample before the null hypothesis is rejected.

From the complete question, the confidence interval is a given as (0.004, 0.176). In this case, the p-value is less than the level of significance and they should conclude that there's a difference between the proportions.

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Therefore, the annual annuity payment can be approximately $6,069,727.

To calculate the size of the annual annuity payment, we can use the present value formula for an ordinary annuity. The formula is given by:

PMT = PV / [(1 - (1 + r)⁻ⁿ) / r]

Where:

PMT = Annual annuity payment

PV = Present value of the annuity

r = Annual interest rate

n = Number of periods

Given:

PV = $230 million

r = 8% = 0.08

n = 40 years

Using the formula, we can calculate the annual annuity payment:

PMT = 230,000,000 / [(1 - (1 + 0.08)⁻⁴⁰) / 0.08]

PMT ≈ $6,069,727

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The Null hypothesis and alternative hypothesis for the given sample of cell phone spent time data of 32 randomly selected adults during lockdown and pre-pandemic times are,

H₀ : μd = 0

Hₐ : μd > 0

So, Correct option is option (d).

We have given that

A study obtained time data of 32 randomly selected young adults spent on their cell phones pre-pandemic and then during the lockdown phase of the pandemic. let us consider

L --> time spent on cell phone by adults during lockdown

P --> time spent on cell phone by adults at prepandemic time

and d = L- P

we want to perform a hypothesis testing on this sample .

The samples are dependent because same adults are being sampled before and after the lockdown.

Also, we need to test if mean time after is higher than mean time before so this is a right tailed test. Hence,

The correct hypotheses will be:

H₀ : μd= 0

Hₐ : μd> 0

Option D is correct.

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The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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Answer:

  24.1 billion

Step-by-step explanation:

One way to write the logistic function is ...

  P(t) = AB/(A +(B-A)e^(-kt))

where A is initial value (P(0)), and B is the carrying capacity (P(∞)). We are told to use relative population growth in the 1990s as the value for k.

In billions, we have ...

  A = 5.3

  B = 100

  k = 0.02/5.3 ≈ 0.003774 . . . . . relative growth rate at 20 M per year

  t = 2450 -1990 = 460

  \(P(t)=\dfrac{530}{5.3+94.7e^{-0.003774t}}\\\\P(460)=\dfrac{530}{5.3+94.7e^{-1.73604}}\approx \boxed{24.1\quad\text{billion}}\)

Answer:

A = 24

Step-by-step explanation:

Figure shown is a trapezoid

Area of a trapezoid = \(\frac{a+b}{2} h\)

where a and b = base lengths and h = height

The trapezoid shown has the following dimensions

Shorter base length (a) = 6

Longer base length (b) = 10

Height (h) = 3

Using these dimensions , plug in the values into the area formula

A = \(\frac{6+10}{2} 3\)

add 6 + 10 = 16

\(A=\frac{16}{2} 3\)

divide 16/2 = 8

\(A = (8)(3)\)

multiply 8 times 3

A = 24

The expected number of smokers in a random sample of 150 students from this university is 15.

To calculate the expected number of smokers in a random sample of 150 students at a university where 10% of students smoke, you simply multiply the total number of students in the sample by the percentage of students who smoke:
Expected number of smokers = Total number of students x Percentage of smokers
= 150 students x 10%
= 150 x 0.10
= 15
So, if we know that 10% of students smoke at this university, and we have a random sample of 150 students, we can calculate the expected number of smokers as follows:

Expected number of smokers = 150 x 0.10 = 15

Therefore, we can expect that there will be approximately 15 smokers in a random sample of 150 students from this university.


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In quantitative research, data collection from the same respondents at 2 or more points (waves) in time is referring to "longitudinal."

A method for gathering and interpreting numerical data is known as quantitative research. It can be used to discover patterns and averages, to make predictions, to verify causal linkages, and to generalize results to larger groups.

Some features regarding quantitative research are-

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