Two weeks ago i bought 20 cupcakes last week I bought 13 help me continue the pattern

The Great Rift Valley of Africa was formed by tectonic-plates diverging from each other, and the land between them sinking or subsiding.

The "Great-Rift-Valley" is a geological feature in East Africa that stretches over 6,000 kilometers (3,700 miles). It is a result of the movement of tectonic plates in the Earth's crust.

The African continent is situated on the African Plate, which is bordered by the Arabian Plate in the northeast. As these plates diverge, the Earth's crust weakens, and the land between them sinks down, creating a large depression known as a rift valley.

This process is known as rifting and has resulted in the formation of the Great Rift Valley of Africa.

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The given question is incomplete, the complete question is

Fill in the banks.

The Great Rift Valley of Africa was formed by tectonic plates ___________ and the land _________.

74%

Find how many times 50 goes into 100. Then, take that number and multiply it by 37. Then you should get your answer.

Emma's luggage may be lost with probability p = 0.1. The luggage and its content are estimated to be worth 316.05. Emma's utility insures against the loss of the luggage. What is the maximum insurance premium I that Emma would be willing to pay?

Solution:To calculate Emma's maximum insurance premium, let's start by calculating her expected utility if she doesn't insure her luggage.U (no insurance) = 0.9 x U (316.05) + 0.1 x U (0)where U (316.05) is Emma's utility function for 316.05 value, and U (0) is Emma's utility function for a loss of the luggage. Emma has not insured her luggage, hence, if it gets lost, she will get 0 value for it.A sum of 316.05 is worth more than 0, Emma will still get a certain amount of utility, which will be larger than 0.

Therefore, Emma's utility function is likely to be positive, so let us assume that U (0) = 0.If we plug this information into the above equation, we will have:U (no insurance) = 0.9U (316.05) + 0.1 × 0 = 0.9U (316.05)Hence, Emma's expected utility, if she doesn't insure her luggage, will be 0.9U (316.05).However, if Emma chooses to insure her luggage, she will pay the insurance premium I. If the luggage gets lost, she will get reimbursed by the insurance company for 316.05. Her expected utility function, if she insures her luggage, will be:

U (insurance) = 0.9U (316.05 – I) + 0.1U (316.05)Where U (316.05 – I) is Emma's utility function for 316.05 – I value. Emma will get this amount if the luggage is not lost, but she has to pay the premium I.If we compare Emma's expected utility when she insures her luggage and when she doesn't insure her luggage, we will have the following inequality:

U (insurance) ≥ U (no insurance)0.9U (316.05 – I) + 0.1U (316.05) ≥ 0.9U (316.05)Let us solve this inequality:0.9U (316.05 – I) + 0.1U (316.05) ≥ 0.9U (316.05)0.9U (316.05 – I) ≥ 0.8U (316.05)U (316.05 – I) ≥ 0.89U (316.05)Since U (316.05 – I) is a decreasing function, it will get smaller as I gets larger.

Hence, to maximize Emma's expected utility, we need to minimize the insurance premium I that she pays to the insurance company.If Emma doesn't insure her luggage, her expected utility will be 0.9U (316.05)Emma will choose to insure her luggage if her expected utility is larger if she insures her luggage.U (insurance) = 0.9U (316.05 – I) + 0.1U (316.05)0.9U (316.05 – I) ≥ 0.8U (316.05)U (316.05 – I) ≥ 0.89U (316.05)Emma will choose to insure her luggage if her expected utility is larger if she insures her luggage. Hence,Emma's maximum insurance premium I that Emma would be willing to pay is $31.35.

If Emma chooses to insure her luggage, she will pay the insurance premium I. Her expected utility function, if she insures her luggage, will be U (insurance) = 0.9U (316.05 – I) + 0.1U (316.05). Emma will choose to insure her luggage if her expected utility is larger if she insures her luggage. Therefore, Emma's maximum insurance premium I that Emma would be willing to pay is $31.35. The utility function is considered decreasing as Emma has to pay more premium.

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The exact value of tan(2arcsin(x)) is 2x / √(1 - x²), where |x| ≤ 1.

To find the exact value of tan(2arcsin(x)), we start by considering the definition of arcsin. Let θ = arcsin(x), where |x| ≤ 1. From the definition, we have sin(θ) = x.

Using the double angle identity for tangent, we have tan(2θ) = 2tan(θ) / (1 - tan²(θ)). Substituting θ = arcsin(x), we obtain tan(2arcsin(x)) = 2tan(arcsin(x)) / (1 - tan²(arcsin(x))).

Since sin(θ) = x, we can use the Pythagorean identity sin²(θ) + cos²(θ) = 1 to find cos(θ). Taking the square root of both sides, we have cos(θ) = √(1 - sin²(θ)) = √(1 - x²).

Now, we can determine the value of tan(arcsin(x)) using the definition of tangent. We know that tan(θ) = sin(θ) / cos(θ). Substituting sin(θ) = x and cos(θ) = √(1 - x²), we get tan(arcsin(x)) = x / √(1 - x²).

Finally, substituting this value into the expression for tan(2arcsin(x)), we obtain tan(2arcsin(x)) = 2x / (1 - x²).

Therefore, the exact value of tan(2arcsin(x)) is 2x / √(1 - x²), where |x| ≤ 1.

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Answer:

To determine the speed, we can use the formula:

speed = distance / time

where distance is measured in feet and time is measured in minutes.

In this case, the distance is 264 feet and the time is 3 minutes. Plugging these values into the formula, we get:

speed = 264 feet / 3 minutes

simplifying, we get:

speed = 88 feet/minute

Therefore, the equipment is traveling at a speed of 88 feet per minute.

The total income is represented by: 5r - 2c - 3p

The rent is $500 (r = 500)

The cable bill is $80 (c = 80)

The phone bill is $40 (p = 40)

Replacing these data into the equation, we get:

Income = 5(500) - 2(80) - 3(40)

Income = 2500 - 160 - 120

Income = $2220

Answer:

Step-by-step explanation:

10 yards by 15 yards

Step-by-step explanation:

Let the dimensions of each plot x yards by y yards.

If three plots are placed as the y-yards side are common to them then,  

The total perimeter will be (6x + 4y) = P = 120 yards {Given} ........... (1)

⇒ 3x + 2y = 60 ........... (2)

Now, the total area of the three plots will be 3xy = A = 450 sq, yards {Given} .......... (3)

Now, solving equations (2) and (4) we get,

⇒ 225 + y² = 30y

⇒ y² - 30y + 225 = 0

⇒ (y - 15)² = 0

⇒ y = 15 yards.

Hence, from equation (4) we get,

x = 150/15 = 10 yards.

Therefore, the dimensions of each plot are 10 yards by 15 yards.

Answer:

If Nellie does not do her homework, the her dad does not take her out for ice cream

(if negative ~q, then negative ~p.)

Answer:

2nd problem

The sum of the angles of the triangle is 180°.

B= 90°

\(2^{-5} \cdot 3 \cdot 2^2 \cdot 3^3\\\\=2^{-5 +2} \cdot 3^{1+3}\\\\=2^{-3} \cdot 3^4\\\\=\dfrac{3^4}{2^3}\\\\=\dfrac{81}{8}\\\\\\\text{So, the answer is C.}\)

Answer:

They would fall in the same year every 10 years

Step-by-step explanation:

Here in this question, we are interrelated in calculating the number of years it will take the alumni reunion and the alumni soccer game to fall in the same year.

Now looking at the number of years, we can see we have every 2 and every 10 years

To get the year in which they happen at the same time, we can simply find the lowest common multiple of 2 and 10 and that would be 10

This can be visualized in a way that;

The reunion has happened now, and will happen in the next 10 years.

Now since the soccer game has happened now, in the next 10 years, we shall be having 5 episodes. This means that it will take up to the 10th year before we have the soccer game and the alumni reunion occurring at the same time and the mathematical reason for this is that , 10 is the lowest common multiple of 10 and 2

Answer:

1 times

Step-by-step explanation:

Hello,

The alumni have reunions every 10 years

But also have football games every 2 years

We have to find how often do the football and reunion fall the same year.

Working with a space of 10 years

In 10 years, reunions happen only once

In 10 years, soccer games happen five times

Assuming we're in the year 2020,

The next reunion would likely occur in year 2030.

But soccer games will happen in year 2022, 2024, 2026, 2028 and finally 2030.

Checking both soccer and reunion coincidence, we can only find one which is in year 2030.

So, soccer games and reunions happen once in 10 years

The inverse of the statement is "If a number does not have exactly two distinct factors, then the number is not prime." Thus Option 2 is the answer.

   When a conditional statement is reversed, the hypothesis and conclusion are both negated. The hypothesis in the original statement is "a number with exactly two distinct factors," while the conclusion is "is prime."

  To make the inverse, we negate both sections. "A number does not have exactly two distinct factors" is the antonym of "A number that has exactly two distinct factors." "Is not prime" is the opposite of "is prime."

    As a result, the inverse statement is "If a number does not have exactly two distinct factors, then the number is not prime."

     It's crucial to remember that a statement's inverse could or might not be accurate. In this instance, the inverse is true since the definition of a prime number is incompatible with the fact that a number has more than two components if it has more than exactly two different factors.

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Therefore, integrate the norm of the curve's tangent vector over a specified interval. An example curve could be y = x^2, with the arc length calculated by integrating the square root of 1 + (2x)^2 over a given interval.

A line integral can determine the arc length of a curve c by integrating the norm of the curve's tangent vector over a specified interval. The formula for arc length is given by the integral of the middle of the curve's derivative with respect to its parameter. This involves taking the square root of the sum of the squares of the components of the derivative and integrating this result over the interval of interest. An example of a curve that is not part of a circle could be the curve defined by the equation y = x^2. To calculate its arc length, we would first need to find its derivative, which is y' = 2x. Then, we would integrate the square root of 1 + (2x)^2 over the interval of interest, such as from x = 0 to x = 2.

Therefore, integrate the norm of the curve's tangent vector over a specified interval. An example curve could be y = x^2, with the arc length calculated by integrating the square root of 1 + (2x)^2 over a given interval.

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The length of the curve r(t) over the interval 0 ≤ t ≤ 2π is approximately 285.97 units.

The length of the curve given by the vector-valued function r(t) over the interval [a, b] is given by the formula:

L = ∫[a,b] ||r'(t)|| dt

where r'(t) is the derivative of r(t) with respect to t and ||r'(t)|| is its magnitude.

In this case, we have:

r(t) = ⟨4cos(5t), 4sin(5t), t^(3/2)⟩

r'(t) = ⟨-20sin(5t), 20cos(5t), (3/2)t^(1/2)⟩

||r'(t)|| = √( (-20sin(5t))^2 + (20cos(5t))^2 + ((3/2)t^(1/2))^2 )

||r'(t)|| = √( 400sin^2(5t) + 400cos^2(5t) + (9/4)t )

||r'(t)|| = √( 400 + (9/4)t )

So the length of the curve over the interval [0, 2π] is:

L = ∫[0,2π] √( 400 + (9/4)t ) dt

Making the substitution u = 20t^(1/2)/3, we get:

du/dt = 10t^(-1/2)/3

dt = (3/10)u^(-1/2) du

When t = 0, u = 0, and when t = 2π, u = 20√(π)/3. Substituting these values and simplifying, we get:

L = ∫[0,20√(π)/3] √( 1 + u^2 ) du

Using the substitution x = sinh(u), we get:

dx/dt = cosh(u)

dt = dx/cosh(u)

When u = 0, x = 0, and when u = 20√(π)/3, x = sinh(20√(π)/3). Substituting these values and simplifying, we get:

L = ∫[0,sinh(20√(π)/3)] √( 1 + sinh^2(x) ) dx

L = ∫[0,sinh(20√(π)/3)] cosh(x) dx

Using the formula for the integral of cosh(x), we get:

L = sinh(sinh(20√(π)/3)) - sinh(0)

L ≈ 285.97

Therefore, the length of the curve r(t) over the interval 0 ≤ t ≤ 2π is approximately 285.97 units.

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Answer:

thats a non-linear function

Step-by-step explanation:

the line is not straight

Based on the samples that the scientists picked, and the weight of these samples, the various sample means are:

The range of the sample means is 0.4 pounds.

The true statements on the mean weights to be used by the scientists are:

First, find the sample means of each sample.

Sample 1:

= (3 + 2 + 6 + 4 + 2) / 5

= 3.4 pounds

Sample 2:

= (2 + 2 + 3 + 7 + 3) / 5

= 3.4 pounds

Sample 3:

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

= 3.6 pounds

Sample 4:

= (5 + 3 + 2 + 5 + 4) / 5

= 3.8 pounds

The range is;

= 3.8 - 3.4

= 0.4

The closer the range of the mean is to 0, the better the sample because it shows that in general, the sample means are the same. This is good for the research because it points to the uniformity of fish weights.

Using all the sample means as an average captures the data better than if a single sample mean is used.

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The value of  the function (f + g)(x) = \(x^{2}\) -5x + 9

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

f(x) = - 2x + 4, g(x) = \(x^{2}\) -3x + 5

(f+g)(x) = f(x) + g(x)

So by adding the two functions

(f + g)(x) = -2x + 4 + \(x^{2}\) -3x + 5

(f + g)(x)  = \(x^{2}\) -5x + 9

In conclusion, the value of \(x^{2}\) -5x + 9

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Answer:

It is a rational number.

Step-by-step explanation:

A rational number is a number that repeats with the same number, or terminates. An irrational number is a number that repeats, but not with a constant number, like pi for example. 3.739 terminates at the end, so it is a rational number.

Hope this helps :)

Answer:

\(8( \frac{x}{4} - 6) > 4\)

\( \frac{8x}{4} - 48 > 4\)

\(2x - 48 > 4\)

\(2x > 4 + 48\)

\(2x > 52\)

\(x > \frac{52}{2} \)

\(x > 26\)

The single natural logarithm expression is ln(2). Therefore, correct answer is (a)

The expression in the form \(e^a=b\) can also be written as In b = a  which is called as logarithmic expression.

Properties of Logarithms:

1. In (mn) = In m + In n

2. In \(a^m =\) m In a

3. In \(e^a\) = a.

The natural logarithm expression is:

4 + ln 2 - ln 4

Apply the product and quotient rule of natural logarithm:

4 + ln 2 - ln 4  = In (4 × 2/4)

Evaluate the quotient:

4 + ln 2 - ln 4  = In (2)

Hence, the single natural logarithm expression is ln(2).

The correct option is (a)

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Answer:

B: ln 4.

Step-by-step explanation:

Answer:

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Parallel lines divide transversals proportionally.

Set proportions and solve for x:

The solution of the given equation is y = y = e^(6x -∞) ,y = e^(6x)

The given equation is a first-order linear differential equation with constant coefficients. Applying the integrating factor, we get:

\(I = e^(int (6 dy/6y)) = e^(ln y)\)

Multiplying both sides of the equation by I:

\(Iy' = 6y5/6 ⇒ dy/y = 6/6 dy ⇒ ln y = 6x + c\)

Therefore, the general solution of the given equation is:

y = e^(6x + c)

Substituting the initial condition, y(0) = 0 to the above equation, we get:

\(0 = e^(6(0) + c) ⇒ c = -∞\)

Therefore, the solution of the given equation is:

y = e^(6x -∞)

Solution 2:

The given equation is a first-order linear differential equation with constant coefficients. Applying the integrating factor, we get:

\(I = e^(int (6 dy/6y)) = e^(ln y)\)

Multiplying both sides of the equation by I:

Iy' = 6y5/6

⇒ dy/y = 6/6 dy

⇒ ln y = 6x + c

Therefore, the general solution of the given equation is:

y = e^(6x + c)

Substituting the initial condition, y(0) = 0 to the above equation, we get:

0 = e^(6(0) + c)

⇒ c = 0

Therefore, the solution of the given equation is:

y = e^(6x)

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The equation in slope-intercept form representing the number of questions on the test is y = 5x + 10.

To write the equation in slope-intercept form, we need to determine the relationship between the number of spelling questions (x) and the number of vocabulary questions (y) on the test.

Given that spelling questions are worth 5 points and vocabulary questions are worth 10 points, we can express the total number of points on the test as 5x + 10y. Since the maximum number of points on the test is 100, we have the equation 5x + 10y = 100.

To write the equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept, we rearrange the equation. First, we divide both sides of the equation by 10 to simplify: x + 2y = 20.

Next, we isolate y by subtracting x from both sides: 2y = -x + 20. Finally, we divide both sides by 2 to solve for y: y = -0.5x + 10.

Therefore, the equation in slope-intercept form representing the number of questions on the test is y = 5x + 10.

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Answer:

sale price

Step-by-step explanation:

price of an item that is being offered at a lower price than usual

The value of the gift card declined by $37.40.

The total cost of all the items purchased has to be determined.

The sum of these items is $37.40

Change in value = value of the gift card - cost of items

$50 - $37.40 = $12.60

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Answer:

Total cost of pens = $1.57 x 1 = $1.57

Total cost of pencils = $1.98 x 2 = $3.96

Total cost of folders = $0.75 x 6 = $4.50

Total cost of highlighter: $3.45 x 1 = $3.45

Total cost of notebooks: $2.95 x 5 = $14.75

Total cost of binders: $3.55 x 2 = $7.10

Total cost of paper: $0.69 x 3 = $2.07

The sum of these items is $37.40

Change in value = value of the gift card - cost of items

$50 - $37.40 = $12.60

Step-by-step explanation:

Answer:

answer of this question is A

Answer:

dollars per mile

$0.90 per mile

Step-by-step explanation:

Since you are interested in the price of a 42-mile ride, you need a unit cost of dollars per mile. The time the trip takes does not matter.

unit price in dollars per mile = (price)/(number of miles)

unit price = $50.40/(56 miles) = $0.90/mile

Answer the unit price is $0.90 per mile