Which exponential functions have been simplified correctly? Check all that apply.

a. The inflow of financial capital to the United States during the 2008 global financial crisis would likely have a downward pressure on U.S. interest rates. When there is an increased demand for U.S. assets, such as Treasury bonds, investors are willing to accept lower yields, leading to a decrease in interest rates.

b. The inflow of financial capital to the United States would likely strengthen the U.S. nominal exchange rate. Increased demand for U.S. assets would lead to an increase in the value of the U.S. dollar relative to other currencies, resulting in a higher nominal exchange rate.

c. If relative prices remain fixed, the inflow of financial capital would likely appreciate the real exchange rate in the United States. The real exchange rate is the nominal exchange rate adjusted for inflation differentials between countries. The inflow of capital increases demand for the U.S. dollar, which leads to an increase in the nominal exchange rate. If relative prices remain unchanged, this increase in the nominal exchange rate would also translate into an increase in the real exchange rate.

d. The likely impact on the trade balance in the United States would be an increase in the trade deficit or a decrease in the trade surplus. When financial capital flows into the United States, it increases the demand for U.S. assets, including goods and services. This increased demand for U.S. assets could lead to an increase in imports, which, in turn, would worsen the trade balance.

e. If Purchasing Power Parity (PPP) does not exist between the United States and other countries, the impact on the trade balance could be different. PPP suggests that exchange rates adjust to equalize the prices of goods and services across countries. If PPP does not hold, it implies that exchange rates may not fully reflect the relative purchasing power between countries. In such a case, the impact of the inflow of financial capital on the trade balance may be less predictable and could be influenced by factors other than relative prices.

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Answer:

30000

Step-by-step explanation:

200x10x15=30000

Answer:

267.3

Step-by-step explanation:

area of a regular polygon =

(perimeter * apothem)/2

perimeter: 9 * 6.6 = 59.4

area: 59.4 * 9 = 534.6

534.6/2 = 267.3

area = 267.3

Answer:

see explanation

Step-by-step explanation:

look at the photo

Answer:

5/14

Step-by-step explanation:

The total number of coins Latanya has if she has 90 nickels and 150 pennies is 240.

The total number of coins Latanya has if she has n nickels and p pennies is n + p.

Latanya finds some nickels and pennies under the couch cushions.

Latanya has 90 nickels and 150 pennies.

Therefore, the number of coins she has can be calculated as follows:

number of nickels = 90

number of pennies = 150

Therefore,

total number of coins = 150 + 90

total number of coins = 240

If she has n nickels and p pennies, the total coins can be calculated as follows:

number of nickels = n

number of pennies = p

total coins = n + p

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The midpoint between the endpoints (9, -1) and (1, 15) is equal to (5, 7).

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Substituting the given parameters into the midpoint of a line segment formula, we have the following;

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Midpoint = [(9 + 1)/2, ((-1) + 15)/2]

Midpoint = [(10)/2, (14)/2]

Midpoint = (5, 7).

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Answer:

-8m + 24 - 32n

Step-by-step explanation:

(-8)(m) + (-8)(-3) + (-8)(4n) = -8m + 24 - 32n

Answer:

22

Step-by-step explanation:

Explanation

Step 1

apply distributive property

Step 2

add similar terms and order

so, the answer is

I hope this helps you

The length of the arc subtending a central angle of 9π/5 radians is 152.12m.

The radius of the given circle r = 26.9m

The measure of the central angle α = \(\frac{9\pi }{5}\) radians

The arc of a circle is defined as the part or segment of the circumference of a circle. Its length is the product of the central angle(in radian) and radius of the circle.

So, the length of the arc subtending a central angle of 9π/5 radians

l = rα

l = 26.9 * 9π/5

l = 152.12m

Therefore, the length of the arc subtending a central angle of 9π/5 radians is 152.12m.

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Answer:

Step-by-step explanation:

since  cos ^2  = 1/4 then cos = 1/2

b/c cot is  tan inverted, then  cot =  cos / sin

so we also know that  \(\sqrt{3}\)/2  will be sin for this same Ф

then

cot =  (1/2)  /  ( \(\sqrt{3}\)/2  )

cot = 1 / \(\sqrt{3}\)

since Ф is in quad III

we know both parts of the fraction will be negative

cot = -1 / -\(\sqrt{3}\)

but we would normally write that as a positive

Answer:

A

Step-by-step explanation:

Precession and nutation are two distinct motions of a spinning top or gyroscope. Precession is a slow, uniform motion that results from the gravitational force acting on a spinning top or gyroscope.

It is a slow, uniform motion in which the spinning object's axis of rotation moves in a cone-like motion.

Nutation is a fast, non-uniform motion that is caused by the torque of a nearby force. It is a rapid, irregular motion that causes the spinning object's axis of rotation to wobble back and forth.

Precession is a regular, predictable motion, whereas nutation is an unpredictable, irregular motion. Precession is typically used to describe the motion of a satellite or planet in its orbit, while nutation is used to describe the motion of a spinning top or gyroscope.

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Precession and nutation are two different types of rotational movements in astronomy.

Precession refers to the slow, conical movement of an object's rotational axis, which changes the orientation of the object over time. In the case of Earth, precession causes the direction of the North Pole to change over time.

Nutation, on the other hand, is a rapid, irregular movement of an object's rotational axis. It is caused by the combined gravitational forces of the Sun, Moon, and other celestial bodies on the Earth. Unlike precession, nutation occurs in small, cyclical changes in the orientation of the rotational axis, causing the axis to move slightly back and forth.

In summary, precession is a slow, systematic change in the orientation of an object's rotational axis, while nutation is a rapid, irregular movement of the axis caused by external forces.

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The lengths of lines KO and LN is; 24cm and 18m respectively.

Since the face of the building is an equilateral triangle and the sections of reinforcement are parallel to side JP;

On this note, since, MK = 18m +6m = 24m.

Similarly, since, ML = 18m

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Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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Answer:

A) f(x)

Step-by-step explanation:

f(x) has 4 x-intercepts, becoz it "cross" the x axis 4 times.

g(x) would have an infinite number of intercepts coz it is a cos function, but it gave a limit to the domain which is 0 to 2\(\pi\), so it only has 2 x-intercepts.

h(x) is the degree of x^3, so in theory, it has 3 x-intercepts.

The function that has the most x-intercept is given by: Option A: f(x)

The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function.

The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 becuase at that value of x, the function f(x) lies on x-axis, where y is 0. Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.

Suppose that we've got a polynomial function as y = p(x),

where p(x) is of degree n (the highest power its variable pertains in any of its composing terms).

Then, the maximum number of roots it can possess for p(x) = c (c is a constant), or p(x) - c = 0 is n

So, the number of roots of p(x) - c = 0 cannot exceed the degree of p(x).

From the graph, we see that:

f(x) intersects x-axis at 4 places, so it has 4 x-intercepts.

g(x) intersects the x-axis at 2 places as in the graph, and therefore, it has 2 x-intercepts.

h(x) is a polynomial of degree 3. The maximum number of intercepts it can have is the maximum number of roots h(x) = 0 can have which is 3(the degree of h(x) ). So it cannot be bigger than 3.

Thus, the function that has the most x-intercept is given by: Option A: f(x)

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Answer:

I wouldn't say this is entirely correct, but I think it's 45%.

Step-by-step explanation:

If you started with $90 and it was reduced 20%, than 25% MORE, the final percentage that was lowered would be the 20% and 25% added together.

The answer is 45%.

(Please do tell me if I got this wrong!!)

The original price reduced to 60%.

A percentage is a ratio or number that can be expressed as a fraction of 100. Additionally, it is denoted by the symbol "%."

On September 1, a dress was priced at $90. On October 1, the price was reduced by 20%.

That means,

the price is now = $90 - (90 x 20 /100) = $72

On November 1, the price was further reduced by 25% of the October 1 price.

The price is now = $72 - ( 72 x 25 / 100) = $54

To find the percentage of original price;

The percentage of original price

= 5400 / 90

= 60%

Therefore, the final price is 60% of the original price.

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296 hot lunches were sold on Friday.

The number of hot lunches sold on Friday can be calculated by multiplying the total number of hot lunches by the relative frequency on Friday:

Hot lunches sold on Friday = 1,350 * 0.22 = 296

Relative frequency is a measure of the number of times an event occurs in a sample, expressed as a proportion of the total number of events. To find the number of hot lunches sold on Friday, we multiply the total number of hot lunches sold in the week by the relative frequency of Friday. This gives us the number of hot lunches sold on Friday, which is 296 in this case. Understanding relative frequency is important in statistics as it helps to summarize data and understand the distribution of events.

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∑ (-1)ⁿ xⁿ/n   is convergent for  x ∈ (−1,1].

Given the series ∑ (-1)ⁿ xⁿ/n

we can use the ratio test by evaluating:

n/(n+1) |x|

So we get two cases,

i) x = 1

∑ (-1)ⁿ xⁿ/n  = (-1)ⁿ/n which is the alternate harmonic series and is convergent.

ii) ∑ (-1)ⁿ xⁿ/n = ∑ (-1)ⁿ  (-1)ⁿ/n = ∑ 1/n which is the harmonic series and is divergent.

In conclusion the series is convergent for x ∈ ( -1, 1].

A power series' radius of convergence is equal to the diameter of the biggest disk at the series' convergence point. A non-negative real number or are both possible. When it is positive, the power series converges to the Taylor series of the analytical function absolutely and evenly on compact sets inside the open disk with radius equal to the radius of convergence.

The radius of convergence is the shortest or smallest of all the estimated distances from the center of the disk of convergence to each individual singularity of a function in the event of multiple singularities (singularities are those values of the argument for which the function is not defined).

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Answer:

We can see that after 2 years, enrollment becomes 35 instead of 15.

35/15=2.333...)

Since it's exponential, take sqrt(2.333...)=about 1.5

So the growth is 50%

Answer:

Step-by-step explanation:

a = -3 ; b = -6  ; c = -11

D = b² - 4ac

 = (-6)² - 4*(-3)*(-11)

 = 36 - 132

 = - 96

\(\sqrt{D}=\sqrt{-96}=\sqrt{96i^{2}} =9.8i\)

\(x =\dfrac{-b+\sqrt{D}}{2a} \ ; \ x =\dfrac{-6-\sqrt{D}}{2a}\\\\\\x=\dfrac{6+9.8i}{2*(-3)} \ ; \ x=\dfrac{6-9.8i}{2*(-3)}\\\\\\x=\dfrac{6}{-6}+\dfrac{9.8}{-6}i \ ; \ x=\dfrac{6}{-6}-\dfrac{9.8}{-6}i\\\\\\x=-1-\dfrac{4.9}{3}i \; \ x=-1+\dfrac{4.9}{3}i\)

Answer:

Answer is 9.

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The probability density function (pdf) of the random variable X is given by f(x) = 0.1. This means that the probability of X taking a specific value within a certain interval is determined by integrating the function f(x) = 0.1 over that interval.

The given statement implies that the probability density function (PDF) of the random variable x is f(x) = 0.1, where x takes on a specific value. It is important to note that the PDF of a continuous random variable provides the relative likelihood of different outcomes occurring. Therefore, the probability of x taking on a specific value is zero, as the PDF of a continuous random variable only gives probabilities for intervals of values.

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Let X be the number of people who experience mild side effects after taking the drug. X follows a binomial distribution with parameters n = 100 (the number of people taking the drug) and p = 0.75 (the probability of mild side effects).

To find the probability that more than 70 people will experience mild side effects, we need to calculate:

P(X > 70) = 1 - P(X ≤ 70)

Using the cumulative distribution function (CDF) of the binomial distribution, we can find:

P(X ≤ 70) = F(70) = ∑(i=0 to 70) [nCi * p^i * (1-p)^(n-i)]

where nCi is the binomial coefficient for choosing i items out of n.

We can use a software or calculator to calculate this sum, or use an approximation like the normal approximation to the binomial distribution.

Assuming normal approximation is appropriate, with mean μ = np = 75 and standard deviation σ = sqrt(np(1-p)) = 3.354, we can calculate the z-score:

z = (70.5 - μ) / σ = (70.5 - 75) / 3.354 = -1.33

Using a standard normal distribution table or a calculator with normal distribution functions, we can find the probability of z-score less than -1.33 is 0.0918, which is the probability of 70 or fewer people experiencing mild side effects.

Therefore, the probability of more than 70 people experiencing mild side effects is:

P(X > 70) = 1 - P(X ≤ 70) = 1 - 0.0918 = 0.9082

Using the binomial distribution, there is a probability of approximately 0.9082 that more than 70 people will experience mild side effects out of 100 people who take the drug.

Step 1

Given:

Required; To pick the phrase that matches the algebraic

The width of the confidence interval increases as the sample size increases and decreases as the confidence interval decreases. The confidence interval decreases as the sample size increases and increases as the confidence level increases.

Sample size is defined as the number of observations used to determine

an estimate of a particular population. The size of the model is drawn by people. Sampling is the process of selecting a group of individuals from a population to estimate the characteristics of the entire population. Select the number of establishments in a population group for analysis.

The sample size increases with the square of the standard deviation and decreases with the square of the difference between the mean under the alternative hypothesis and the mean under the null hypothesis.

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Solution:

Note that:

Finding the area of triangle:

Finding the perimeter of triangle:

All five answers are (1) 285.7 ft2 (2) 1056 cm2 (3) 105 mm3 (4) 108 cm3 (5) 628 mm3 in accordance with the provided assertion.

In mathematics, volume refers to the amount of space present within a specific 3D object. As an example, the dimensions of a fish aquarium are three feet long, one foot broad, and two feet height.

By increasing the length, width, and height, or 3x1x2, which also equals six, the volume is determined. Consequently, the fish tank has a 6 cubic foot size.

(1) The lateral area of a cone can be calculated using the formula L = πrℓ, where r is the radius and ℓ is the slant height. Using the given values, we have:

L = π(7)(13) ≈ 285.7 ft²

Rounding to the nearest tenth, the answer is 285.7 ft².

(2) A = B + (1/2)Pl, where B is the base area, P is the base circumference, l is the slope height, and A is the surface area, can be used to determine the surface area of a square pyramid. Since the pyramid's foundation is square, we have:

B = (24)² = 576 cm²

The perimeter of the base is 4 times the base length, so we have:

P = 4(24) = 96 cm

Now we can use the formula to find the surface area:

A = 576 + (1/2)(96)(16) = 1056 cm²

Therefore, the surface area of the square pyramid is 1056 cm².

(3) The volume of a rectangular prism can be calculated using the formula V = lwh,

where

l is the length

w is the base

h is the height

V is the volume.

Substituting the given values, we have:

V = (5)(7)(3) = 105 mm³

Therefore, the volume of the rectangular prism is 105 mm³.

(4) The formula V = (1/3)Bh, where B is the base area, h is the height, and V is the volume, can be used to determine the volume of a square pyramid. Since the pyramid's foundation is square, we have:

B = (9)² = 81 cm²

Now we can use the formula to find the volume:

V = (1/3)(81)(4) = 108 cm³

Therefore, the volume of the square pyramid is 108 cm³.

(5) The volume of a cone can be calculated using the formula V = (1/3)πr2h, where r is the radius, h is the height, and V is the volume. Substituting the given values, we have:

V = (1/3)π(10)²(6) ≈ 628.3 mm³

Rounding to the nearest whole number, the answer is 628 mm³.

Therefore, the volume of the cone is 628 mm³.

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