I spent $5,200 in interest on a loan. If I paid my
loan off over 5 years at a rate of 8%, what was
the initial amount of money I borrowed?

Answer:

the answer is 1

Step-by-step explanation:

2+(-1)

2-1

1

+ and - always result in - so +(-1) is -1 and 2-1 is 1.

Answer:

1

Step-by-step explanation:

Negative 1 is used as a minus sign. I canceled the plus and now the equation is 2-1

The statement opportunity cost for Germany to produce 1 beer is 1/2 motorcycles is true.

The German economy would be better off if it produced beer and traded motorcycles with the US.

Germans would benefit from specializing in producing beer and engaging in trade with the United States since their opportunity cost is lower (1/2 is less than 3).

A country is said to be having a comparative advantage in producing a good if it can produce it at a lower opportunity cost. Germany has a lower opportunity cost in producing beer so it has a comparative advantage in making beer.

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Except falsifiability all of the following are standards used to determine the best explanation.

Given standards for scientific method,

Now,

It is important for science/mathematics to be falsifiable because for a theory to be accepted it must be able to be proven false. Otherwise, theories that are arrived through testing cannot be accepted. They are only accepted if their falsifiability can be disproved.

A scientific hypothesis, according to the doctrine of falsifiability, is credible only if it is inherently falsifiable. This means that the hypothesis must be capable of being tested and proven wrong.

Thus integrity , simplicity , power are standards used to determine the best explanation for scientific method.

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Answer:

4^8

Step-by-step explanation:

If the second 4 is an exponent, as in (4^2)^4, then multiply the exponents.

(4^2)^4 = 4^(2 * 4) = 4^8

Answer:

nine  million, three  hundred - thousand, six hundred ninety - five

Step-by-step explanation:

nine  million, three  hundred - thousand, six hundred ninety - five

9,000,000.                     300,000.                  600.           95.

Answer:

Step-by-step explanation:

nine million three hundred thousand six hundred and ninety five

The probability that valley 1 is also infected is 15%

The math term probability is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Here we have know that two valleys are sometimes infected with tree rot.

The probability of rotting valley 1 = 35%

The probability of rotting valley 2 = 60%

And the probability that at least one is infected = 80%

When we convert these values into decimal then we get,

The probability of rotting valley 1 = 0.35

The probability of rotting valley 2 = 0.6

And the probability that at least one is infected = 0.8

Then the probability that valley 1 is also infected is

=> P = 0.35 + 0.6 - 0.8

=> P = 0.15

When we convert it into percentage then we get,

=> P = 15%.

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Answer:

Obtuse

Step-by-step explanation:

Believe it's a right triangle (12,16,20) 4 from everything

Step-by-step explanation:

Answer:

x > -7

-7x > 49

Multiply both sides by (-1) (Reverse inequality)

(-7x) (-1) < 49 (-1)

Simplify

7x < -49

Divide both sides by 7

7x/7 < -49/7

Simplify = x > -7

Answer:

1,420,236

Step-by-step explanation:

According to the problem, computation of the given data are as follows,

Total number of applicants = 35,505,900

Applicants admitted = 4% of total number of applicants

So, Number of successful applicants = Applicant admitted percent × Total number of applicant

By putting the value, we get

Number of successful applicants = 35,505,900 × 4%

= 1,420,236

Answer:

128*         angle EFZ &angle BYG

Step-by-step explanation:

The definite integral, taken from 0 to 3, of the expression 3(y − 2)(2y+1) with respect to y, evaluates to 27/2.

To evaluate the integral ∫(0 to 3) 3(y − 2)(2y+1) dy, we first need to expand the expression inside the integral:

3(y − 2)(2y+1) = 6y² - 9y - 6

Now we can integrate this expression with respect to y,

using the power rule of integration:

∫(0 to 3) 6y² - 9y - 6 dy = [2y³/3 - (9/2)y² - 6y] from 0 to 3

Evaluating this expression at the upper and lower limits of integration, we get:

Therefore, the value of the integral ∫(0 to 3) 3(y − 2)(2y+1) dy is 27/2.

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The Standard Deviation of sample means is 1.072 and Population standard deviation is 1.708.

a. Since we roll a fair die two times, there are 6 possible outcomes for each roll. Therefore, there are 6 x 6 = 36 different samples.

b. The possible samples are:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

To calculate the mean and standard deviation of the sample means and the distribution of the population, follow these steps:

1. Calculate the sample mean for each sample: (sum of sample values)/2
2. Calculate the population mean: (sum of all sample means)/36
3. Calculate the variance of the sample means: sum of [(each sample mean - population mean)^2]/36
4. Calculate the standard deviation of the sample means: square root of variance
5. Calculate the population standard deviation: square root of [(sum of (each die value - population mean)^2)/6]

Mean of sample means: (3.5)
Population mean: (3.5)
Standard Deviation of sample means: (1.072)
Population standard deviation: (1.708)

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Answer:

(14, - 3 )

Step-by-step explanation:

Under the translation < 6, 0 >

Add 6 to the x- coordinate and 0 to the y- coordinate, that is

B(8, - 3 ) → B'(8 + 6, - 3 + 0 ) → B'(14, - 3 )

Answer:

If every line parallel to two lines intersects both regions in line segments of equal length, then the two regions have equal areas. In the case of your problem, every line parallel to the bases of the two parallelograms will intersect them in lines segments, each with a width of ℓ.

There are infinitely many parallelograms with the same area and base due to the variability of the height.

We have,

There is always more than one parallelogram with the same area and base because the height of the parallelogram can vary while keeping the base and area constant.

The formula to calculate the area of a parallelogram is:

Area = base × height

If the base and area of a parallelogram are fixed, we can rearrange the formula to solve for the height:

height = Area/base

Since the height can be any value as long as it satisfies the above equation, there are infinitely many possible heights for a given base and area.

And for each height, there will be a unique parallelogram with that base and area.

Imagine a rectangle as a special case of a parallelogram where all angles are 90 degrees.

For a given base and area, you can have an infinite number of rectangles by varying the height.

Each rectangle will have different side lengths, but they will all have the same base and area.

Thus,

The variability of the height while keeping the base and area constant allows for the existence of multiple parallelograms with the same area and base.

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The equivalent form f(x)+g(x) of algebric equations f(x)=2x²+3x-1 and g(x)=2(x-2)² is 4x² - 5x + 7.

Firstly, Let us simplify the first given algebraic equation g(x),

g(x) = 2(x-2)²

= 2(x² - 4x + 4)

= 2x² - 8x + 8

We can determine f(x) + g(x) because f(x) + g(x) is not a type composition in which one function alters the structure of the other during recombination (x), By merely combining the condensed versions of f(x) and g (x),

f(x) + g(x)

= (2x² + 3x - 1) + (2x² - 8x + 8)

= (2+2)x² - (3+5)x + (8-1)

= 4x² - 5x + 7

Therefore, the equivalent form of f(x) + g(x) is 4x² - 5x + 7.

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y(x) = tan(x + C) where C is an arbitrary constant of integration. Thus, the equilibrium solutions are y = 1 and y = -1. The non-equilibrium solutions are the values of y that make y' not equal to 0.

y(x) = tan(x + C)

Where C is an arbitrary constant of integration.

The solution y(x) = tan(x + C) is a family of functions indexed by the arbitrary constant C. The constant C cannot be determined from the information given in the problem, and so the general solution contains all possible specific solutions.

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Answer:

C. 1,000

Step-by-step explanation:

Jenny starts at 2,000 and ends at 3,000

3,000 - 2,000 = 1,000

Hope this helps :)

There is sufficient evidence to believe that the number of household pets leaving the shelter over the weekend is different from the proportion of wildlife animals leaving the shelter over the weekend.

To determine if there's sufficient evidence,

Let us define the null and alternative hypotheses for this test as follows:

Null hypothesis (H0): The proportion of household pets leaving the shelter over the weekend is the same as the proportion of wildlife animals leaving the shelter over the weekend.

Alternative hypothesis (Ha): The proportion of household pets leaving the shelter over the weekend is different from the proportion of wildlife animals leaving the shelter over the weekend.

The test statistic for two sample test is given by:

z = (p1 - p2) / sqrt(p * (1 - p) * (1/n1 + 1/n2))

where

p1 and p2 are the proportions of household pets and wildlife animals leaving the shelter over the weekend, respectively,

p is the pooled proportion,

n1 and n2 are the sample sizes for household pets and wildlife animals, respectively.

Pooled proportion is

p = (x1 + x2) / (n1 + n2)

where x1 and x2 are the number of household pets and wildlife animals leaving the shelter over the weekend, respectively.

Given

-n1 = 376, n2 = 52, x1 = 29, x2 = 10

p = (29 + 10) / (376 + 52) = 0.091

The observed proportions are:

p1 = x1 / n1 = 29 / 376 = 0.0771

p2 = x2 / n2 = 10 / 52 = 0.1923

The test statistic value

z = (0.0771 - 0.1923) / sqrt(0.091 * (1 - 0.091) * (1/376 + 1/52)) = -3.04

By using a standard normal distribution table,

The p-value is 0.00238.

Since the p-value (0.00238) is less than the level of significance (0.01), we reject the null hypothesis and conclude that there is sufficient evidence to indicate a difference in the number of animals leaving the shelter over the weekend for household pets and wildlife animals.

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Answer:

x = 21.4

Step-by-step explanation:

We need to use the law of sins

sin 42       sin x

--------- = ----------

22              12

12 sin 42 = 22 sin x

12 sin 42 /22 = sin x

Taking the inverse sin of each side

sin^-1(12/22 sin 42) = sin^-1(sin x)

21.40637223 =x

To the nearest tenth

x = 21.4

Answer:

  -x^2 +8x -6

Step-by-step explanation:

Distribute the minus sign and collect terms.

  (3x -8) -(x^2 -5x -2)

  = 3x -8 -x^2 +5x +2

  = -x^2 +8x -6

Answer:

Its E

Step-by-step explanation:

Just add the set of number stogether and pick the highest number.

So, the variance of the number of tornadoes in a year given that at least one tornado occurs is 3.

The Poisson distribution is a discrete probability distribution that describes the number of events that occur in a fixed interval of time or space, given the average number of events per interval.

For a Poisson distribution with mean λ, the variance is equal to λ.

Given that at least one tornado occurs in a year, the mean number of tornadoes is 3. Therefore, the variance is also equal to 3.

So, the variance of the number of tornadoes in a year given that at least one tornado occurs is 3.

It's worth noting that this result is based on the assumption that the number of tornadoes follows a Poisson distribution with mean 3, which may not always be the case in real-world scenarios. The actual number of tornadoes in a given year can be influenced by various factors such as climate, weather patterns, and geography.

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Answer:

Let x be the first unknown angle, and y be the second unknown angle.

We know that the sum of the three angles in a triangle is 180 degrees, so:

85 + 9kx + 10kx = 180

where k is a constant representing the ratio of the other two angles.

Simplifying the equation, we get:

19kx = 95

Dividing both sides by 19k, we get:

x = 5/k

Since the ratio of the other two angles is 9:10, we know that:

y = 9kx = 9k(5/k) = 45

So the measures of the two unknown angles are:

x = 5/k and y = 45

We cannot find the exact measures of x and y without more information, but we know that x and y are in a ratio of 9:10 and their sum is 180 - 85 = 95 degrees. We can set up the following equation to solve for k:

5/k + 45/k = 95

50/k = 95

k = 50/95

Using this value of k, we can find the measures of x and y:

x = 5/k = 5/(50/95) = 9.5

y = 9kx = 9(50/95)(9.5) = 47.37

Therefore, the measures of the two unknown angles are x = 9.5 degrees and y = 47.37 degrees (rounded to two decimal places).

Step-by-step explanation:

She will travel a distance of 62.8 feet × 5 revolutions = 314 feet.

Calculate the circle of the carousel (the distance around the outside) and multiply it by the number of revolutions to determine how far Sierra will move after five rotations.

The following equation can be used to determine the carousel's circumference:

Circumference = 2πr

Where "radius" refers to the carousel's radius and "" is an irrational integer roughly equivalent to 3.14. (in this case, 10 feet).

Substitute the values in the above equation, we get

Circumference = 2 × 3.14 × 10 feet

Circumference = 62.8 feet

Since Sierra will make five revolutions, she will travel a distance

= 62.8 feet × 5 revolutions = 314 feet.

Remember that this is only an estimate because the precise distance may have varied slightly depending on the carousel's speed and Sierra's position on it, among other things.

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Answer:

I think its b

Step-by-step explanation:

Because since betty planted 20 pumkkin seeds you can divied 20 and 5 to get 4 and multiply 4 and 2 to get 8

Answer: Willis will take 3 hours to paint the room by himself.

Step-by-step explanation:

Given: Time taken by James to complete job by himself = 6 hours

Let Time taken by Willis to complete job by himself = t hours

Together they take 2 hours.

\(\dfrac{1}{6}+\dfrac{1}{t}=\dfrac{1}{2}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{2}-\dfrac{1}{6}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{3-1}{6}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{2}{6}\\\\\Rightarrow\ t=\dfrac{6}{2}\\\\\Rightarrow\ t=3\)

So,  Willis will take 3 hours to paint the room by himself.

Answer:

y= 6/19

hope it helps

Answer:

To perform McNemar's test, we need to find the number of discordant pairs, i.e., the pairs of individuals who change their response from before to after college. In this case, there are 23 students who said "yes" before college but "no" after college, and 11 students who said "no" before college but "yes" after college. Therefore, there are 23 discordant pairs.

The test statistic for McNemar's test is calculated as:

z = (|b-c| - 1) / √(b+c)

where b is the number of discordant pairs who responded "yes" before college, and c is the number of discordant pairs who responded "no" before college.

In this case, b = 23 and c = 11, so:

z = (|23-11| - 1) / √(23+11)

z = 1.96

Therefore, the test statistic is 1.96