The money supply in Freedonia is $200 billion. Nominal GDP is $800 billion and real GDP is $400 billion. Assuming that velocity is stable, if real GDP grows by 10 percent this year, and if the money supply does not change this year, then a. nominal GOP will stay the same. b. the inflation rate will be zero c. nominal GDP will grow by 10 percent. d. none of the above are correct.

Answer:

Answer: C 2:3

Step-by-step explanation:

total students = 25

total girls = 15

total boys = 25-15 = 10

boys:girls = 10:15

divide by 5 to get 2:3

So the answer is 1.3 after rounding to 10.

The Laplace transform of the motion equation is mx(t) + dx(t) + kx(t) = f(t).

Given: Motion equation is mx(t) + dx(t) + kx(t) = f(t); X(s) and

F(s) be the Laplace transforms of the position x(t) and external force f(t) respectively.

Transfer function is G(s)= X(s)/F(s) = 1/ms² + ds + k

To derive a transfer function of a mass-spring-damper system from its equation of motion, we have to follow these steps:

Step 1: Take the Laplace transform of the motion equation.

Laplace Transform of the given equation is,  mX(s)s² + dX(s)s + kX(s) = F(s)

Step 2: Write X(s) in terms of F(s)X(s) = F(s) / m s² + d s + k

Step 3: Now the transfer function can be derived using the ratio of X(s) to F(s).

Transfer Function = G(s) = X(s) / F(s)G(s) = 1 / ms² + ds + k

Hence, the transfer function of a mass-spring-damper system from its equation of motion is G(s) = 1 / ms² + ds + k. 

In order to derive a transfer function of a mass-spring-damper system from its equation of motion, the following steps are necessary:

  Take the Laplace transform of the motion equation.

The Laplace transform of the motion equation is mx(t) + dx(t) + kx(t) = f(t).

X(s) and F(s) are the Laplace transforms of the position x(t) and external force f(t), respectively.

Learn more about motion equation

brainly.com/question/31314651

#SPJ11

When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

For more such questions on container

https://brainly.com/question/29398973

#SPJ8

Answer:

29.5 hours

Step-by-step explanation:

Amityville to Denton is 1625 miles.

Since we know that Sarah drives at 55 mph we can divide 1625/55 and get 29.45454... and I assume that they want it rounded so it will be around 29.5 hours

Answer:

29.552727272727273 hours

Step-by-step explanation:

rounded to nearest minute is 29 hours and 55 minutes.

Answer:

if ∠1 = 70°, then ∠5= 70°

Hence, option (A) is correct.

Step-by-step explanation:

Given

∠1 = 70°

To determine

We need to determine angle ∠5

From the diagram, it is clear that a transversal line crosses the two parallel lines, the angles in the matching corner would be corresponding angles.

As angle ∠5 is the corresponding angle of angle ∠1 = 70°.

Therefore,

if ∠1 = 70°, then ∠5= 70°

Hence, option (A) is correct.

The statements that can be used to determine independent events are given as follows:

If two events are independent, the multiplication of the probabilities of each event is equals to the probability of both events, that is:

P(A and B) = P(A) x P(B).

Which means that the first statement is correct.

The conditional probability formula is given as follows:

P(B|A) = P(A and B)/P(A).

However, for independent events, we know that:

P(A and B) = P(A) x P(B).

Hence:

P(B|A) = P(A) x P(B)/P(A).

P(B|A) = P(B).

The same is true for the opposite, meaning that:

P(A|B) = P(A).

Meaning that the last statement is correct.

The Venn probability P(A or B) = P(A) x P(B) - P(A and B) can also be used to determine if the events are independent, when it assumes a value of zero.

More can be learned about independent events at https://brainly.com/question/7965468

#SPJ1

A scatterplot that shows the number of hours studied on the x-axis and the number of errors on the y-axis would best support the teacher's observation.

Error in math is an incorrect answer to a mathematical equation or problem. It can be caused by a variety of factors, such as inaccurate calculations, misreading instructions, or not understanding the problem. Error in math can be frustrating and can lead to poor grades, but it can also be an opportunity for learning and growth. With the proper guidance and understanding, students can learn from their mistakes and become better mathematicians.

The scatterplot would likely show a negative correlation, with the number of errors decreasing as the number of hours studied increases. This indicates that as students study more, their performance on multiplication tests improves. It could also show an outlier or two, which could indicate that some students are able to learn multiplication facts more quickly than others.

To know more about error click-
https://brainly.com/question/28001423
#SPJ1

112 percent *97

= (112/100)*97

= (112*97)/100

= 10864/100 = 108.64

Answer:

96,000

Step-by-step explanation:

.8 x 120,000 = 96,000

mueves el decimal sobre el porcentaje que deseas encontrar, luego lo multiplicas por el total. por ejemplo quiere 80% entonces mueves el decimal para que sea .8 o si quierias 55% entonces es .55 y el total es el 120,000 el numero que tienes. (:

Answer:96000

Step-by-step explanation:

120000/x=100/80

(120000/x)*x=(100/80)*x       - we multiply both sides of the equation by x

120000=1.25*x       - we divide both sides of the equation by (1.25) to get x

120000/1.25=x  

96000=x  

x=96000

Answer:

Option C

Step-by-step explanation:

Since, measure of all sides of the triangle has been given in the picture,

By applying cosine rule in the given triangle,

AC² = AB² + BC² - 2(AB)(BC)cos(B)

11² = 16² + 16² - 2(16)(16)cos(B)

121 = 256 + 256 - 512.cos(B)

121 - 512 = - 512.cos(B)

cos(B) = \(\frac{391}{512}\) = 0.763672

B = \(cos^{-1}(0.763672)\)

B = 40.2°

Therefore, measure of angle B is 40.2°.

Option C is the answer.

Answer:

9/4

Step-by-step explanation:

Answer: 11

In rectangle diagonals are equal and bisect each other.

Therefore,

2×4x=88

8x=88

x=88÷8

x=11

Step-by-step explanation:

The probability that two children selected at random from Mrs. Attaway's first-grade class are girls and one is a boy is 0.120.

To find the probability that two children selected at random from Mrs. Attaway's class are girls and one is a boy, we need to calculate the number of favorable outcomes (selecting two girls and one boy) and divide it by the total number of possible outcomes.

The total number of children in the class is 5 girls + 16 boys = 21 children.

To calculate the probability, we need to determine the number of ways to select two girls from the five available girls and one boy from the 16 available boys. This can be done using combinations.

The number of ways to select two girls from five is given by the combination formula:

C(5, 2) = 5! / (2! * (5 - 2)!)

= 5! / (2! * 3!)

= (5 * 4) / (2 * 1)

= 10

Similarly, the number of ways to select one boy from 16 is given by the combination formula:

C(16, 1) = 16

The total number of favorable outcomes is the product of these two combinations: 10 * 16 = 160.

Now, let's calculate the total number of possible outcomes when selecting three children from the class:

C(21, 3) = 21! / (3! * (21 - 3)!)

= 21! / (3! * 18!)

= (21 * 20 * 19) / (3 * 2 * 1)

= 1330

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = favorable outcomes / total outcomes

= 160 / 1330

≈ 0.120 (rounded to three decimal places)

Therefore, the probability that two children selected at random from Mrs. Attaway's first-grade class are girls and one is a boy is 0.120.

To learn more about probability: https://brainly.com/question/13604758

#SPJ11

An element with a mass of 780 grams decays by 16.3% per minute. To find the amount of the element remaining after 16 minutes, we can use the following formula: `A = P(1 - r)ⁿ`, where `A` is the amount remaining, `P` is the initial amount, `r` is the rate of decay, and `n` is the number of minutes.

Using this formula, we can plug in the given values and solve for `A`:

```
P = 780 grams
r = 0.163 (since the element decays by 16.3% per minute)
n = 16 minutes

A = P(1 - r)ⁿ
A = 780(1 - 0.163)¹⁶
A ≈ 115.3 grams (rounded to the nearest 10th of a gram)
```

Therefore, after 16 minutes, approximately 115.3 grams of the element are remaining.

To know more about initial amount visit:

https://brainly.com/question/32209767

#SPJ11

Answer:

y=-2/7x-2

Step-by-step explanation:

Just move the 2x to the other side, then divide both sides by 7.

If you doubled a penny every day, you would have $5,368,709.12

You can see that the decision is rather straightforward: having a single penny that doubles every day for a month are preferable to receiving $1 million upfront. This is due to compound interest's strength.

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest.

It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely calculated on the principal sum.

Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.

If I double this particular penny every day, I would have 30 extra pennies, plus my original one. I have $0.31 literal dollars

On day 30, if you doubled a penny every day, you would have $5,368,709.12.

Know more about compound interest at:

https://brainly.com/question/28020457

#SPJ4

Answer: y = 5y - (-2) < 17 =5y + 16

Answer:  not sure. but as long as he saves his money wisely and doesn't spend frivilously

Step-by-step explanation:

The percentage of the profit gain by karen on a pack of 8 bottles  is 220%.

Karen buys a pack of bottles of water. = 8

Karen sells all 8 bottles of water for rupees =  50p each

=  50p/100 each

= 0.5 rupees

Total rupees for 8 bottles = 8 x 0.5 = 4

The pack costs  = 1.25

Profit % = (Profit / C.P.) × 100

Profit = SP - CP

=  4 - 1.25

= 2.75

then using these values in equation we get :

profit = \(\frac{4 - 1.25}{1.25} * 100\)

profit = (2.75/1.25 )x 100

profit = 2.2 x 100 = 220

profit = 220%

The percentage of the profit gain by karen on a pack of 8 bottles  is 220%.

To know more about profit

https://brainly.com/question/11018349

#SPJ1

Answer:

The notation f⁻¹(-3) refers to the value(s) of x for which f(x) = -3.

However, the function f is not given in the prompt. Therefore, we cannot determine the value(s) of x for which f(x) = -3 or find f⁻¹(-3) without knowing the definition of f.

Step-by-step explanation:

The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

To learn more about thickness click here: brainly.com/question/23622259

#SPJ11

The sampling technique used in the scenario of selecting five auto repair classes from a local technical school and interviewing all of the students from each class is called "Cluster Sampling."

Cluster Sampling is a type of probability sampling method where the units of analysis are organized into groups, called clusters, and a random sample of these clusters is selected.

In this scenario, the auto repair classes are the clusters and the students are the units of analysis.

By selecting five classes, all of the students from each class are included in the sample. This method is often used when it is difficult or impractical to get a complete list of all the units of analysis in a population.

In conclusion, cluster sampling is a useful technique when it is challenging to get a complete list of all the units of analysis in a population, as it reduces the time and resources required while still giving a relatively accurate representation of the population.

To know more about sampling here.

https://brainly.com/question/28975411

#SPJ4

Answer:

Step-by-step explanation:

y = -2x +2

y - 3 = -2(x -3)

y - 3 = -2x + 6

y = -2x + 9

Answer:

\(14.1\)

Step-by-step explanation:

Since we have two sides of a triangle and the angle between them, we can use the Law of Cosines.

For any triangle, the Law of Cosines states:

\(b^2=a^2+c^2-2ac\cos B\), where \(a\), \(b\), and \(c\) are all interchangeable.

Substituting given values, we have:

\(b^2=9^2+19^2-2(9)(19)\cos 45^{\circ},\\b^2=200.169480834,\\b\approx \boxed{14.1}\)

Answer:

EA

Step-by-step explanation:

Answer:

i am not able to understand sorry can u ask properly again and follow me i by mistakely deleted my app i have download it again i have to make my followers again

Answer:

Step-by-step explanation:

Rebecca's car insurance been reduced by 18%

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

Given that, Last year, Rebecca's car insurance cost her £2043. This year it only cost her £1675.26.

Percentage decrease = (Final value - initial value) / initial value × 100

Final value = £1675.26

Initial value = £2043

Percentage decrease = (2043 - 1675.26) / 2043 × 100

= 367.74 / 2043 × 100

= 0.18 × 100

= 18 %

Hence, Rebecca's car insurance been reduced by 18%

Learn more about percentage, click;

https://brainly.com/question/29306119

#SPJ2

Answer:

5i√10

Step-by-step explanation:

hope this answers your question

:)

Answer:

5√10

Step-by-step explanation:

Answer:

JL ⊥ KM

Step-by-step explanation:

JL ⊥ KM would make the quad a rhombus because JKLM is a parallelogram since opposite sides are congruent.  If the diagonals of a parallelogram are perpendicular, then the quad must be a rhombus.

JL must be perpendicular to KM because in a parallelogram if diagonals are perpendicular then the quadrilateral JKLM is a rhombus.

Given :

The following steps can be used in order to determine the correct statement that shows that JKLM is a rhombus:

Step 1 - Remember a quadrilateral has four sides and the sum of the interior angles of a quadrilateral is 360 degrees.

Step 2 - According to the given data, KL ≅ JM, JK ≅ LM, and KA ≅ MA.

Step 3 - So, to make JKLM a rhombus, JL must be perpendicular to KM because in a parallelogram if diagonals are perpendicular then the quadrilateral JKLM is a rhombus.

Therefore, the correct option is B).

For more information, refer to the link given below:

https://brainly.com/question/14462098