write 3.72* 10 power of -2 in standard form

A Venn diagram is a graphic organizer utilized to show relationships between sets. The Venn diagram uses circles or other shapes to show the commonalities and distinctions between the two or more sets.

It comprises of two overlapping circles, each circle representing a set. The common parts between two sets are illustrated in the overlapping region. The number of elements is shown in each set. The common region is represented by the intersection of two sets. \(n(A)=9, n(B)=13, n(A∩B)=8\); We know the number of elements in set A and set B and their intersection.

Using the formula for the union of two sets, we can find\(n(A∪B).n(A∪B)= n(A) + n(B) - n(A∩B)n(A∪B)= 9 + 13 - 8n(A∪B)= 14\)Therefore, the number of elements in the union of A and B is 14. A diagram is presented below to illustrate the relationship between A and B. \(\text{Venn diagram of set A and set\(B}\)\)

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The distance from the sun to the other focus is 5.01 × 10⁹ m.

(a) The distance from the center of an ellipse to a focus is an where a is the semi major axis and e is the eccentricity. Thus, the separation of the foci ( in the case of Earth's orbit ) is;

2ae = 2(1.50 × 10¹¹)(0.0167) = 5.01 × 10⁹ m.

(b) To express this in terms of solar radii, we set up a ratio;

(5.01 × 10⁹)/(6.96 × 10⁸) = 7.2

Thus, we can conclude that the distance from the sun to the other focus is 5.01 × 10⁹ m.

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Complete question is;

The Sun's center is at one focus of Earth's orbit. How far from this focus is the other focus, (a) in meters and (b) in terms of the solar radius, 6.96 × 10⁸ m? The eccentricity is 0.0167, and the semimajor axis is 1.50 × 10¹¹ m.

Explanation

the length of an arc is given by:

where r is the radius and theta is the angle

then

Step 1

Let

radius=13

angle=68

replace

I hope this helps you

The correct answer is option (C) 55 minutes.

Let's break down the information given in the problem:

To find out how long it takes for Lauren to reach Andrea, we need to determine the time it takes for Andrea to cover half the distance between them. Once Andrea reaches the halfway point, Lauren will also have traveled the same distance.

Let's denote the time it takes for Andrea to reach the halfway point as "t" minutes. Since the distance decreases at a rate of 1 kilometer per minute, after "t" minutes, the distance between Andrea and Lauren will be reduced by "t" kilometers.

Now, let's calculate the distance traveled by Andrea in "t" minutes:

Distance = Rate × Time

Since Andrea is traveling three times as fast as Lauren, her rate is 3 times the rate of Lauren.

Distance traveled by Andrea in "t" minutes = (3 × 1) × t = 3t kilometers

The total distance between Andrea and Lauren at that time will be:

Distance between Andrea and Lauren = 20 - t kilometers

Since they meet at the halfway point, the distance traveled by Andrea (3t) will be equal to half the total distance (20 - t)/2:

3t = (20 - t)/2

To solve this equation, we can multiply both sides by 2:

6t = 20 - t

Now, solve for "t":

6t + t = 20

7t = 20

t = 20/7

Therefore, it will take Andrea 20/7 minutes to reach the halfway point.

Since Lauren continues biking for 5 more minutes after Andrea stops, the total time it takes for Lauren to reach Andrea is:

Total time = t + 5 = 20/7 + 5

To calculate this, we can convert 5 minutes to a fraction with a denominator of 7:

5 minutes = 35/7 minutes

Total time = 20/7 + 35/7 = (20 + 35)/7 = 55/7

So, Lauren will reach Andrea after 55/7 minutes.

To find the answer option that matches this time, we can calculate 55/7 and compare it to the answer choices:

55/7 ≈ 7.86

Among the given answer choices, the closest option to 7.86 is (C) 55. Therefore, the answer is (C) 55 minutes.

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The injury probability p that makes the decision maker indifferent between entering now and waiting until next year is approximately 0.26.

To calculate this probability, we need to set the expected values of entering now and waiting until next year equal to each other and solve for p. Let EMV₁ be the expected value of entering now and EMV₂ be the expected value of waiting until next year. Then we have:

EMV₁ = -1000p + 5000(1-p)

EMV₂ = 0.9(-1000p) + 0.1(5000)

Setting EMV₁ equal to EMV₂, we get:

-1000p + 5000(1-p) = 0.9(-1000p) + 0.1(5000)

Solving for p, we get:

p ≈ 0.26

Therefore, if the probability of injury is greater than 0.26, the decision maker should wait until next year to enter the market, and if the probability of injury is less than 0.26, the decision maker should enter the market now.

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The appropriate regression model depends on the stationarity properties of both the dependent and independent variables, as well as the error term. The researcher can use a standard OLS regression model with first-order differencing of both Y and X.

In the first scenario, both Y and X are I(0), which means they are stationary time series. In this case, the researcher can perform a standard linear regression analysis, as the stationary series would lead to a stable long-run relationship. The answer from this model will be reliable and less likely to suffer from spurious regressions. In the second scenario, Y is I(2) and X is I(0). This implies that Y is integrated of order 2 and X is stationary. In this case, the researcher should first difference Y twice to make it stationary before performing a regression analysis. However, this approach might not be ideal as the integration orders differ, which can lead to biased results.

In the third scenario, Y and X are both I(1) and the error term is I(0). This indicates that both Y and X are non-stationary time series, but their combination might be stationary. The researcher should employ a co-integration analysis, such as the Engle-Granger method or Johansen test, to identify if there is a stable long-run relationship between Y and X. If co-integration is found, then an error correction model can be used for more accurate predictions.

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Answer:

dont get the question

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

12x + 7x = 19x

-7 + +9 = 2

Answer:

d

Step-by-step explanation:

Answer:

h = 1

Step-by-step explanation:

\(h = 1\)

\( \frac{ - 6}{1} + 10 = - 6 + 10 = 4\)

\(7 > 4\)

Crime rates in the UCR (Uniform Crime Report) are expressed as the number of reported crimes per 100,000 population.

This allows for a standardized comparison of crime levels across different areas and time periods, taking into account population size. The UCR presents raw figures, crime rates, and changes in both the number and rate of crime over time to provide a comprehensive view of crime trends.

This is calculated by dividing the number of reported crimes by the population of the area and multiplying the result by 100,000. This helps to standardize the data and allows for comparison across different jurisdictions and time periods. Additionally, the UCR also presents changes in crime rates over time, allowing for the identification of trends and patterns in crime.

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The distance between the third base and the player is 150 feet.

Pythagoras' theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base, and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle of 90°. The sides of a right triangle (say a, b, and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.

In the diagram attached, we can see the locations of the 1st base, 2nd base, 3rd base, and Home plate.

Since these four points form a square of which diagonals are equal in size.

So if we find the distance between the 1st and 3rd base that will be equal to the distance between the Home plate to the second base.

To find the nearest distance,

By applying "Pythagoras' Theorem"

\(nearest \ distance =\sqrt{120^2+90^2}\\\\=\sqrt{22500}\\\\=150\ feet.\)

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Answer: A & C

Step-by-step explanation: 3 + 4 = 7     5 -3 = 2

Answer:

P=76 ft

Step-by-step explanation:

P=19(4)

P=76

Answer:

B

Step-by-step explanation:

It only has numbers less than 1, when multiplying that means you can't get over 1

the answer is B

hope this helps : )

15% of the students scored higher than Henry on the accounting exam.

Percentiles are a measure of the relative standing of a value within a set of values. The nth percentile is a value such that n% of the values are less than or equal to that value.

So, if Henry's score is in the 85th percentile, it means that 85% of the scores in the class are less than or equal to his score.

Therefore, 100% - 85% = 15% of the scores in the class are higher than Henry's score. So, 15% of the students scored higher than Henry on the accounting exam.

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x(t) and y(t) approach 0 as t approaches infinity, we can conclude that the system behaves like a center at the origin

To solve the system of differential equations x' = 10x² and y' = 3y², we will treat them as separable equations and solve them individually.

For the equation x' = 10x²:

Separate the variables and integrate:

∫(1/x²) dx = ∫10 dt

-1/x = 10t + C₁ (where C₁ is the constant of integration)

x = -1/(10t + C₁)

For the equation y' = 3y²:

Separate the variables and integrate:

∫(1/y²) dy = ∫3 dt

-1/y = 3t + C₂ (where C₂ is the constant of integration)

y = -1/(3t + C²)

Given the initial point (x(0), y(0)) = (a, b), we can substitute these values into the solutions:

x(0) = -1/(10(0) + C₁) = a

C₁ = -1/a

y(0) = -1/(3(0) + C₂) = b

C₂ = -1/b

Substituting the values of C₁ and C₂ back into the solutions, we get:

x(t) = -1/(10t - 1/a)

y(t) = -1/(3t - 1/b)

Based on this solution, we can analyze the behavior of the system at the origin (0,0). Let's evaluate the limit as t approaches infinity:

lim (t->∞) x(t) = -1/(10t - 1/a) = 0

lim (t->∞) y(t) = -1/(3t - 1/b) = 0

Since both x(t) and y(t) approach 0 as t approaches infinity, we can conclude that the system behaves like a center at the origin.

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The complete question is :

The system x' = 10x2, ý = 3y2 has an isolated critical point at (0,0), but the system is not almost linear. Solve the system for an initial point (x(0), y(0)) = (a, b), where neither a nor b are zero (recall how to solve separable equations). Use t for your time variable: x(t) = y(t) = Based on this solution, the system behaves like what at the origin? Bahavior: Type "sink", "source", "saddle", "spiral sink", "spiral source", "center".

Answer: The Error Bound for Proportions (EBP) gives the maximum amount of error that can be tolerated when estimating a population proportion from a sample proportion.

To find the EBP at the 95% level, we can use the following formula:

EBP = z*(sqrt((p*(1-p))/n))

where:

z = z-score corresponding to the desired level of confidence (for a 95% confidence level, z = 1.96)

p = sample proportion (0.31, based on the survey results)

n = sample size (1379)

Substituting the given values, we get:

EBP = 1.96*(sqrt((0.31*(1-0.31))/1379))

EBP ≈ 0.0324

Rounding to four decimal places, the Error Bound for Proportions (EBP) at the 95% level is 0.0324. This means that we can be 95% confident that the true population proportion of CEOs who are extremely concerned about the availability of key skills lies within the range of (0.31 - 0.0324) to (0.31 + 0.0324), or approximately 0.2776 to 0.3424.

Ralph received his June flash card bill, which includes a previous balance and a finance charge because he did not pay his May bill in full.

Ralph's June flash card bill reflects the consequences of not paying his May bill in full. When a credit card balance is not paid in full by the due date, the remaining amount is carried over to the next billing cycle, resulting in a previous balance. This previous balance represents the unpaid amount from the previous month, which is still owed.

Additionally, credit card companies apply finance charges to outstanding balances that are not paid in full. A finance charge is the cost of borrowing money from the credit card issuer. It is typically calculated based on the outstanding balance and the applicable interest rate.

Therefore, Ralph's June bill includes a previous balance, which represents the unpaid amount from May, and a finance charge, which is the cost incurred for carrying that balance. These charges serve as a reminder for Ralph to pay his credit card bills in full to avoid accumulating additional costs and interest charges in the future.

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Answer:

1.5 or 1 ½ pages per min

Step-by-step explanation:

7.5/5=1.5

She reads 1 ½ pages per min

Answer: 1.5 pages per minute

Step-by-step explanation:

Divide the total number of pages she read by 5, the amount of time it took her. So it should look like this: 7.5/5

The answer is 1.5 pages per minute.

The matched answers are:

1. semicircle

2. central angle

3. Radius

4. Secant

5. center

6. tangent

7. diameter

8. minor arc

9. chord

10. major arc

A circle is the locus of points equidistant from a given point called the center of the circle.

A circle can be described if its radius and the center of the circle is known.

Analysis:

1. RCH  is called a semicircle when a diameter divides a circle into two equal parts, a part is called the semicircle.

2. ∠RAH is the central angle, because it is the angle subtended at the Center of the circle.

3. CA is the radius of the circle, a line drawn from the center to any point on the circumference of the circle.

4. MR is a secant, a line that cuts the circle into two parts.

5. A is the center of the circle.

6. MT is the tangent, because line MT touches the circle at a point T.

7. CH is the diameter of the circle, a line that divides the circle into two semi circles.

8. CT is the minor arc, the curved line that is found in the smaller part of the divided circle.

9. HT is chord, it is a line that divides the circle into two unequal parts.

10. CRH is  major arc, the curved line of the bigger portion of the divided circle.

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Answer:

Read below.

Step-by-step explanation:

a. reflection over the x-axis, translate 2 units up

b. rotate 90° counterclockwise or 270° clockwise

c. use a scale factor of 2 and translate 3 units down, 3 units left

d. translate 8 units right, 7 units up

I'm not so sure about c since I do not like scale factors.

Answer:Total hours worked by John in his garden=3 5/8 hours.

Step-by-step explanation:

Time spent planting =1 1 /2 hours planting

Time spent trimming = 2 1 /8 hours

Total hours worked by John in his garden= Time spent planting +Time spent trimming

=1 1/2 + 2 1/8( add whole numbers together and fractions together)

= 3 4+1 /8

3 5/8 hours.

The probability that one is selected is the likelihood

The probability that one is selected at least once is 0.704

The sample space is given as:

S = {1,2,3}

The probability that 1 is not selected at all is:

P'(None) = 2/3

The probability that one is selected at least once is calculated using the following complement rule

P(At least once)  = 1 - P(None)^3

This gives

P(At least once) = 1 -(2/3)^3

Evaluate

P(At least once) = 0.704

Hence, the probability that one is selected at least once is 0.704

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(a) Forecast: Linear regression  the next year is approx 191.6007.

(b) MSE: Mean Squared Error is approximately 249.1585.

(c) MAPE: Mean Absolute Percent Error is approximately 10.42%.

(a) (a) Forecast using linear regression:
To forecast the number of disk drives for the next year, we can use linear regression to fit a line to the given data points. The linear regression equation is of the form y = mx + b, where y represents the number of disk drives and x represents the year.

Calculating the slope (m):
m = (Σ(xy) - n(Σx)(Σy)) / (Σ(x^2) - n(Σx)^2)

Σ(xy) = (1)(140) + (2)(160) + (3)(190) + (4)(200) + (5)(210) = 2820
Σ(x) = 1 + 2 + 3 + 4 + 5 = 15
Σ(y) = 140 + 160 + 190 + 200 + 210 = 900
Σ(x^2) = (1^2) + (2^2) + (3^2) + (4^2) + (5^2) = 55

m = (2820 - 5(15)(900)) / (55 - 5(15)^2)
m = (2820 - 6750) / (55 - 1125)
m = -3930 / -1070
m ≈ 3.6729

Calculating the y-intercept (b):
b = (Σy - m(Σx)) / n
b = (900 - 3.6729(15)) / 5
b = (900 - 55.0935) / 5
b ≈ 168.1813

Using the equation y = 3.6729x + 168.1813, where x represents the year, we can predict the number of disk drives for the next year. To do so, we substitute the value of x as the next year in the equation. Let's assume the next year is represented by x = 6:

y = 3.6729(6) + 168.1813
y ≈ 191.6007

Therefore, according to the linear regression model, the predicted number of disk drives for the next year is approximately 191.6007.

(b) Calculation of Mean Squared Error (MSE):

To calculate the Mean Squared Error (MSE), we need to compare the predicted values obtained from linear regression with the actual values given in the data.

First, we calculate the predicted values using the linear regression equation: y = 3.6729x + 168.1813, where x represents the year.

Predicted values:

Year 1: y = 3.6729(1) + 168.1813 = 171.8542
Year 2: y = 3.6729(2) + 168.1813 = 175.5271
Year 3: y = 3.6729(3) + 168.1813 = 179.2000
Year 4: y = 3.6729(4) + 168.1813 = 182.8729
Year 5: y = 3.6729(5) + 168.1813 = 186.5458
Next, we calculate the squared difference between the predicted and actual values, and then take the average:

MSE = (Σ(y - ŷ)^2) / n

MSE = ((140 - 171.8542)^2 + (160 - 175.5271)^2 + (190 - 179.2000)^2 + (200 - 182.8729)^2 + (210 - 186.5458)^2) / 5

MSE ≈ 249.1585

The Mean Squared Error (MSE) for the linear regression model is approximately 249.1585.

This value represents the average squared difference between the predicted values and the actual values, providing a measure of the accuracy of the model.

(c) Calculation of Mean Absolute Percent Error (MAPE):

To calculate the Mean Absolute Percent Error (MAPE), we need to compare the predicted values obtained from linear regression with the actual values given in the data.

First, we calculate the predicted values using the linear regression equation: y = 3.6729x + 168.1813, where x represents the year.

Predicted values:

Year 1: y = 3.6729(1) + 168.1813 ≈ 171.8542
Year 2: y = 3.6729(2) + 168.1813 ≈ 175.5271
Year 3: y = 3.6729(3) + 168.1813 ≈ 179.2000
Year 4: y = 3.6729(4) + 168.1813 ≈ 182.8729
Year 5: y = 3.6729(5) + 168.1813 ≈ 186.5458

Next, we calculate the absolute percent error for each year, which is the absolute difference between the predicted and actual values divided by the actual value, multiplied by 100:

Absolute Percent Error (APE):

Year 1: |(140 - 171.8542) / 140| * 100 ≈ 18.467
Year 2: |(160 - 175.5271) / 160| * 100 ≈ 9.704
Year 3: |(190 - 179.2000) / 190| * 100 ≈ 5.684
Year 4: |(200 - 182.8729) / 200| * 100 ≈ 8.563
Year 5: |(210 - 186.5458) / 210| * 100 ≈ 11.682
Finally, we calculate the average of the absolute percent errors:

MAPE = (APE₁ + APE₂ + APE₃ + APE₄ + APE₅) / n

MAPE ≈ (18.467 + 9.704 + 5.684 + 8.563 + 11.682) / 5 ≈ 10.42

The Mean Absolute Percent Error (MAPE) for the linear regression model is approximately 10.42%.

This value represents the average percentage difference between the predicted values and the actual values, providing a measure of the relative accuracy of the model.

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Answer:

125

Step-by-step explanation:

1^3 = 1

2^3 = 8

3^3 = 27

4^3 = 64

5^3 = 125

The inference from given boxplot is : The visiting team had more variability in the number of shots taken.

In this question we have been given two boxplots.

For the boxplots that the coach made,

for the home team:

Whiskers range is:16 to 32

So, the minimum value = 16

the maximum value = 32

the box ranges from 20 to 23. A line divides the box at 22.

so, the first quartile = 20

the third quartile = 23

the Median = 22

interquartile range(IQR) = 23 - 20

                                      = 3

And for the visiting team

Whiskers range :14 to 32

This means, the minimum value is 14 and the maximum value = 32

As the box ranges from 16 to 24 and a line divides the box at 18,

the first quartile is 16, the third quartile = 24 and the median = 18

So, the interquartile range (IQR) = 24 - 16

                                                   = 8

From above data analysis the inference is that the visiting team had more variability in their shots, because their distribution has a higher interquartile range (8 > 3)

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Given question is incomplete.

The complete question is:

A hockey coach recorded the number of shots taken by the home team and the number taken by the visiting team in 20 games. He displayed the results in the box plots below.A box plot titled Number of Shots Taken by home team players. The number line goes from 10 to 32. The whiskers range from 16 to 32, and the box ranges from 20 to 23. A line divides the box at 22.

Number of Shots Taken by Home Team Players

A box plot titled Number of Shots Taken by visiting team players. The number line goes from 10 to 32. The whiskers range from 14 to 32, and the box ranges from 16 to 24. A line divides the box at 18.

Number of Shots Taken by Visiting Team Players

Which describes an inference that the coach might make after comparing the medians of the two data sets?

Answer:

Answer: 112°

Step-by-step explanation:

Angles in a Circle

An inscribed angle is formed between two chords whose vertices lie on the circumference of a circle. The figure shows three chords: TU, SU, and ST. SU happens to also be a diameter because it goes through the center of the circle V.

ST and SU form an inscribed angle of 34°. The corresponding central angle is TVU and its measure is

\(m\angle TVU=2*34^\circ=68^\circ\)

The required measure of the arc ST is the measure of the angle SVT. Note that SVT and TVU are complementary, thus:

\(m\angle TVU+m\angle SVT=180^\circ\)

Solving for the measure of SVT:

\(m\angle SVT=180^\circ-m\angle TVU\)

\(m\angle SVT=180^\circ-68^\circ=112^\circ\)

Answer: 112°

Answer:

A. 56 degrees

Step-by-step explanation:

Just took the Unit Test on Edg (2021)!!

Answer:10

Step-by-step explanation:

Answer: The answer is 10.

Step-by-step explanation:

These steps will help you!

STEP 1: You need to multiply them and use the process of elimination.

8 is obiviously too little.

9 is still too little.

10 when you multiply it with $1.78, it's simple enough that it equals just right!

11 is too over.

STEP 2: Try multiplying 1.78 x 10.

         1.78

      x    10          

               0

+  1  7  8  0         _______always add the 0.

 $ 1 7 . 8  0

Mark also has $1.20 left to spare.

STEP 3: Declare the answer!

Mark can buy 10 stamp packets and have $1.20 left for himself.

Hope this helps!