Abigail is playing hide-and-seek with Gavin and Katie. Gavin is hiding 16 feet south of Abigail, and Katie is hiding 12 feet east of Gavin. How far apart are Abigail and Katie?

Answer:

12 percent

Step-by-step explanation:

Technically its 11.7647 but I'm pretty sure you would round that to 12 percent, if not 12 percent 11.8 percent. Hope this helps!

The correct interpretation of the P-value in this scenario is: "There is a 5.4% chance that a sample mean of 144 grams or greater will occur by chance if the true mean weight is 140 grams."

The P-value represents the probability of obtaining a sample mean as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true. In this case, the null hypothesis would state that the mean weight of the Gala apples is 140 grams.

Since the P-value (0.054) is greater than the significance level (α = 0.05), it is not statistically significant at the 0.05 level. This means that we do not have strong evidence to reject the null hypothesis. However, the P-value is relatively close to the significance level, indicating that there is a moderate probability of observing a sample mean of 144 grams or greater if the true mean weight is actually 140 grams.

Therefore, we can interpret the P-value as indicating that there is a 5.4% chance that a sample mean of 144 grams or greater will occur by chance alone if the true mean weight of Gala apples is 140 grams.

For more such questions on P-value

https://brainly.com/question/13786078

#SPJ8

the 90% confidence interval for p - um is (-0.816, 2.916), which can be rounded to (-0.82, 2.92). The closest option to this interval is (c) (-5.084, 7.284).

The point estimate for the difference in mean annual return is:

a - m = 7.3 - 6.2 = 1.1

To find the margin of error for a 90% confidence interval, we use the t-distribution with 16 degrees of freedom (conservative df) and a 5% significance level (90% confidence level):

t* = 1.745

The margin of error is then:

ME = t* * sqrt[(s1^2/n1) + (s2^2/n2)]

= 1.745 * sqrt[(0.093^2/17) + (0.124^2/17)]

= 0.916

The 90% confidence interval is:

(a - m) ± ME

1.1 ± 0.916

Thus, the 90% confidence interval for p - um is (-0.816, 2.916), which can be rounded to (-0.82, 2.92). The closest option to this interval is (c) (-5.084, 7.284).

learn about confidence interval,

https://brainly.com/question/20309162

#SPJ11

The total number of shares is 750000

Henry owns 17%

percentage is expressed in terms of 100

Thus, the number of shares that he owns is

17/100 * 750000

= 127500

Yes. As long as it is y = mx+b.

Expressions that are tested by the 'if' statement is called conditions.

A condition is an expression that evaluates to either 'True' or 'False', and it determines whether the code block within the 'if' statement is executed. The 'if' statement allows the program to make decisions and execute different codes based on whether the condition is 'true' or 'false'. For example, in Python, an 'if' statement might look like this:

if x > 10:

   print("x is greater than 10")

In this example, the condition being tested is 'x > 10', which will evaluate as 'True' or 'False' depending on the value of x. If the condition is 'True', then the code block within the 'if' statement (in this case, the print statement) will be executed. If the condition is 'False', then the code block within the 'if' statement will be skipped.

To learn more about python, refer:-

https://brainly.com/question/30427047

#SPJ4

Answer:

3000

Step-by-step explanation:

To simplify, 1 significant figure means a number that isn't zero. Although the zeros in 3000 do count as significant figures so this is a weird one.

The shaded area of the 22mm face of the cylinder is approximately 380 square millimeters.

To find the shaded area of the 22mm face of the cylinder, we need to determine the area of the circular face.

The formula for the area of a circle is:

Area = π * radius^2

The radius of the circular face is half of the diameter, which is 22mm, the radius would be 22mm / 2 = 11mm.

Substituting the radius into the area formula:

Area = π * (11mm)^2

Calculating the value:

Area ≈ 3.14159 * (11mm)^2

≈ 3.14159 * 121mm^2

≈ 380.1327mm^2

Rounding the area to the nearest whole number:

Area ≈ 380mm^2

Therefore, the shaded area of the 22mm face of the cylinder is approximately 380 square millimeters.

To read more about cylinder, visit:

https://brainly.com/question/9554871

#SPJ11

The Matlab & Simulink model consists of a Clock block to generate a time signal, a Gain block to multiply the time signal by 2, and a Differential Equation block to solve the given differential equation. The Scope block is used to visualize the behavior of the variable x over time.

To construct a Matlab & Simulink model for the given mathematical model, we can use Simulink's Differential Equation block and a Clock and Gain block. Here's a step-by-step guide:

1. Open Simulink in Matlab.

2. Drag and drop a Clock block from the Simulink Library Browser into the model.

3. Drag and drop a Gain block from the Simulink Library Browser into the model.

4. Double-click on the Gain block and set the Gain value to 2.

5. Drag and drop a Differential Equation block from the Simulink Library Browser into the model.

6. Double-click on the Differential Equation block and enter the equation `d²x + 3 + 4*x + 6 = 5*cos(2*t)`.

7. Connect the output of the Clock block to the input of the Gain block, and the output of the Gain block to the input of the Differential Equation block.

8. Connect the output of the Differential Equation block to a Scope block from the Simulink Library Browser.

9. Run the simulation.

The Scope block will show the behavior of the value of x over time according to the given mathematical model.

In conclusion, The Clock block provides the independent variable t, and the Differential Equation block evaluates the given equation to compute the value of x. The simulation shows the dynamic response of x as influenced by the equation and the time signal.

Learn more about Differential Equation here:

brainly.com/question/31811922

#SPJ11

The function g is defined by:

g(u) = - (1/lambda) * ln(1 - u) for 0 < u < 1.

The random variable X = g(U) has the exponential (lambda) distribution.

(i) To create a random variable X that has cdf F, and you have a number picked uniformly on (0,1), you should do the following:

Let U be a uniform (0,1) random variable. To construct a random variable X=F^(-1)(U) so that X has the cdf F, take the inverse of the cdf F, denoted as F^(-1), and apply it to the uniformly distributed random variable U.

(ii) To find the function g for an exponential distribution with parameter lambda, you should set F as the exponential cdf, which is given by:

F(x) = 1 - e^(-lambda * x)

Now, you can find the inverse function F^(-1)(u):

1. Set u = F(x): u = 1 - e^(-lambda * x)
2. Solve for x: x = - (1/lambda) * ln(1 - u)

So, the function g is defined by g(u) = - (1/lambda) * ln(1 - u) for 0 < u < 1. The random variable X = g(U) has the exponential (lambda) distribution.

To learn more about exponential distribution visit : https://brainly.com/question/22692312

#SPJ11

The probability that the three friends are seated next to each other is 1/420

The total number of ways to seat the 7 people is 7! To find the number of ways to seat the three friends next to each other, we need to consider the number of ways to seat the other 4 people around them. So the number of favorable outcomes is 4!

The probability that the three friends are next to each other is then given by the ratio of the number of favorable outcomes to the total number of outcomes: (4!)/(7!) = 4!/5040 = 1/420.

So the probability that the three friends are seated next to each other is 1/420.

To learn more about probability, refer:-

https://brainly.com/question/9793303

#SPJ4

Ans

Step-by-step explanation:]\

To use the simple interest formula, I = Prt, we substitute in the values for ... The money you put in the bank is called the principal, P, and the bank pays ... of t years at an annual interest rate r, the amount of interest, I, earned is ... Nathaly deposited $12,500 in her bank account where it will earn 4% interes

Answer:

D

Step-by-step explanation:

Rolling a die and getting a certain number will not change the chances of you getting the same number a second time. A normal die will always have a 1/2 chance of rolling an even number. However, the other answer choices will make the likelihood of getting the same type of event again slimmer as you remove one of the objects from being chosen again. An example for the first option would be drawing an ace from a deck of 52 cards where you only have 4 aces, so the chance on the first draw would have been 4/52 or a 7.7% chance while the next draw will be a 3/51 or 5.9% chance.

Answer:

The fraction of the pocket money she left is 1/8.

Step-by-step explanation:

Let the total pocket money is p.

Spent on Monday = p/2

Amount left = p - p/2 = p/2  

Spent on Tuesday = 2/3 of p/2 = p/3

Amount left = p/2 - p/3 = p/6

Spent on Wednesday = 1/4 of p/6 = p/24

Amount left = p/6 - p/24 = p/8

So, the fraction of the pocket money she left is 1/8.  

Therefore, the center of the circle is located at (0, 6), and the length of the radius is approximately equal to 7.43.

To determine the coordinates of the center and length of the radius of the circle, we need to rewrite the given equation in standard form, which is\((x - h)^2 + (y - k)^2 = r^2\), where (h, k) represents the center coordinates and r represents the radius.

Given equation: \(x^2 + y^2 - 12y - 20.25 = 0\)

To complete the square, we need to add and subtract the appropriate terms on the left side of the equation:

\(x^2 + y^2 - 12y - 20.25 + 36 = 36\)

\(x^2 + (y^2 - 12y + 36) - 20.25 + 36 = 36\)

Simplifying further:

\(x^2 + (y - 6)^2 = 55.25\)

Comparing this equation with the standard form, we can identify the following values:

Center coordinates: (h, k) = (0, 6)

Radius length:\(r^2\) = 55.25, so the radius length is √55.25.

Therefore, the center of the circle is located at (0, 6), and the length of the radius is approximately equal to 7.43.

Learn more about circle here:

https://brainly.com/question/12930236

#SPJ11

The definite integral that represents the area of the region enclosed by the polar curve r = 1 sin θ is ∫[a, b] 1/2 r^2 dθ

To determine the definite integral that represents the area of the region, we integrate the expression 1/2 r^2 with respect to θ over the interval [a, b], where a and b are the limits of the region.

In this case, the polar curve r = 1 sin θ represents a circle with radius 1 centered at the origin. As θ varies from 0 to π, the curve traces half of the circle in the positive direction. To find the area of the region enclosed by this curve, we integrate the expression 1/2 r^2 over this interval.

The expression 1/2 r^2 represents the area of a sector of the circle with radius r and central angle θ. Integrating this expression with respect to θ gives us the total area enclosed by the curve.

By evaluating the definite integral over the interval [a, b], we can find the area of the region enclosed by the polar curve r = 1 sin θ.

To know more about area click here

brainly.com/question/13194650

#SPJ11

Answer:

52

Step-by-step explanation:

42, 45, 58, 63

The mean is the sum divided by the number of terms

(42+ 45+ 58+ 63)/4

208/4

52

Answer:

Step-by-step explanation:

42 + 45 + 58 +631 + 422 + 473 + 52 = 1723

then divide by 7 to get 246.142857

hope this helps :)

Answer:

712÷6=118 remainder 4

No it is not evenly divisible by 6

Answer:

7.3 if 48 is a number (I'm not sure if you meant 4,8 or 48)

4 if you meant 48 to be separate

Step-by-step explanation:

Mean means average so you add up all the numbers then divide the answer by how many numbers there are, so 44/11=4

The true statements are:

The coordinates of the shape are given as:

Start by plotting the coordinates of ABCD on the coordinate plane.

Next, connect the dots on the plane

From the connected dots, we can see that the shape formed is a square

Start by calculating the distance between adjacent points using the distance formula

\(d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}\)

So, we have:

\(AB = \sqrt{(10 -6)^2 + (-6 +9)^2} = 5\)

\(BC = \sqrt{(6 -3)^2 + (-9 +5)^2} = 5\)

\(CD = \sqrt{(3 -7)^2 + (-2 +5)^2} = 5\)

\(DA = \sqrt{(7 -10)^2 + (-2 +6)^2} = 5\)

The perimeter (P) of the shape is calculated as:

\(P = 4 \times AB\)

\(P = 4 \times 5 = 20\)

The area (A) of the shape is calculated as:

\(A =AB \times BC\)

\(A =5 \times 5 = 25\)

Hence, the perimeter and the area of the shape is 20 units, and 25 unit squares

Read more about coordinates at:

https://brainly.com/question/17206319

We find that the function that could be a stretch of the exponential decay is \(f(x) = 2\cdot \left(\frac{1}{6} \right)^{x}\). (Correct choice: C)

Exponential functions are trascedent functions whose form is described below:

\(y = a\cdot r^{x}\)     (1)

Where:

There are two conditions for a stretch factor and exponential decay: (i) a > 1, (ii) 0 < r < 1. Thus, we find that the function that could be a stretch of the exponential decay is \(f(x) = 2\cdot \left(\frac{1}{6} \right)^{x}\). (Correct choice: C)

The picture is missing and it cannot be found, but statement is still solvable as there is only one choice that responds the question.

To learn more on exponential functions: https://brainly.com/question/11487261

#SPJ1

C. The slope is negative two-thirds, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases two-thirds of an inch every hour.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

The relationship of the candlestick between height and time is represented by a straight line passing through the points (0, 8) and (3, 6).

Slope(m) = (6 - 8)/(3 - 0).

Slope(m) = - 2/3.

Taking any of the points we have,

6 = - (2/3)×3 + b.

6 = - 2 + b.

b = 8.

y = - (2/3)x + 8.

learn more about lines and slopes here :

https://brainly.com/question/3605446

#SPJ1

Select all that apply

Question options :

The median height of the sample must be between 59 and 63 inches.

Another random sample of 20 trees is likely to have a mean between 57 and 65 inches.

The mean height of these 20 trees is likely to be the same as the mean height of all trees in the back field .

The mean height of these 20 trees is likely to be the same as the mean height of a second random sample of 20 trees.

Shawn would be more likely to get an accurate estimate of the mean height of the population by sampling 40 trees instead of sampling 20 trees.

Answer:

The median height of the sample must be between 59 and 63 inches.

The mean height of these 20 trees is likely to be the same as the mean height of all trees in the back field .

The mean height of these 20 trees is likely to be the same as the mean height of a second random sample of 20 trees.

Shawn would be more likely to get an accurate estimate of the mean height of the population by sampling 40 trees instead of sampling 20 trees

Explanation:

The mean absolute deviation is the summary of absolute deviations from the central point or average of a data set. The central point measurement can be the mean, median or mode of the data set. An average absolute deviation can be used instead of a standard deviation to measure dispersion from central point.

In the above case, a sample is taken of 20 trees and there is a mean absolute deviation of 2, hence, median can be between 59 and 63. Also sample represents population, therefore mean of another sample taken is likely to be same as the previous one taken. Mean invariably gets more accurate as sample size increases too.

Answer:

Step-by-step explanation:

Sorry I can't explain how it is done. It is very difficult to explain on paper.

Answer:

2.048, 2.48, 2.4812, 2.5

From lowest to highest

Step-by-step explanation:

Answer

2.048 ,2.48, 2.4812, 2.5

Step-by-step explanation:

Answer:

\((x+8)(x+3)\)

Step-by-step explanation:

\(x^2+11x+24\\\\=(x+s_1)(x+s_2)\\\\and\:we\:have\:that\\\\s_1+s_2=11\\\\s_1s_2=24\\\\so\:by\:guessing\:we\:can\:say:\\\\s_1=8\\\\s_2=3\\\\=(x+8)(x+3)\)

Given:

A straight-line graph  has gradient 4  and crosses the y axis at (0, −3).

To find:

The equation of the given graph.

Solution:

The slope intercept form of a line is:

\(y=mx+b\)            ...(i)

Where, m is the slope of the line and b is the y-intercept.

A straight-line graph  has gradient 4. It means the slope of the line is 4.

\(m=4\)

Line crosses the y axis at (0, −3). So, y-intercept is -3.

\(b=-3\)

Putting m=4 and b=-3 in (i), we get

\(y=(4)x+(-3)\)

\(y=4x-3\)

Therefore, the equation of the given line graph is \(y=4x-3\).

Answer:

The answer is option B.

Step-by-step explanation:

Before the regulations were applied to the field of chemistry, the elements, their characteristics and other information related to them were so disorganized that this was causing the progress in the field to slow down.

So the committees decided to regulate things such as the names of any newly discovered elements, any properties it had so that it could be put to use in a more effective way.

The correct answer for this question is option B.

I hope this answer helps.

The early committees regulated how the newly discovered elements were named.

Around the  mid-1800s to the early 1900s, chemical discoveries soared rapidly due to the invention of new equipment that made research a lot more easier.

Around 1919, the international union of pure and applied chemistry set up committees to regulate the naming of new elements and compounds hence strict rules were set up for the naming of newly discovered elements and compounds.

Hence, the early committees regulated how the newly discovered elements were named.

Learn more: https://brainly.com/question/15905749