Consider the given probability histogram of a binomial
random variable.



What are the center and shape of the distribution?
0.4
A. Center: 2
Shape: symmetric

B. Center: 2.5
Shape: symmetric

C. Center: 2.5
Shape: slightly skewed

D. Center: 3
Shape: uniform

As you can see below, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.

The associative law in mathematics states that the grouping of numbers in an addition or multiplication operation does not affect the result. In other words, you can regroup terms within parentheses without changing the value of the expression.

Using the associative law, we can regroup the terms in the expression s + (r + 75) by removing the parentheses and rearranging the terms:

s + (r + 75) = (s + r) + 75

The expression (s + r) + 75 is equivalent to s + (r + 75) because the addition operation is associative.

Let's take an example to illustrate this:

Suppose s = 10 and r = 20.

Using the original expression:

s + (r + 75) = 10 + (20 + 75) = 10 + 95 = 105

Using the expression with regrouped terms:

(s + r) + 75 = (10 + 20) + 75 = 30 + 75 = 105

As you can see, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.

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The length of the side b of the right triangle is 76 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees. Therefore, the side b of the right triangle can be found as follows:

tan 30° = opposite / adjacent side

where

opposite side = a = 44 units

adjacent side = b

Therefore,

tan 30° = 44 / b

cross multiply

b = 44 / tan 30

b = 44 / 0.57735026919

b = 76.2102710661

Therefore,

b = 76 units

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Check the picture below.

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~5 - 2~~)^2 + (~~7 - 1~~)^2} \implies d=\sqrt{( 3 )^2 + ( 6 )^2} \\\\\\ d=\sqrt{ 9 + 36 } \implies d=\sqrt{ 45 }\implies d\approx 6.7\)

Answer:

what

Step-by-step explanation:

Answer:

x=3

y= -1

Step-by-step explanation:

with 1 equation you can solve for 1 variable. With 2 equations you can solve for 2 variables. This is solvable.

6x-7y = 25

15x+3y = 42

first simplify to make easier to work with

6x-7y = 25 can not be factored further

15x+3y = 42 can be divided by 3 on both sides

5x+y = 14

----- then you have

6x-7y = 25

5x+y = 14

solve by substitution:

isolate y in second equation

5x+y = 14 ---->    y= 14-5x

put y into first equation

6x-7(14-5x) = 25

6x- 98 --35x =25

6x- 98 +35x =25

41x =123

x=3

to get y, substitute x into equation

5x+y = 14

5(3) +y=14

15+y=14

y=-1

hope this helps !

The equation of the line is x = 7 which is parallel to the y-axis and passes through the point (7,0)

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

We have:

The line that is parallel to the y-axis and passes through the point (7,0)

As we know the line equation:

Parallel to the y-axis

x = c

Passes through the point (7,0)

x = 7

Thus, the equation of the line is x = 7 which is parallel to the y-axis and passes through the point (7,0)

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Answer:

Negative slope

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer:

C

Step-by-step explanation:

1 cm = 10 mm. Length of book : 28 cm. Length of book = 280 mm. This shows that measurements in mm are the same but look to have a higher number .

The conversion factor provided states that 1 cm is equal to 10 mm, which means that 1 cm is made up of 10 individual millimeters.

The length of my book in when measured in millimeters is 280 mm.

In centimeters, this is therefore:

= 280 mm / 10 cm /mm

= 28 cm

Although the numerical value appears higher when expressed in millimeters, it is important to note that the actual length of the book remains the same.

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Answer:

B. making an inference.

Step-by-step explanation:

The drama teacher's decision to add another performance time on Saturday is a result of making an inference based on the information that 80% of last year's sold-out plays occurred during weekend performances. By observing this pattern, the drama teacher infers that adding another performance on Saturday will likely attract a larger audience and increase the chances of having a sold-out show.

Answer:

x ≈ 24.4

Step-by-step explanation:

Since the 2 legs of the triangle are congruent, both 26, then the triangle is isosceles.

The line segment x is a perpendicular bisector and divides the isosceles triangle into 2 congruent right triangles, with base 18 ÷ 2 = 9

Using Pythagoras' identity in either of the 2 right triangles, then

x² + 9² = 26² , that is

x² + 81 = 676 ( subtract 81 from both sides )

x² = 595 ( take the square root of both sides )

x = \(\sqrt{595}\) ≈ 24.4 ( to the nearest tenth )

Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

\(\[ y = 1.3642x + 3.2324 \]\)

To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:

\(\[ y = 1.3642(7) + 3.2324 \]\)

Simplifying the equation, we get:

\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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The time spent higher than 26 meters above the ground is 0.42 minutes. Answer: 0.42

A Ferris wheel is 30 meters in diameter and boarded from a platform that is 4 meters above the ground.

The six o'clock position on the Ferris wheel is level with the loading platform.

The wheel completes 1 full revolution in 2 minutes.

We have to find how many minutes of the ride are spent higher than 26 meters above the ground.

So, let's start with some given data,Consider the height of a person at the six o'clock position = 4 meters

So, the height of a person at the highest point = 4 + 15 = 19 meters (since the diameter is 30 meters, the radius will be 15 meters)

Also, the height of a person at the lowest point = 4 - 15 = -11 meters

Therefore, the Ferris wheel completes one cycle from the lowest point to the highest point and back to the lowest point.

So, the total distance travelled will be = 19 + 11 = 30 meters.

Also, we are given that the wheel completes 1 full revolution in 2 minutes.

We need to calculate the time spent higher than 26 meters above the ground.

So, the angle between the 6 o'clock position and 2 o'clock position will be equal to the angle between the 6 o'clock position and the highest point.

This angle can be calculated as follows:

Angle = Distance travelled by the Ferris wheel / Circumference of the Ferris wheel * 360 degrees

Angle = 30 / (pi * 30) * 360 degrees

Angle = 360 degrees / pi

= 114.59 degrees

So, the total angle between the 6 o'clock position and the highest point is 114.59 degrees.

Now, we need to find out how much time is spent at an angle greater than 114.59 degrees.

This can be calculated as follows:

Time = (Angle greater than 114.59 degrees / Total angle of the Ferris wheel) * Total time taken

Time = (180 - 114.59) / 360 * 2 minutes

Time = 0.42 minutes

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Step-by-step explanation:

At first let's understanding the question,

In this following questions it has given that;

Difference of two numbers is 19. If the smaller number is 18, we have to find the greater

number.

According to the question:-

let the Greater no is =G

in question, The smaller no is =18

The difference of two no is =19

Solution:-

From the question,

Final answer:-

\(\therefore\) The greater no is 37.

Answer:

1.45 x 10   {2}

Step-by-step explanation:

The term "100 points" usually indicates a high level of achievement or success in a particular area.

The term "100 points" can refer to a number of different things depending on the context. For example, in sports, it could refer to a team scoring 100 points in a game.

In wine tasting, it could refer to a perfect score given to a wine by a critic or judge. In school, it could refer to receiving a perfect score on an exam or assignment worth 100 points.

It's important to note that while a perfect score of 100 points is often seen as the ultimate goal, it's not always necessary or even possible in some situations. In many cases, simply doing your best and striving for improvement is enough to be considered successful.

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Answer:

96

Step-by-step explanation:

Given that :

Standard deviation (s) = 2km

Error in estimation is within 0.4 km ; Error (E) = 0.4 km

Using the relation :

Sample size = ((Zα/2 * s) /E)^2

Using α = 0.05

The Zcritical at 0.05 = Z0.025 = 1.96

Sample size = ((1.96 * 2) / 0.4)^2

Sample size = (3.92 / 0.4)^2

Sample size = 9.8²

Sample size = 96.04

Required sample size = 96

Answer:

x = 6.24

Step-by-step explanation:

x =

Tan32° = OPP/ADJ

Tan32° = x/10

0.624 = x/10

cross-multiply

x = 6.24

Answer:

The expected rate of return is 6.3%.

The standard deviation is of 11.29%.

Step-by-step explanation:

Expected rate of return

Multiply each rate by its probability. So

\(E = 0.1(-20) + 0.2(0) + 0.4(7) + 0.2(15) + 0.1(25) = 6.3\)

The expected rate of return is 6.3%.

Standard deviation:

Square root of the difference squared between each value and the mean, multiplied by the probability. So

\(S = \sqrt{0.1(-20-6.3)^2 + 0.2(0-6.3)^2 + 0.4(7-6.3)^2 + 0.2(15-6.3)^2 + 0.1(25 - 6.3)^2} = 11.29\)

The standard deviation is of 11.29%.

The optimal Bayesian classifier is the one that minimizes the probability of misclassification. This can be achieved by choosing the class that has the highest posterior probability given the observed data. In this case, we need to compare the conditional class probabilities P2(t) and P0(I) for each data point and choose the class with the higher probability.

To find the optimal Bayesian classifier, we need to find the values of a and b that define the decision boundary between the two classes. This can be done by setting P2(t) = P0(I) and solving for x:

P2(t) = P0(I)
Pr(Y; = 1|X, = x) = Pr(Y; = 0[Xi = 1)
1 - P2(I) = P2(I)
2P2(I) = 1
P2(I) = 0.5

Now we can solve for x to find the decision boundary:

0.5 = Pr(Y; = 1|X, = x)
0.5 = P2(I)
x = a + b

Therefore, the optimal Bayesian classifier is of the form:

if Xe [a, b] then yi = 1
if Xe [b, a] then yi = 0

where a and b are the values of x that satisfy P2(I) = 0.5.

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Answer:

68+97i

Step-by-step explanation:

work shown and pictured

Answer:

68+97i

Step-by-step explanation:

(39 + 34i) + (76 + 89i) - (47 +26i).

Distribute the minus sign

(39 + 34i) + (76 + 89i) + (-47 -26i)

Combine like terms

(39+76-47)+(34i+89i-26i)

68+97i

Answer:

the driver tried to fix it by lighting up the engine thinking it would start again. it didnt and the entire engine set on fire. the bus doors were closed and everyone was trapped inside. everybody inside burnt to a crisp as the fire spread and local residents heard their screams as their skin melted. the end...

Answer:

32

Step-by-step explanation:

4y + 8 and y = 6 ( plug in 6 to y )

4 x 6 + 8

24 + 8 = 32

For the statement "If a polygon lacks right angles, then it is a parallelogram.", the counter example is -

Option A : a right triangle

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

A counterexample for a conditional statement is an example that satisfies the hypothesis (the first part of the statement) but does not satisfy the conclusion (the second part of the statement).

In this case, the statement is "If a polygon lacks right angles, then it is a parallelogram."

A right triangle is a polygon that lacks right angles, but it is not a parallelogram.

Therefore, a right triangle is a counterexample for this statement.

A square, a regular hexagon, and a rectangle all have right angles, so they are not counterexamples for this statement.

Therefore, the triangle is the counterexample.

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Answer:

Both A and B

Step-by-step explanation:

Both a and b. A three-way intersection can be referred to as a T-intersection or a Y-intersection, depending on the shape of the intersection. In a T-intersection, one road intersects another road perpendicularly, forming a T-shape. In a Y-intersection, one road splits into two branches, forming a Y-shape.