If an 8-foot ladder is placed 3 feet from the wall, what is the approximate height it will reach on the wall?

11 feet
7 feet
5 feet

The statement is True only for independent events and False otherwise. The statement "p (A ∩ B) = p(A). p(B)" is not always true for any two events A and B defined on a sample space S of an experiment.

This equation only holds true if A and B are independent events, meaning that the occurrence of one event does not affect the probability of the other event happening. In other words, p(A|B) = p(A) and p(B|A) = p(B).

If A and B are dependent events, meaning that the occurrence of one event affects the probability of the other event happening, then the equation does not hold true. In this case, the probability of A and B occurring together (p(A ∩ B)) would be less than the product of the probabilities of A and B occurring separately (p(A).p(B)).

Therefore, the statement is not always true and depends on whether A and B are independent or dependent events.

Learn more about experiment here:

brainly.com/question/28198971

#SPJ11

The dimension of the rectangle that has the maximum area is 7.5 by 7.5 feet.

Let the length of the rectangular field be x and the width be y

Now the perimeter is 30

Therefore 2(x + y)=30

or, x + y = 15

or, y = 15 - x

Area of the rectangle = xy

Now we substitute the value of y

area = x ( 15 - x ) = 15x - x²

Now for the maximum area we have to differentiate the area function.

f(x) = 15x - x²

f'(x) = 15-2x

Now the differentiated function is equated to 0 to get the value of x for which the area is  maximum.

15-2x = 0

or, x =7.5

therefore y -= 15 - x = 1 5 - 7.5 = 7.5 feet.

Hence for the area to be maximum the dimension of the field should be 7.5feet by 7.5 feet .

To learn more about rectangle visit:

https://brainly.com/question/12019874

#SPJ9

20

y'all homeworks are easy lølllll

The completed statements with regards to the similar right triangles are;

ΔDNF ~ ΔDEN and ΔDNF ~ ΔFEN

If DE = 10 and EF = 15, then ND = 5·√(10)

Similar triangles are triangles that have the same shape but may have different side lengths.

The angle ∠DNF is a right angle, therefore, ΔDNF is a right triangle.

\(\overline{NE}\) ⊥ \(\overline{DF}\), therefore, triangles ΔDEN and ΔFEN are right triangles

The angle ∠NDE is congruent to ∠FNE (Complementary angles to the same angle, ∠NFD)

Therefore; ΔDNF is similar to triangle ΔDEN and ΔDNF is similar to triangle ΔFEN by Angle-Angle, (AA) similarity postulate.

Therefore, we get;

The similar triangles, ΔDNF, ΔDEN and ΔFEN indicates;

EN/DE = EF/EN

(EN)² = (DE) × (EF)

(EN)² = 10 × 15 = 150

EN = √(150) = 5·√6

(ND)² = (DE)² + (EN)²

Therefore; (ND)² = 10² + 150 = 250

ND = √(250) = 5·√(10)

Learn more on similar triangles here: https://brainly.com/question/29782809

#SPJ1

The P-value is less than a = 0.01, and they should conclude that there is a difference between the proportions.

The confidence interval for the difference between the proportion of male and female drivers who have received a speeding ticket is (0.011, 0.087), which means that we are 99% confident that the true value of the difference in proportions falls within this interval.

To test the null hypothesis H: PM = Pw versus H: PM ≠ Pw, we need to see if the confidence interval includes the null value of 0. If it does not, then we can reject the null hypothesis and conclude that there is a significant difference between the proportions of male and female drivers who have received a speeding ticket.

Since the confidence interval does not include the null value of 0, we can conclude that there is a significant difference between the proportions of male and female drivers who have received a speeding ticket. The P-value is less than a = 0.01, which means that the probability of obtaining a difference in proportions as extreme as or more extreme than the one observed, assuming that the null hypothesis is true, is less than 0.01. Therefore, we reject the null hypothesis and conclude that there is a statistically significant difference between the proportions of male and female drivers who have received a speeding ticket. The correct answer is c. The P-value is less than a = 0.01, and they should conclude that there is a difference between the proportions.

To learn more about proportions visit:

https://brainly.com/question/30657439

#SPJ11

Answer:

$215.26

Step-by-step explanation:

717.53*30%= $215.26

Using the mean formular, the sum of the four scores that are not the median would be 360.

Average or mean score = 450 / 5

Mean score = 90

Hence, median score = mean score = 90

The sum of the 4 scores that are not the median can be calculated thus :

Sum of the 4 scores = 450 - 90 = 360

Hence, the sum of the 4 scores that are not the median is 360.

Learn more :https://brainly.com/question/25638609

Answer:

-15

Step-by-step explanation:

Answer: y=-4x+1

Step-by-step explanation:

The slope-intercept form of a line is y=mx+b. Therefore, y needs to be on one side of the equation, and the x term and constant need to be on the other. Rearrange the equation to make this true:

4x+y=1

(4x+y)-4x=1-4x

y=1-4x

y=-4x+1

Answer:

C)   4(5c -2d)

Step-by-step explanation:

You would need to find the greatest commen factor in the equation.

it would end up being 4 since it is the biggest number that can divide between 8 and 20.

20/ 4 = 5

8/4 = 2

so you would leave the varibles since you can't take them out and put 4 on the outside of the parantheses.

4(5c -2d)

Answer:

Option C:   4(5c -2d)

Step-by-step explanation:

Have a nice day! :-)

Answer:

sum of angles in atriangle=180°

Step-by-step explanation:

w-45°+w-37°+w+19°=180°(sum of angles in a triangle)

3w=180°+45°+37°-19°

3w=243°

w=81°

Answer:

The answer would be 4,450

Step-by-step explanation:

:)

Answer:

a line that continually approaches a given curve but does not meet it at any finite distance.

Step-by-step explanation:

Answer:

2.56 divided by 4 so $0.64 a pound

Step-by-step explanation:

2.56 divided by 4 = 0.64

Answer:

there will only be one 3

Step-by-step explanation:

see cause the first 3 of both numbers are 2 but only the last one of both numbers are 3 .

Answer:

99 percent

Step-by-step explanation:

I sat this because u have to add them together and that gives you the answer or u can subtract

a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

Learn more about subspace

brainly.com/question/30318872

#SPJ11

Answer: The answer is F

Step-by-step explanation:

The type of graph that groups data values into classes is a histogram.

A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class. The frequency is usually on the vertical axis while the class is usually on the horizontal axis. The class is a group assigned to numbers that are similar.

To learn more about histograms, please check: https://brainly.com/question/14473126

#SPJ1

Cluster sampling is a sampling technique used in statistics and research methodology where a population is divided into groups, or clusters, and a sample is randomly selected from each cluster to be included in the study.

This method is often used when it is difficult or impractical to obtain a simple random sample of individuals from a large and diverse population. For example, in a study of public schools in a state, it may be easier to randomly select a sample of schools and then include all students in those schools in the study, rather than attempting to randomly select individual students from the entire state.

The advantages of cluster sampling include lower costs and greater efficiency than other sampling techniques, particularly when working with large populations. However, it can also increase the risk of sampling bias and decrease the precision of estimates if the clusters are not representative of the larger population. Therefore, it is important to carefully choose clusters that are as heterogeneous as possible within and as similar as possible between clusters.

Learn  more about cluster sampling here: brainly.com/question/11003935

#SPJ4

Therefore , the solution of the given problem of square comes out to be

RS= 3 √3/4 unit.

Euclidean geometry states that a square is a quadrilateral square has four equal sides plus four equal angles. A rectangle has two adjacent sides that are of the same length is another name for it. An equilateral quadrilateral is one that has a square as one of its four equal sides and four equal angles. A square angle is one that is 90 degrees or straight. The diagonals of the square are also split at a 90 degrees and are equally spaced. a rectangle next to it that has two sides of equal length. four equal-length sides and four right angles make up a quadrilateral. a parallelogram with a right angle formed by two neighboring, equal sides. rectangle with straight sides.

Here,

Given :

PQ⊥RS

=> c−a=b−d.1)

=> PQ=  3 √3/4

​=> PQ² = 27/16

​=> 1+(a−c)² =27/16

​

=> RS= √(b−d)² +1   (3)

=> By equation (1),(2)and (3)

RS= 3 √3/4

Therefore , the solution of the given problem of square comes out to be

RS= 3 √3/4 unit.

To know more about square visit:

https://brainly.com/question/14198272

#SPJ4

​

​

The equation x³ + 256 = 0 has a value of x = -6.35

The equation is given as

x³ + 256 = 0

To determine the solution graphically, we simply enter the equation in a graphing calculator

And then, we write out where the equation intercepts the x-axis

Using the above as a guide, we have

x³ + 256 = 0

Plot the graph (see attachment)

From the graph, we have

x = -6.35 (approximately)

Hence, the solution to the equation is x = -6.35

Read more about equations at

https://brainly.com/question/27887972

#SPJ1

The perimeter of the Christian's sandbox is 24 feet.

The given two quadrialterals are similar

Let us find the remaining lengths of Christian's sandbox

By proportional equation

36/8=18/x=27/y=18/z

4.5=18/x=27/y=18/z

x=18/4.5 = 4

y=27/4.5 = 6

z=4

The perimeter is sum of all the sides

So perimeter of Christian's sandbox is 8+6+4+4

24 feet

Hence, the perimeter of the Christian's sandbox is 24 feet.

To learn more on Similar figures click:

https://brainly.com/question/25882965

#SPJ1

Answer: 17. is A and 18 is most likely G

Step-by-step explanation:

Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

The distance between the two aircraft is: 2.29 km.

We have to find the vector from the ground under the controller of the first airplane

The position vector from ground of first plane is

\(r_1=(19.2km)(cos25 ^\circ)i +(19.2km)(sin25 ^\circ)j+(0.8km)k =(17.4i+8.11j+0.8k)km\)

The position vector of second plane is:

\(r_2=(17.6km)(cos20 ^\circ)i +(17.6km)(sin20 ^\circ)j+(1.1km)k =(16.5i+6.02j+1.1k)km\)

Finding the displacement from the first plane to second

The displacement from the first plane to the second plane is:

\(r_2-r_1=(-0.863i-2.09j+0.3k)km\)

with magnitude :

\(= > \sqrt{(0.863)^2+(2.09)^2(0.3)^2}km=2.29km\)

Learn more about Distance at:

https://brainly.com/question/29796666

#SPJ4

The given question is incomplete, complete question is:

An air-traffic controller observes two aircraft on his radar screen. The first is at altitude 800m, horizontal distance 19.2km, and 25.0 degree south of west. The second aircraft is at altitude 1100m, horizontal distance 17.6km, and 20.0 degree south of west. What is the distance between the two aircraft? (Place the x axis west, the  y axis south, and the z axis vertical.)

Answer:

a) 0

Step-by-step explanation:

Given that TRAP × 9 = PART and  T, R, A, P all have different integer values (that is their values are different). TRAP and PART are both made up of four integers digits, that means 1000 ≤ TRAP and PART ≤ 9999. This means that TRAP × 9 ≤ 10000. The value of R can be gotten from:

\(TRAP<\frac{10000}{9}<1112(rounding \ to \ the \ next \ whole \ number)\)

T cannot be 0, therefore T= 1, Since their values are different, R cannot be equal to T, we get that R can only be 0