A 45-45-90 triangle is shown below. Find the length of A and B. Leave answer in simplified radical form.

The null hypothesis can be rejected at the 0.05 or 5 % level of significance according to Decision Rule.

The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental results are reliable. Depending on whether the population or sample under consideration is viable, this hypothesis is either rejected or not. Or to put it another way, the null hypothesis is a hypothesis that assumes that the sample observations are the product of chance. It is claimed to be a claim made by surveyors who wish to look at the data. The symbol for it is H0.

Given :  n = 8          

\(\large \bar{X}=105.20 \\\\ \larg\frac{\sigma}{\sqrt{n}}=1.77 \\ \\ \large \alpha=0.05 \large \mu_0=100\)

a )  We want to find the 95% confidence interval for mean

Therefore ,

\(\large (105.20-Z_{0.05}*1.77,105.20+Z_{0.05}*1.77)\\\\\large (105.20-1.64*1.77,105.20+1.64*1.77)\\\\\large (105.20-2.9028,105.20+2.9028)\)

(102.2972,108.1028)

b )  Hypothesis :  

\(\large H_0:\mu=100 \\ \\ \large H_1:\mu\neq 100\)

The test statistic under H is given by ,

\(\large Z\rightarrow N(0,1)\\\\ \large Z =\frac{105.20-100}{1.77}\\\\ \large =\frac{5.20}{1.77}\\\\\large =2.9379\)

\(P value \large =P(Z > |Z_{cal}|)\)

=P(Z>2.9379)

=0.001652

Decision Rule :  If P value \(< \large \alpha\)  then reject  at  \(\large \alpha\) % level of significance accept otherwise

Here , P value = 0.001652 < \large \alpha = 0.05

Therefore , reject H at 5% level of significance.

Learn more about Null Hypothesis:

https://brainly.com/question/15980493

#SPJ4

Answer:

Chloe will earn $100 outright plus $7 dollars for every lap she swims for her school.

Step-by-step explanation:

A) In both cities = 0.3

B) In neither cities = 0.2

Given,

P(Industry in Shanghai) = P(A) = 0.7

P(Industry in Beijing) = P(B) = 0.4

P(Industry in Shanghai or Beijing)  = P(A∪B) = 0.8

a) We need to find the probability that the industry is located in both Shanghai and Beijing.

That is we need to find P(A∩B)

P(A∪B) = P(A) + P(B) - P(A∩B)

Substituting the values we get,

0.8 = 0.7 + 0.4 - P(A∩B)

P(A∩B) = 0.3

Thus, the probability that the industry is located in both Shanghai and Beijing is 0.3.

b) Now, we need to find the probability that it is not in either cities

Probability = 1 - Probability(Industry in Shanghai or in Beijing)

                = 1 - P(A∪B)

                = 1 - 0.8

                = 0.2

Learn more about probability here: https://brainly.com/question/13335415

#SPJ4

The question is incomplete. Completed question is given below.

The probability that an American industry will locate in Shanghai, China, is 0.7, the probability that it will locate in Beijing, China, is 0.4, and the probability that it will locate in either Shanghai or Beijing or both is 0.8. What is the probability that the industry will locate

A. in both cities?

B. in neither city?

For all given Quadrilaterals none has enough information provided in the problem to definitively say - if they are a parallelogram.Hence, option E is correct for all.

If a quadrilateral is a parallelogram, it satisfies the following properties:

It is important to note that in order to definitively conclude that a quadrilateral is a parallelogram, all four properties must be satisfied. If only one or some of the properties are met, it does not necessarily guarantee that the quadrilateral is a parallelogram.

Figure 1-: Adjacent angles are 105 and 75 degrees, which satify the condition of opposite angles being equal but except this no other information is provided, Hence, we don't have enough information to say figure 1 is a parallelogram.

Figure 2-: Diagonals bisect each other and make angle 65 degree with each other. Given that Diagonal 1 bisects Diagonal 2 and the opposite sides of the quadrilateral are equal, by using SAS criterion, the congruency of triangles formed by the diagonals can be derived to say that the opposite angles of the quadrilateral are also equal . However, we still need more information about parallelism of sides to definitively say given quadrilateral is a parallelogram.

Figure 3-: One pair of opposite side is equal in length ,while other pair of line is parallel to each other.This information is insufficient to determine if given quadrilateral is a parallelogram.

Learn more about parallelogram here:

https://brainly.com/question/29147156

#SPJ1

Answer:

y = x^58/5

Step-by-step explanation:

Nothing further can be done with this topic. just remove the parentheses and it becomes x^58 and u cannot dive because they’re like terms

The probability that the second ball you draw is gold is 0.619.

What is the probability?

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Here, we have

Given: a room contains several urns 13 urns contain two gold balls, 6 urns contain one gold ball and one silver ball, 20 urns contain two silver balls.

Conditional probability is a measure of the probability of an event occurring given that another event has occurred.

Here given event is that first ball is gold. Hence sample space will have 13+8 = 21 urns.

For second ball to be gold, urn should have 2 gold balls hence it has 13 urns under above condition.

Probability = 13/21 = 0.619

Hence, the probability that the second ball you draw is gold is 0.619.

To learn more about the probability from the given link

https://brainly.com/question/7965468

#SPJ4

The solution of the inequality 3(n - 6) > 2(n + 12) will be less than 42. Then the correct option is D.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

3(n - 6) < 2(n + 12)

Simplify the inequality, then we have

3(n - 6) < 2(n + 12)

3n - 18 < 2n + 24

3n - 2n < 24 + 18

n < 42

The solution of the inequality 3(n - 6) > 2(n + 12) will be less than 42. Then the correct option is D.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ1

12. Answer

w+(9+3)

13. Answer

17+12+y+z

Answer:

noooo he/she left...

Step-by-step explanation:

The required answer is the all of the given points (A, B, C, and D) are on the unit circle.

The unit circle is a circle with a radius of 1 unit centered at the origin of a coordinate plane. Points on the unit circle can be represented by their coordinates (x, y), where x is the cosine of the angle and y is the sine of the angle.

To determine which of the following points is on the unit circle, we need to check if the coordinates satisfy the equation x^2 + y^2 = 1. If the coordinates satisfy this equation, then the point is on the unit circle.

consider the points given and check if they are on the unit circle:

- Point A: (1, 0)
- Point B: (0, -1)
- Point C: (-√2/2, √2/2)
- Point D: (0, 1)

Checking each point:

- Point A: (1, 0)
   - 1^2 + 0^2 = 1 + 0 = 1
   - The coordinates satisfy the equation, so point A is on the unit circle.

- Point B: (0, -1)
   - 0^2 + (-1)^2 = 0 + 1 = 1
   - The coordinates satisfy the equation, so point B is on the unit circle.

- Point C: (-√2/2, √2/2)
   - (-√2/2)^2 + (√2/2)^2 = 2/4 + 2/4 = 4/4 = 1
   - The coordinates satisfy the equation, so point C is on the unit circle.

- Point D: (0, 1)
   - 0^2 + 1^2 = 0 + 1 = 1
   - The coordinates satisfy the equation, so point D is on the unit circle.

In conclusion, all of the given points (A, B, C, and D) are on the unit circle because their coordinates satisfy the equation x^2 + y^2 = 1.

To know about unit circle . To click the link.

https://brainly.com/question/11987349

#SPJ11

Answer:

30

Step-by-step explanation:

The LCM of 2,3,5 is the result of multiplying all prime factors the greatest number of times they occur in either number. The LCM of 2,3,5 is 2⋅3⋅5 = 30

Answer:

30

Step-by-step explanation:

Its that easy. I got the answer from online.

Answer:

is the longest side in a triangle

Step-by-step explanation:

is the longest side in a triangle

Answer:

It is the longest side of a right triangle.

Step-by-step explanation:

A right triangle has two legs, then the (i call it a slope) hypotenuse connects the two from the top of one of leg to the end of the bottom leg.

you can calculate the hypotenuse via the Pythagorean theorem. which is A^2+B^2=C^2

Or: Leg 1^2+ Leg 2^2= Hypotenuse^2

Answer:

\(2 x^{2} + 3x + 3 - 1\)

We can writey + dy = 2x1x2 / (x1+x2) + 2x1Δx2/ (x1+x2) + 2x2Δx1/(x1+x2)+ 2Δx1Δx2/ (x1+x2)On subtracting y from both sides, we getdy = 2x1Δx2/ (x1+x2) + 2x2Δx1/ (x1+x2) + 2Δx1Δx2/ (x1+x2)

Given y= x1/(x1+x2)  we need to find the total differential of y.It is given that, y= x1/(x1+x2)Let us assume, x1 = x1+Δx1, x2 = x2+Δx2. On substituting these values, we get + dy = (x1 + Δx1)/ (x1 + Δx1 + x2 + Δx2)We know that dy = y - (x1 + Δx1)/ (x1 + Δx1 + x2 + Δx2)

On further simplification, we get,dy = (Δx1(x2+Δx2))/(x1+Δx1+x2+Δx2)²-(Δx1x2)/((x1+Δx1+x2+Δx2)²)Since Δx1 and Δx2 are very small, we can neglect their squares and products, i.e., Δx1², Δx2², and Δx1.Δx2

Hence the total differential of y= x1/(x1+x2) is given by dy = (-x1x2/(x1+x2)²) dx1 + (x1²/(x1+x2)²) dx2. Note: x1 and x2 are independent variables.

Therefore, dx1 and dx2 are their differentials.Given y=2x1x2 /(x1+x2) Let us assume, x1 = x1+Δx1, x2 = x2+Δx2. On substituting these values, we gety + dy = 2(x1 + Δx1)(x2 + Δx2)/ (x1 + Δx1 + x2 + Δx2)On simplifying, we gety + dy = (2x1x2+2x1Δx2+2x2Δx1+2Δx1Δx2)/(x1+Δx1+x2+Δx2)

Since Δx1 and Δx2 are very small, we can neglect their squares and products, i.e., Δx1², Δx2², and Δx1.Δx2

Hence the total differential of y=2x1x2 /(x1+x2) is given by dy = (2x2/(x1+x2)²) dx1 + (2x1/(x1+x2)²) dx2.

For more such questions on subtracting

https://brainly.com/question/28467694

#SPJ8

Mrs. Thakur will receive Rs 9331.2 after 2 years, with an interest rate of 8% compounded annually.

To find the total amount Mrs. Thakur will receive after 2 years,

We need to calculate the compound interest.

The formula for compound interest is: A = P * (1 + r/100)^n

Where A is the final amount, P is the principal (Rs 8000),

r is the interest rate (8%), and n is the number of years (2).

So,

A = 8000 * (1 + 8/100)^2

A = 8000 * (1.08)^2

A = 8000 * 1.1664

A = 9331.2

Therefore, Mrs. Thakur will receive Rs 9331.2 after 2 years

Read more about compound interest at

https://brainly.com/question/24274034

#SPJ1

Answer:

7 y /5

Step-by-step explanation:

Answer:

g(5)=-2(5)+1

g(5)=-10+1

g(5)=-9

To approximate the solution and maximize the given objective function we need to find the steepest ascent direction and iteratively update the values of x₁ and x₂ to approach the maximum value of z.

The method of steepest ascent involves finding the direction that leads to the maximum increase in the objective function and updating the values of the decision variables accordingly. In this case, we aim to maximize the objective function z = -(x₁ - 3)² - (x₂ - 2)².

To find the steepest ascent direction, we can take the gradient of the objective function with respect to x₁ and x₂. The gradient represents the direction of the steepest increase in the objective function. In this case, the gradient is given by (∂z/∂x₁, ∂z/∂x₂) = (-2(x₁ - 3), -2(x₂ - 2)).

Starting with initial values for x₁ and x₂, we can update their values iteratively by adding a fraction of the gradient to each variable. The fraction determines the step size or learning rate and should be chosen carefully to ensure convergence to the maximum value of z.

By repeatedly updating the values of x₁ and x₂ in the direction of steepest ascent, we can approach the solution that maximizes the objective function z. The process continues until convergence is achieved or a predefined stopping criterion is met.

Learn more about fraction here:

https://brainly.com/question/10354322

#SPJ11

Answer:

3 tiles

because 1/4+1/4+1/4=3/4

I hope this helps you!

If the force and acceleration are in the same direction, the mass of the object would be 0.83 kg.

The mass of the object cannot be determined with the given information. Acceleration is related to force and mass through Newton's Second Law: F = ma. However, in this case, we are given the acceleration and force, but not the mass. To find the mass, we would need either the acceleration and the force, or the force and the mass.

However, if we assume that the force and acceleration are both in the same direction, we can use the formula F = ma to find the mass. Rearranging the formula, we get m = F/a.

Substituting the given values, we get:

m = 10 N / 12 m/s²

m = 0.83 kg

So, if the force and acceleration are in the same direction, the mass of the object would be 0.83 kg.

Learn More about acceleration

https://brainly.com/question/26408808

#SPJ4

Complete Question:

A moving train accelerates at a rate of 12 meters per second. What would your mass be if the applied force were 10N?

The probability of being born on a Tuesday is= 18/343

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The likelihood that an event will occur increases with its probability.

A straightforward illustration is tossing a fair (impartial) coin.

The coin is fair, thus the outcomes "heads" and "tails" are equally likely; the likelihood of "heads" is equal to the likelihood of "tails"; and because there are no other conceivable outcomes, the likelihood of either "heads" or "tails" is 1/2 (which is also an acceptable spelling).

Hence, The probability of being born on a Tuesday is= 18/343.

learn more about probability click here:

brainly.com/question/13604758

#SPJ4

Answer:

\((3 - 5i) + ( - 2 + 8i) \\ 3 - 5i -2 + 8i \\ 3 - 2 - 5i + 8i \\ 1 + 3i \\ \)

Answer:

George rate of baking cakes is ten cakes per day and it is double of Greta rate of baking cake.

George rate of baking pies is ten pies per day and it is two and a half times of Greta's rate of baking pies. There ratio for baking cakes is 1:2 for Greta and George respectively and for baking pies is 1:2.5 for Greta and George respectively

Check the picture below.

notice, the pairs in the Unit Circle are the (cosine , sine) pair, which are equivalent to (x , y) values in a cartesian plane.

Answer:

D on edg 2022

Step-by-step explanation:

In the usual topological space, None of the given options (a, b, c, d) accurately represents A^2.

In the usual topological space, the notation A^2 refers to the set of all possible products of two elements, where each element is taken from the set A. Let's calculate A^2 for the given set A = {1/n: n is a natural number}.

A^2 = {a * b: a, b ∈ A}

Substituting the values of A into the equation, we have:

A^2 = {(1/n) * (1/m): n, m are natural numbers}

To simplify this expression, we can multiply the fractions:

A^2 = {1/(n*m): n, m are natural numbers}

Therefore, A^2 is the set of reciprocals of the product of two natural numbers.

Now, let's analyze the given options:

a) A^2 ≠ a, as a is a specific value, not a set.

b) A^2 ≠ ϕ (empty set), as A^2 contains elements.

c) A^2 ≠ R (the set of real numbers), as A^2 consists of specific values related to the product of natural numbers.

d) A^2 ≠ (O) (the empty set), as A^2 contains elements.

Therefore, none of the given options (a, b, c, d) accurately represents A^2.

Learn more about topological space here:-

https://brainly.com/question/32645200

#SPJ11

Mean is 7

HOPE THIS HELPS YOUUUUU!!!!

Answer:

Step-by-step explanation:

Area of rectangle= Length x Breadth

= 34x 52

= 1768