A variable contains five categories. It is expected that data are uniformly distributed across these five categories. To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24. Using α = 0.01, the observed value of chi-square is:_______

Answer: A

Step-by-step explanation: The line is linear as it changes at a constant rate which means it’s also proportional as proportional means as x changed so does y.

The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.

y² = x

Take the derivative of both sides with respect to x, assuming y = y(x) :

2y dy/dx = 1

dy/dx = 1/(2y)

Solve for y when dy/dx = 1 :

1 = 1/(2y)

2y = 1

y = 1/2

When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.

This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :

x = y²   ⇒   y = y² + 3   ⇒   y² - y + 3 = 0

has no real solution for y.

Answer:

The Probability that the sample average was 289 yards or less

P(x⁻≤ 289) = P( Z≤ -1.909) =  0.0287

Step-by-step explanation:

step(i):-

Mean of the Population = 292.5 yards

Standard deviation of the Population = 14.2 yards

sample size 'n' =60 drives

               N = 4244 drives

Step(ii):-

Let X⁻ be random sample average

\(Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }\)

Let  X⁻ = 289

\(Z = \frac{289 -292.5}{\frac{14,2}{\sqrt{60} } }\)

Z  = - 1.909

The Probability that the sample average was 289 yards or less

P(x⁻≤ 289) = P( Z≤ -1.909)

                = 0.5 -A(1.909)

                = 0.5 -0.4713

               = 0.0287

Conclusion:-

The Probability that the sample average was 289 yards or less = 0.0287

Step-by-step explanation:

The ONE  solution to this system of two lines is the point where the two lines cross   at   (1,4)

Answer:

51°

Step-by-step explanation:

Reference angle (θ) = ?

Opposite side length = 31

Hypotenuse length = 40

Apply SOH, which is;

Sin θ = Opp/Hyp

Plug in the values

Sin θ = 31/40

θ = sin^{-1}(31/40)

θ = 51° (neatest whole degree)

Answer:

-10

Step-by-step explanation:

You just set 0 into your relationship

\(4 \times ( {0}^{5} ) + 4 \times ( {0}^{4} ) - 10\)

it's equal to -10

Answer:

D

Step-by-step explanation:

(16x +1) -5x

you basically subtract the -5x from 16x

11x +1

Answer:

8x and 0

Step-by-step explanation:

Answer:

the value of expression is 58

Step-by-step explanation:

3(2x-y)+(3+x)²

substitute x =4 and y=5

3(2(4)-5)+(3+4)²

3(8-5)+(7)²

3(3)+49

9+49

58

Answer:

Step-by-step explanation:

I take it that this is some sort of ratio.  Start by solving the brackets on the left.

Brackets: 1/3 - 1/10

Brackets: 10/30 - 3/30

Brackets: 7/30

Brackets^2: 49/900

Brackets^2 - 1/5: 49/900  - 180/900

Brackets^2 - 1/5: -131/900

(2/5)^2 = 4/25

The way this read, it should be

\(\frac{\frac{-131}{900} }{\frac{4}{25} }\)

Which when you invert and multiply becomes

\(\frac{-131}{900} * \frac{25}{4}\)

which finally becomes

\(\frac{-131}{144}\)

Answer:

q=6 creates a verticle line at x=6 shaded to the left and encludes the line.

Step-by-step explanation:

9 + q <= 15

q <= 15 - 9 = 6

Answer:

11t.

hope this helps you

Step-by-step explanation:

8. 120° - Obtuse angle

9. 40° - Acute angle

10. 180° - Straight angle

11. 90° - Right angle

Answer:

Here we will show you how to convert the improper fraction 74/9 to a mixed number (aka mixed fraction). We start by setting up the fraction below.

   74  

   9  

Step 1 - Find Whole Number

Calculate out how many times the denominator goes into the numerator. To do that, divide 74 by 9 and keep only what is to the left of the decimal point:

74 / 9 = 8.2222 = 8

Step 2 - Find New Numerator

Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.

74 - (9 x 8) = 2

Step 3 - Get Solution

Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer. 74/9 as a mixed number is:

8

   2  

   9  

Improper Fraction To Mixed Number Converter

74/9 as a mixed number is not the only problem we solved. Go here to convert another improper fraction to a mixed number.

What is 74/10 as a Mixed Number?

Here is the next improper fraction on our list that we converted to a mixed number.

Using the integers −9 to 9 at most one time each, place a digit in each box (1, 3) and (9, 3) or (-9, 3) to create endpoints for the longest possible line segment both numerically and graphically whose midpoint is (1, 3).

To find the endpoints of the longest possible line segment with midpoint (1, 3), we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is ((x₁+x₂)/2, (y₁+y₂)/2).

In this case, we know the midpoint is (1, 3), so we can set up two equations using the variables for the endpoints (x and y) and solve for them:

(x₁ + x₂)/2 = 1

(y₁ + y₂)/2 = 3

We also know that the line segment must be as long as possible, so the endpoints should be as far away from each other as possible. To maximize the distance between the endpoints, we can choose one endpoint to be -9 and the other endpoint to be 9. This gives us:

(x₁ + x₂)/2 = 1 => x₁ + x₂ = 2

(y₁ + y₂)/2 = 3 => y₁ + y₂ = 6

Now we can solve for x₁ and y₁, since x₂ and y₂ will be 2-x₁ and 6-y₁ respectively:

x₁ + (2-x₁) = 2 => x₁ = 1

y₁ + (6-y₁) = 6 => y₁ = 3

So the endpoints of the longest possible line segment with midpoint (1, 3) are (1, 3) and (9, 3) or (-9, 3), and its length is 8 units.

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The polynomials completely factorized have the following expressions;

50). x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

51). x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

52). x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

53). x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

For the polynomial x³ - 3x² - 26x - 12 divisible by x - 6;

(x³ - 3x² - 26x - 12)/(x - 6) = x² + 3x + 2

x² + 3x + 2 = (x + 1)(x + 2)

so;

x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

For the polynomial x³ - 12x² + 12x + 80 divisible by x - 10;

(x³ - 12x² + 12x + 80)/(x - 10) = x² - 2x - 8

x² - 2x - 8 = (x + 2)(x - 4)

so;

x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

For the polynomial x³ - 18x² + 95x + 126 divisible by x - 9;

(x³ - 12x² + 12x + 80)/(x - 9) = x² - 9x + 14

x² - 9x + 14 = (x - 2)(x - 7)

so;

x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

For the polynomial x³ - x² + 21x + 45 divisible by x + 5;

(x³ - x² + 21x + 45)/(x + 5) = x² - 6x + 9

x² - 6x + 9 = (x - 3)(x - 3)

so;

x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

Therefore, by complete factorization the expressions (x - 6)(x + 1)(x + 2), (x - 10)(x + 2)(x - 4), (x - 9)(x - 2)(x - 7), and (x + 5)(x - 3)(x - 3) are the factors of their respective polynomial.

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Answer:

approximately 28.26 square feet

Step-by-step explanation:

The formula for the area of a circle is A = pi(r)^2. So, the radius is half of the diameter, meaning it's 3 feet. Then we square it to get 9, and multiply by pi, or 3.14. This leads us to the approximated answer of 28.26 square feet.

The area is:

28.27 square feet

Work/explanation:

Since the tabletop is circular, we use the formula for a circle's area, which is: \(\bf{A=\pi r^2}\).

We have the diameter, and to find the radius, we divide the diameter by 2, which gives us 6 ÷ 2 = 3 feet, so the radius of the tabletop is 3 feet.

Now, here's a diagram for you;

\(\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 3\ ft}\end{picture}\)

Plug in the data:

\(\sf{A=\pi\times3^2}\)

\(\sf{A=\pi\times9}\)

\(\sf{A=28.27\:ft^2}\)

Step-by-step explanation:

hope it helps you.......

\(\\ \sf\longmapsto 699^2\)

\(\\ \sf\longmapsto (700-1)^2\)

\(\\ \sf\longmapsto 700^2-2(700(1)+(1)^2\)

\(\\ \sf\longmapsto 490000-1400+1\)

\(\\ \sf\longmapsto 488600+1\)

\(\\ \sf\longmapsto 488601\)

Answer:

As an autistic dyslexic person, i can confirm your question is held in a silly way as possible

Check the picture below.

Make sure your calculator is in Degree mode.

\(\tan(53^o )=\cfrac{\stackrel{opposite}{17}}{\underset{adjacent}{x}}\implies x=\cfrac{17}{\tan(53^o )}\implies x\approx 12.81~meters\)

Answer:

I guess it is $105.Not so sure about my answer...

The net worth of the landscaping company is given by:

$187.205.

How to calculate the net worth?

The net worth of a company or of a person is given by the sum of all assets of the person subtracted by the sum of all debts of the person.

In the context of this problem, the assets, and it's values, of the company are given as follows:

Owned Inventory: $48,760.

Cash: $126,790.

Savings account: $32,436.

Owned equipment: $20,700.

Accounts receivable: $15,640.

Property value: $225,678.

Hence the sum of the assets is given by:

Assets = 48760 + 126790 + 32426 + 20700 + 15640 + 225678 = $469,994.

The debts of the company, with it's values, are given as follows:

Small Business Loan: $76,400.

Building Mortgage: $189,429.

Other debt: $16,970.

Hence the sum of the debts is given by:

Debts = 76400 + 189429 + 16970 = $282,799.

Then the net worth of the company is:

Net worth = Assets - Debt = 469,994 - 282,799 = $187,205.

Part A :

Yes, the statement is true that  P( A and B ) = 0 .

Given,

Event A and Event B are mutually exclusive.

Thus P ( A and B ) = 0

Part B:

A and B are mutually exclusive events if they do not occur at the same time.

This means that A and B do not share any common outcomes and

P(A and B) = 0.

Part C:

Let,

The sample space W = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Let A = {1, 2, 3, 4, 5}, Y = {4, 5, 6, 7, 8}, and B = {7, 9}.

A and B do not have any numbers in common so P(A and B) = 0.

Hence, A and B are mutually exclusive.

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Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

3.1 Activity: Procedural and Conceptual Understanding in Action

Content Area: Fractions

Problem: Comparing Fractions

Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.

Activity Steps:

Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).

Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.

After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:

What does it mean for one fraction to be greater than or less than another?

Can you explain why we need a common denominator when comparing fractions?

How can you visually represent and compare fractions to better understand their relative sizes?

Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.

Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.

Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.

Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.

By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.

3.2 Example: Conceptual Knowledge vs. Procedural Knowledge

Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.

Example: Division of Fractions

Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.

Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.

In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

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Step-by-step explanation:

The value of b will be 43° as it is vertically opposite angle.. !!

Answer:

1560 cm²

Step-by-step explanation:

4*5*22 = 440 cm²

25*8*10 = 2000 cm²

find the difference between the two numbers to find the volume of the solid part of the box

Brₐinliest plz close to leveling up

Step-by-step explanation:

here is my step by step so first you look at the two inner angles which in this case are B and C then you multiply them together to get your angle D.

Answer:

A.) obtuse angle  

B.)  180 degrees

C.) 95 degrees

Step-by-step explanation:

C.) 80 - 85 = 95