12. Which of the following is a false statement?
A. Natural numbers are closed under division.
B. Integers are closed under subtraction.
C. Even numbers are closed under multiplication.
D. Real numbers are closed under addition.

Area of a circle is PI x r^2

The radius of the large circle is shown as 8 m

The diameter of A is the radius of the large circle which is 8 m so the radius would be 4 m

The radius of the small circle would be 2m

Area of large circle = pi x 8^2 = 64pi = 200.96 square m

Area of middle circle = pi x 4^2 = 16pi = 50.24 square m.

Area of small circle = pi x 2^2 = 4pi = 12.56 square m.

The area of the shaded region = large - middle + small

Area = 64pi - 16pi + 4pi = p2pi square m or 200.96 -50.24 + 12.56 = 163.28 square m.

1. The Fill ups are as follow:

AB² +  BC² = AC. AD + AC. CD

2. Segment addition postulate

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

BC/ AC = CD/ BC and AB/ AC = AD/ AB

Now, BC² = AC. CD  and AB² = AC. AD

Using, Addition Property of Equality

AB² +  BC² = AC. AD + AC. CD

and, AB² +  BC² = AC (AD + CD)  [factor]

AD + CD = AD (segment addition postulate)

Learn more about Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ2

PLATO

i got it correct :)

Option A "Reject the hypothesis" is the appropriate conclusion in this case.

As per the question,

Based on the results from the simulation trials, Peter should conclude that his hypothesis should be rejected.

The simulation showed that finches are a guaranteed bird type for only 80% of the birds, which is lower than the observed percentage of 75% finches at Peter's bird feeder.

This indicates that the predicted percentage of finches continuing at the same rate is not supported by the simulation results.

Therefore, option A "Reject the hypothesis" is the appropriate conclusion in this case.

To learn more about the hypothesis here:

https://brainly.com/question/18064632

#SPJ1

An 86% confidence interval for the difference in age to leave mother is -3.10091

What is confidence Interval?

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.

Given, Gorilla Baby sample

x means x bar here so, \(x_{1}\) = 3.21

\(s_{1}\) = 0.81

\(n_{1}\) = 64

Human Baby sample

x means x bar here so, \(x_{2}\) = 19.1

\(s_{2}\) = 2.16

\(n_{2}\) = 200

Confidence interval needs t score

t score = 1.18

86% confidence interval = \(x_{1}\) - \(x_{2}\) ± tc \(\sqrt{s^{2} {1} / n_{2} + s^{2} {2} / n_{2}\)

= 3.21 - 19.1 ± 1.18 √0.81²/64 +2.16²/200

= 3.21 - 19.1 ± 1.18 √0.033

= -3.10091

An 86% confidence interval for the difference in age to leave mother is -3.10091

The detail question is here,

A study based on the Association primate Ebmarah looked at the average age a baby gorilla leaves it’s mother versus the average age the human baby leaves it’s mother . Naturally they are different , so we don’t want a hypothesis test. Instead, find an  86% confidence interval  for the difference in age to leave mother.

Gorilla:

Sampled 64 babies

Stayed with mother on average 3.21 years

Standard deviation:  0.81

Human:

Sampled  200 babies

Stayed with mother on average 19.1 years

Standard deviation:  2.16

Matched  pairs  standard deviation :0.23

To learn more about confidence interval visit:

brainly.com/question/24131141

#SPJ4

The central angle measure, x, for the Baseball slice in the circle graph is 50.4 degrees.

Given that, a survey was conducted in which 2400 people were asked to name their favorite sport to watch and the table below shows their answers: Sport percentage of people are:

Football 29%

Soccer 9%

Baseball 14%

Basketball 8%

Hockey 8%

Other 32%

We need to find the central angle measure, x, for the Baseball slice in the circle graph.

For this, we need to use the formula that gives the central angle measure in degrees for a sector of a circle:

Central angle measure = (Percentage/100) × 360°

Now, using the above formula, we can calculate the central angle measure for each sport as shown below:

Football: (29/100) × 360° = 104.4°

Soccer: (9/100) × 360° = 32.4°

Baseball: (14/100) × 360° = 50.4°

Basketball: (8/100) × 360° = 28.8°

Hockey: (8/100) × 360° = 28.8°

Other: (32/100) × 360° = 115.2°

The sum of all central angle measures should be 360°, which is the measure of a full circle.

So we can check if the calculations are correct: 104.4° + 32.4° + 50.4° + 28.8° + 28.8° + 115.2° = 360°

We see that the sum is indeed 360°, so the calculations are correct. The central angle measure for the Baseball slice is 50.4°.

Therefore, the central angle measure, x, for the Baseball slice in the circle graph is 50.4 degrees.

For more such questions on central angle, click on:

https://brainly.com/question/10945528

#SPJ8

Step-by-step explanation:

50-20=30

30÷2=15

therefore the sons age is 15

(1) The value of x is determined as 16.8.

(2) The measure of length VX is calculated as 4.1.

(3) The measure of angle UWV is 69.5⁰.

The value of the missing lengths of the triangle is calculated by applying the following formula;

(1) For the two similar triangles, the value of x is calculated as follows;

20 / (28 - x) = 30 / x

20x = 30 (28 - x )

20x = 840 - 30x

20x + 30x = 840

50x = 840

x = 840 / 50

x = 16.8

(2) The measure of length VX is calculated by applying trig ratios.

tan 63 = 8 / VX

VX = 8 / tan 63

VX = 4.1

(3) The measure of angle UWV is calculated as follows;

angle T = 360 - (94 + 127) = 139

angle UWV = ¹/₂ x 139 (angle at circumference is half of angle at center)

angle UWV = 69.5⁰

Learn more about trig ratios here: https://brainly.com/question/10417664

#SPJ1

Answer:

[3,∞)

Step-by-step explanation:

[3,∞)

Hope that helps

Answer:

Add both of the function together.

Step-by-step explanation:

s(x) + a(x) = 450 + 6(x - 2)

Answer:

1) The function that represents how the money in her suit case is s(x) = 450

The function that represents the amount she is able to make from baby sitting is a(x) = 6(x - 2)

Given that the values of the two function are the same units, dollars, and the amount are to be put to the same use for spending money for her first year of college, the combination of the two functions is the sum of their values given as follows;

f(x) = s(x) + a(x) = 450 + 6(x - 2)

2) For simplification, we expand the second term and add the constant terms as follows;

f(x) = 450 + 6·x - 12

f(x) = 450 + 6·x - 12

f(x) = 438 + 6·x

The sum of the two terms becomes, f(x) = 438 + 6·x

Answer:

1

Step-by-step explanation:

1+1 wshydvdygdhdurhueueuyehehejidud

Answer:

30

Step-by-step explanation:

you have to look at carefully

Answer:

x = 67

y = 169

Step-by-step explanation:

We know that (x-1) + 52 + (y-7) = 180 because they're all on the same straight line. We also know that x-1 = 66, because they are alternate interior angles.

Solve for x:

x-1 = 66

x = 67

Now solve for y:

(67-1) + 52 + (y-7) = 180

y = 169

Answer:

A majority of the data will lie between 38 and 46.

Step-by-step explanation:

It can be said that a majority of the data of a distribution lies within 1 standard deviation of the mean.

In this question:

Mean of 42, standard deviation of 4.

42 - 4 = 38

42 + 4 = 46

A majority of the data will lie between 38 and 46.

Answer:

- 28

Step-by-step explanation:

Step 1:

8 - 4x        Equation

Step 2:

8 - 4 ( 9 )     Input x value

Step 3:

8 - 36        Multiply

Answer:

- 28          Subtract

Hope This Helps :)

Answer:

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.

Answer:

Prime numbers are positive integers that have only 2 factors: Itself, and 1.

For example, 13 is a prime number because it has only 2 factors that are: 1 and 13.

1 is NOT a prime number as it only has 1 factor which is 1.

Answer:

Checking your credit history and credit scores can help you better understand your current credit position. Regularly checking your credit reports can help you be more aware of what lenders may see. Checking your credit reports can also help you detect any inaccurate or incomplete information.

Step-by-step explanation:

hope this helps if not let me know have a blessed day

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expressionns.

Given the algebraic expressions,

\(\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2\)

Substituting 2 for x in the first expression gives:

(1/2 × 2) + 4

1 + 4

5

Substituting 2 for x in the second expression gives:

2 + 6 - (1/2 ×2) - 2

8 - 1 - 2

8 - 3

5

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Learn more about algebraic expressions from:https://brainly.com/question/395066

#SPJ1

Answer:

65

Step-by-step explanation:

We know that one angle is 50 degrees, so the angle supplementary to it will be 180-50, or 130 degrees.

Since these two lines are parallel, then the angle supplementary to 2x will be equal to 50 degrees, giving us 2x = 130 degrees, and x = 65 degrees.

Let me know if this helps!

Answer:

Correct option is B)

n(AUB)=n(A)+n(B)−n(A∩B)

     =75+45−35

=85

number of students owing car or stereos=85

number of students neither car nor stereo =100−85=15

The number of students who do not own either a car or an iPod is 25.

Union of two given sets is the smallest set which contains all the elements of both the sets.

Intersection of two given sets is the largest set which contains all the elements that are common to both the sets

The union of two sets is given by

n(A∪B) = n(A) + n(B) -n(A∩B)

Where,

A and B are the two sets.

∪ is the union

∩ is the intersection.

According to the given question.

Total number of students in a college = 100

Total number of students who own iPods, n(A) = 55

Total number of students who own cars, n(B) = 25

Number of students who own both cars and iPods, n(A∩B) = 5

Therefore,

The number of students who own cars or iPods is given by

n(A∪B) = n(A) + n(B) - n(A∩B)

⇒n(A∩B) = 55 + 25 - 5

⇒ n(A∪B) = 75

So, the number of students who do not own either a car or an iPod

= 100 - 75

= 25

Hence, the number of students who do not own either a car or an iPod is 25.

Find out more information about intersection and union of sets here:

https://brainly.com/question/4709512

#SPJ2

Answer:

x= 27/2

Step-by-step explanation:

Answer:

17.8

Step-by-step explanation:

You have to add 9.2 and 63 and the subtract from 90. Hope this helped! <3

Any point on a parabola, which has a U-shape and is defined as having an equal distance from both a fixed point (known as the focus) and a fixed straight line (known as the directrix), and the graph is given below.

Use the vertex form y=-a(x+h)²+k, to determine the values of  a,h and k.

a=-2

h=5

k=1

Opens down

Find the vertex (h,k)

(5,1)

Using formula, calculate the distance from the vertex to the parabola's focus.

1/4a

Substitute the value of a into formula.

1/4.2

Multiply 4 by 2

1/8

Find the focus.

The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down.

(h,k,+p)

Substitute the known values of h, p & kinto the formula and simplify.

(5,9/8)

Determine the axis of symmetry by tracing the line through the vertex and the focus.

x=5

To Find the directrix

The directrix of a parabola is the horizontal line found by subtracting p from the y coordinate k of the vertex if the parabola opens up or down.

y=k-p

Substitute the known values of p & k into the formula and simplify.

-y=7/8⇒-7/8

Using the property of the parabola to analyze and graph the parabola.

Direction: Opens down

Vertex: (5,1)

Focus: (5,9/8)

Axis of Symmetry x=5

Directrix: y=-7/8

To learn more about parabola refers to:

brainly.com/question/64712

#SPJ1

Answer:

the answer is 2,3,and 5

Step-by-step explanation:

Answer:

2, 3, and 5

Step-by-step explanation:

Answer:

19,683

Step-by-step explanation:

\(27^4-9^5+3^9\) is divisible by 25

The expression is given as:

\(27^4-9^5+3^9\)

Express all terms of the expression as a base of 3

\(27^4-9^5+3^9 = (3^3)^4-(3^2)^5+(3^9)\)

Remove the brackets

\(27^4-9^5+3^9 = 3^{12}-3^{10}+3^9\)

Factor out 3^9 from the expression

\(27^4-9^5+3^9 = 3^9(3^{3}-3^{1}+1)\)

Evaluate all exponents

\(27^4-9^5+3^9 = 3^9(27-3+1)\)

Simplify

\(27^4-9^5+3^9 = 3^9(25)\)

The above equation means that:

Hence, \(27^4-9^5+3^9\) is divisible by 25

Read more about factors and multiples at:

https://brainly.com/question/15560501

The velocities of the boat and the person relative to the shore are 1.337 m/s and 2.896 m/s, respectively.

We can use the conservation of momentum equation:

(mboat + mperson) * vboat = mperson * vperson

(160 kg + 70 kg) * vboat = 70 kg * (0.80 m/s + vperson)

230 kg * vboat = 56 kg * (0.80 m/s + vperson)

vboat = (56/230) * (0.80 m/s + vperson)

vperson = 0.80 m/s + vboat

vperson = 0.80 m/s + (56/230) * (0.80 m/s + vperson)

(174/115) * vperson = (504/115) * m/s

Dividing both sides by (174/115), we get:

vperson = 2.896 m/s

vboat = (56/230) * (0.80 m/s + vperson)

Substituting the value of vperson, we get:

vboat = 1.337 m/s

Learn more about velocity on

https://brainly.com/question/25749514

#SPJ1

On a 160-kg boat that is at rest with its bow pointed to the shore, a 70-kg person begins to walk from the bow to the stern at 0.80 m/s relative to the boat. What are the velocities of the boat and the person relative to the shore? Neglect the resistance of water to motion.