Number 14 is the question

Number 14 Is The Question

Answers

Answer 1

The measure of x = 93 degree and y = 36 degree.

What is Angle Sum Property?

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees.

The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle.

Given:

As, <QRP= 51

So, <QRP = <QPR= 51 {Angles opposite to equal sides are also Equal}.

In ΔPQR

<P+ <Q+ <R= 180

51 + 51 + <Q= 180

<Q= 180- 102

<Q= 78 degree.

So, <y = 1/2 <Q= 78/20 = 36 degree.

and, In small left Triangle

36 + 51+ x= 180

x = 180 - 87

x= 93 degree.

Hence, the measure of x = 93 degree and y = 36 degree.

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Related Questions

A scuba diver was at a depth of -9 feet and dove another 7 feet to see a school of fish. What is the current depth of the diver?

Answers

Answer:

-16

Step-by-step explanation:

what grade are you in bro?

Marina needs to earn at least each month to cover her living expenses. Her income comes from a commission that she earns on everything she sells. What is the minimum amount she needs to sell in order to earn ?

Answers

Answer:

Step-by-step explanation:

Amount sold = $23000

Percentage rate = 15%

Total salary = Amount sold × Percentage rate = $23000 × (15 / 100) = $3450

Answer is $3450

What is 40/1000 in decimal form

Answers

Answer: 0.04

Step-by-step explanation:

Divided by 1000 mean we will move the decimal to the left 3 times

So 40 divided by 1000= 0.04

Answer:

0.04

Step-by-step explanation:

Which table of ordered pairs represents a proportional relationship?
X: -3 -4 -5
Y: 3 2 1

X: -1 -3 -5
Y: 1 3 5

X: -2 -4 -6
Y: -5 -7 -9

X: -2 -3 -4
Y: 0 -1 -2

Answers

Answer:

X: -1 -3 -5

Y: 1 3 5

Step-by-step explanation:

Divide y by x for all the points. If the quotients are different, it is not proportional. If the quotients are equal, it is a proportional relationship.

A.

3/(-3) = -1

2/(-4) = -1/2

Not Proportional

B.

1/(-1) = -1

3/(-3) = -1

5/(-5) = -1

Proportional

C.

-5/(-2) = 5/2

-7/(-4) = 7/4

Not proportional

D.

0/(-2) = 0

-1/(-3) = 1/3

Not Proportional

help me pls math lol

Answers

the answer would be 15000

Answer: 15,000

Step-by-step explanation:

please i need help fast!!!

Answers

Answer:c

Step-by-step explanation:

0.796 divided by 9.95

Answers

Answer:

0.08

Step-by-step explanation:

00.8 if you divide 0.796 by 9.95 which if u have a calculator or anything to solve it, it will give you 00.8

10. Given a, b E Z, prove that if a²(b² - 2b) is odd, then both a and b are odd.
11. Given m, n = Z, prove that if 25 + mn, then 5 m or 5 tn.
12. If m, n E Z and m + n is even, prove that m² + n² is even.
13. Prove that an integer n is even if and only if n² + 2n + 9 is odd.
14. If a is an odd integer, prove that a² + 3a + 5 is odd.

Answers

Answer:

10. Given a, b E Z, if a²(b² - 2b) is odd, then both a and b must be odd numbers. This is because the only way for the product of two numbers to be odd is if both of the numbers are odd. In other words, if a and b are both even, then a²(b² - 2b) would be an even number, and if one of a and b is odd and the other is even, then a²(b² - 2b) would be an even number. So the only way for a²(b² - 2b) to be odd is if both a and b are odd.

11. Given m, n E Z, if 25 + mn is divisible by 5, then either m or n must be divisible by 5. This is because if both m and n are not divisible by 5, then the product mn will not be divisible by 5, and 25 + mn would not be divisible by 5. However, if either m or n is divisible by 5, then the product mn will be divisible by 5, and 25 + mn would be divisible by 5. So if 25 + mn is divisible by 5, then either m or n must be divisible by 5.

12. If m, n E Z and m + n is even, then m² + n² is also even. This is because the sum of two even numbers is always even, and the square of an even number is always even. So if m + n is even, then both m and n must be even, and m² and n² would both be even. Therefore, the sum m² + n² is also even.

13. An integer n is even if and only if n² + 2n + 9 is odd. This is because the square of an even number is always even, and the sum of two even numbers is always even. So if n is even, then n² and 2n are both even, and the sum n² + 2n + 9 would be odd. On the other hand, if n² + 2n + 9 is odd, then the sum of the first two terms, n² + 2n, must be even. Since the square of an even number is always even, this means that n must be even. So n is even if and only if n² + 2n + 9 is odd.

14. If a is an odd integer, then a² + 3a + 5 is also odd. This is because the product of two odd numbers is always odd, and the sum of two odd numbers is always even. So if a is odd, then a² and 3a are both odd, and the sum a² + 3a + 5 would be even. Since the sum of two odd numbers is always even, this means that a² + 3a + 5 is odd. Therefore, if a is an odd integer, then a² + 3a + 5 is also odd.

Step-by-step explanation:

What is 2 plus or minus -3?​

Answers

Answer:

5

Step-by-step explanation:

2 minus -3 is 5

This giant Rubber Duck has been recreated in many cities around the world, including Hong Kong, Pittsburgh, Toronto, Baku, and Sydney. The largest duck so far is in Saint-Nazaire, France. The duck measures 26 by 20 by 32 meters. A normal-sized rubber duck is about 3.5 inches at its widest part. What is the scale factor for this giant duck? Round your answer to the nearest whole meter.

Answers

The scale factor used in making the giant duck that duck measures 26 by 20 by 32 meters is 225

How to find the scale factor

Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying.

For the duck the measures 26 by 20 by 32 meters represent the factored image, the original image is 3.5 inches for the lowest

comparing the lowest for both the original size and the giant duck

converting 3.5 inches to meters 0.0889 meters

let the scale factor be k

solving for the factor

0.0889 * k = 20

k = 20 / 0.0889

k = 224.97

k = 225

This factor for the giant duck is 225

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A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams. Information was collected on several teams and was used to obtain the regression equation ŷ = 4.9x + 15.2, where x represents the attendance (in thousands) and ŷ is the predicted number of wins. Which statement best describes the meaning of the y-intercept of the regression line? When the number of wins is 0, the predicted attendance is 0. When the number of wins is 0, the predicted attendance is 15,200. When the attendance is 0, the predicted number of wins is 4.9 When the attendance is 0, the predicted number of wins is 15.2.

Answers

The option that has the statement that best describes the the meaning of the y-intercept of the regression line is the option;

When the attendance is 0, the predicted number of wins is 15.2

What is a regression line?

A regression is a representation of a linear relationship between an input and an output variable. It is a model of the relationship between the variables presented in a linear form.

The regression equation is; [tex]\hat {y}[/tex] = 4.9·x + 15.2

Where:

x = The game attendance (in thousands)

[tex]\hat{y}[/tex] = The predicted number of times the team wins

The y-intercept represents the point at which the graph of the regression line equation intersects or touches the y-axis, which is the point where the x-value is 0, therefore, at the y-intercept, we get;

x = 0, [tex]\hat{y}[/tex]  = 4.9 × 0 + 15.2 = 15.2

At the y-intercept, [tex]\hat {y}[/tex] (the predicted number of wins) = 15.2

The description of the y-intercept is therefore, that when there is 0 attendance, the predicted number of wins of a base ball team is 15.2

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What is the slope of (- 1/4 and 2 5?

Answers

A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics. The slope of (-1/4, 2/5) is 5/4.

Given two points (x1, y1) and (x2, y2), the slope can be calculated using the formula:

Slope = (y2 - y1) / (x2 - x1)

Therefore, the slope of (-1/4, 2/5) is:

Slope = (2/5 - (-1/4)) / (-1/4 - (-1/4))

Slope = (2/5 + 1/4) / 0

Slope = (3/4) / 0

Slope = 5/4

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Please help me to show your work for this. I know it's 7, but we need to show our work. 5.6 x 1.25

Answers

Answer:

Linked below.

Step-by-step explanation:

To solve, first line up your numbers. Then, multiply the ones place of the digit by the numbers on top individually. Write this below.

Do the same with all other places except add a zero each time there is one more row.

which list could not be the measures of lengths of the threee sides of a give triangle

Answers

Based on the triangle inequality theorem, the list that could not be the measures of lengths of the three sides of a give triangle is: D. 12 yd, 35 yd, 20 yd.

What is the Triangle Inequality Theorem?

The triangle inequality theorem expresses the relationship between the three lengths of sides that can form a triangle. If the sides are are a, b, and c, it states that:

a + b > c

a + c > b

c + b > a.

Considering this set of three sides, 5cm, 12 cm, 15 cm, we have:

5 + 12 > 15

17 > 15 [true]

5 + 15 > 12

20 > 12 [true]

12 + 15 > 5

27 > 5 [true]

Therefore, the measures of lengths 5cm, 12 cm, 15 cm, will form a triangle.

Same applies to 2 ft, 6 ft, 5 ft and 11 mi, 4 mi, 12 mi, except 12 yd, 35 yd, 20 yd.

This is because, 12 + 20 > 35 is not true.

Therefore, the answer is: D. 12 yd, 35 yd, 20 yd

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Complete Question:

Which list could not be the measures of lengths of the three sides of a given triangle?

A. 5cm, 12 cm, 15 cm

В. 2 ft, 6 ft, 5 ft

C. 11 mi, 4 mi, 12 mi

D. 12 yd, 35 yd, 20 yd

Given N(-3,-7), O(-4,-2), P(1, -7), and Q(-2, y). Find y
such that NO|| PQ.

Answers

Answer:

  y = 8

Step-by-step explanation:

Given N(-3,-7), O(-4,-2), P(1, -7), and Q(-2, y), you want to find y such that NO ║ PQ.

Graph

When we plot the points, we see that point O is 1 unit left and 5 units up from point N. Point Q is on a line 3 units left of P, so it will need to be 3×5 = 15 units up from P in order for PQ to have the same slope as NO:

  y = -7 +15 = 8

The value of y is 8; the point Q is (-2, 8).

Abraham Lincoln was featured on a poster that uses a scale of 1 inch = 4/9 feet. If the height of Lincoln on the poster is 14 1/4 inches, what is Lincoln's actual height? 9 A) 6'5" B) 6'4" C) 6'3" D) 6'2" E) 6'1"​

Answers

Answer: 6 ft 4 inches

Step-by-step explanation:

the coach must select 88 players to travel to an away game. how many ways are there to select the players who will travel?

Answers

The coach can select the players in 1081575 ways .

A combination is a technique for finding the number of possible arrangements in a set of items where the order of the selection is irrelevant. .

The formula for determining the number of possible arrangements by selecting only a few objects from a set with no repetition is expressed mathematically as follows:

[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]

Where:n denotes the total number of elements in a set,

k denotes the number of selected objects

! - the factorial

Factorial (noted as "!") is the sum of all positive integers that are less than or equal to the number preceding the factorial sign.

For instance, [tex]3! = 1 * 2 * 3 = 6[/tex].

Given,

Total number of players,n = 25

Number of selected players,r = 8

Number of ways that players are selected is determined by,

[tex]25C_8=\frac{25!}{8!(25-8)!}\\\\=\frac{15511210043330985984000000}{(40320)*(355687428096000)}\\\\=1081575[/tex]

Thus, by combination, the selection can be done in 1081575 ways.

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Your question is incomplete  , here is the complete question.

There are 25 players in a basketball team. The coach must select 8 players to travel to an away game. How many ways are there to select the players who will travel?

A triangle has two sides measuring 8. 5 cm and 15 cm. What is the greatest whole number length possible for the third side? explain.

Answers

The greatest whole number possible length for the given measures of triangle is 23 cm.

As given in the question,

Measure of two side-length of a given triangle are :

Let 'x' be the side length = 8.5cm

And 'y' be the side length = 15cm

'z' be the side length of the third side of a triangle.

Sum of two sides is greater than third side and difference of two sides is smaller than the third side.

y - x < z < y + x

⇒ 15 - 8.5 < z < 15 + 8.5

⇒ 6.5 cm < z < 23.5cm

Greatest whole number representing length of the third side of a triangle is  less than 23.5 .

⇒ z = 23cm

Therefore, the length of the third side of a triangle represented by greatest whole number is equal 23cm.

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Fill in the missing number. 70% of = 70 Submit

Answers

Answer:

100

Step-by-step explanation:

70 % is .7 in decimal

   .7 * x = 70    divide both sides by .7

     x = 100

Step-by-step explanation:

you mean

70% of x = 70

right ?

you know that the "whole" is represented by 100% ?

this is easy here, but in general, when in doubt, find either 100%, calculate 1% as 100%/100 and find the desired %, or you find 1% directly and calculate the needed % (incl. 100%) out of this.

so, we know, 70% = 70

that means

1% = 70%/70 = 70/70 = 1

and then

100% = 1%×100 = 1×100 = 100

so,

70% of 100 = 70

now you see, why I said this is easy in this case here. because % and the absolute numbers have the same units. so, this goes 1:1.

a street light is at the top of a 17 foot tall pole. a 6 foot tall woman walks away from the pole with a speed of 4 ft/sec along a straight path. how fast is the tip of her shadow moving when she is 35 feet from the base of the pole?

Answers

The tip of her shadow moving when she is 35 feet from the base of the pole is 8.77 feet.

Let H = the height of the pole.

h = the height of the woman.

x = the length of the woman's shadow.

s = the distance from the pole to the woman.

By similar triangles,  H/h = (s + x)/x  or  Hx = h(s + x).

Differentiating, H dx/dt = h(ds/dt + dx/dt)

⇒ 17 dx/dt = 6(6 + dx/dt)

                  = 36 + 6 dx/dt

                  = 13 dx/dt

                  = 36

⇒ dx/dt = 36/13 ft/sec = 2.77 ft/sec for how fast her shadow is lengthening.

The speed of the tip of her shadow would be this speed added to her traveling speed: 2.77 + 6 = 8.77 ft/sec.

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Given the function h (x) = -10x + 5, find the corresponding range values when the domain is {-1,2,4]
-35
35
000000
15
- 15
25
-25
W

Answers

The range of the function f(x) = 5 -10x for domain {-1, 2, 4}  is { 15, -15, -35}

What is Domain and Range of a function ?

A function's domain and range are its constituent parts. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A B exists that maps every element of A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R. The collection of photos is the function's range. In general, a function's domain and range are denoted as follows:

Domain(f) = {x ∈ R} and range(f)={f(x) : x ∈ domain(f)}

"All the values" that are input into a function are referred to as the domain of a function. The collection of all potential inputs for a function is its domain. Think of this box as the f(x) = 2x function. The domain is only the collection of natural numbers when the input values are x = 1,2,3,4,..., and the values that are returned are referred to as the range. However, f(x) = 2x is often defined for all real values of x, and as a result, its domain is the set of all real numbers, which is represented by  (-∞, ∞). The general formulae for determining the domain of various types of functions are listed below. The set of all real numbers, or R, is used here.

The collection of all a function's outputs is its range. Example: Let's have a look at the function f: A->B, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output. Set of even natural numbers is the range. The components of the co-domain that are mapped are known as the pictures, while the elements of the domain are known as pre-images. The set of all pictures of the domain's elements in this case serves as the function's range, as does the set of all of its outputs.

Domain of the function x = {-1,2,4}

The function is  f(x) = 5 - 10x

range when x = -1

f(x) = 5 - 10*(-1) = 15

when x = 2

f(x) = 5 - 10* 2 = -15

and x= 4

f(x) = 5 - 10*4 = -35

The range of the function for domain {-1, 2, 4}  is { 15, -15, -35}.

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The range of the function f(x) = 5 -10x for domain {-1, 2, 4}  is { 15, -15, -35}

What is Domain and Range of a function ?

The domain of a function is the set of all possible inputs for the function. It is the set of all x-values which will make the function "work", and will output real y-values. The range of a function is the set of all possible outputs of the function. It is the set of all y-values which can be produced by the function for the given set of x-values. In other words, it is the set of values that result when the function is applied to all the elements of the domain. In order for a function to be defined, both the domain and the range must be specified.

Domain of the function x = {-1,2,4}
The function is  f(x) = 5 - 10x
range when x = -1
f(x) = 5 - 10*(-1) = 15
when x = 2
f(x) = 5 - 10* 2 = -15
and x= 4
f(x) = 5 - 10*4 = -35
The range of the function for domain {-1, 2, 4}  is { 15, -15, -35}.

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there is no such thing as a group of answer choices sound argument that is also valid. valid argument that is also sound. valid argument that is not sound. sound argument that is not valid.

Answers

There is no such thing like Sound argument that is not valid.

What is an argument that is valid?

Any argument whose conclusion is not supported by its premises is invalid (i.e., faulty). That is, the conclusion could still be wrong even though all the premises are true.

Because validity of the argument is a requirement for soundness

A valid argument is one in which we can demonstrate that, if its premises are true, its conclusion will also be true.A good argument is one with just true premises and is valid.A sound argument cannot be given false premises.A sound argument cannot support a valid one.

An argument is valid and contains all true premises if it is sound. The argument is sound, so if all of the premises are true, the conclusion must also be true. It follows that the conclusion of a sound argument must be true since all of its premises are true.

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How do you find the minimum and maximum of a quadratic function?

Answers

For a quadratic function f(x) = ax² + bx + c, we can find the minimum and maximum value using the formula -b/2a or by graphing the function.

We know that the general form of quadratic function is f(x) = ax² + bx + c ; a ≠ 0

The graph of quadratic function is a parabola. The graph is parabola that either opens upward or downward.

For a quadratic function is f(x) = ax² + bx + c,

if a is positive (a > 0) then the parabola opens upward.

In this case you will be finding the minimum value of f(x) at the vertex of parabola.

if a is negative (a < 0), then the parabola opens downward.

In this case you will find its maximum value of f(x) at the vertex of parabola.

Also, the value of -b/2a will tell you the minimum or maximum value of f(x) which is the vertex of the parabola.

Therefore, to find the minimum and maximum of a quadratic function f(x) = ax² + bx + c :

1) find vertex of function from the graph

2) use formula -b/2a

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find the are of the parallelogram 10in by 9.8 and 5.6

Answers

The area of the parallelogram that has a base of 98 in. and a height of 5.6 in. is calculated as: 54.88 in.².

What is the Area of a Parallelogram?

The area of a parallelogram is calculated as the product of its base length and its height. That is:

Area of parallelogram = base × height.

From the image given, we have the given dimensions of the parallelogram that we can use to find its area:

Base = 9.8 in.

Height = 5.6 in

Plug in the values:

Area of parallelogram = 9.8 × 5.6

Area of parallelogram = 54.88 in.²

Therefore, the exact answer is, 54.88 in.².

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Geometry HL question. Statements and proofs.

Answers

The proof that shows that ΔPRS ≅ ΔQSR by HL congruence theorem is explained below.

How to Prove that two Triangles are Congruent by HL?

The HL congruence theorem can be used to prove that two triangles are congruent to each other if we can show that the two triangles are right triangles that have a pair of corresponding congruent legs, and a pair of congruent hypotenuse.

The proof for stating that triangles PRS and QSR are congruent is given below.

Statement                                          Reasons                                                  

1. QS ≅ PR, PS ⊥ RS, QR ⊥ RS          1. Given

2. <RSP and <SRQ are right angles  2. Definition of perpendicular

3. SR ≅ RS                                          3. Reflexive property of congruency

4. ΔPRS ≅ ΔQSR                                4. HL

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14h 45min 78s + 5h 18min 37s

Answers

answer

20hours 4 min 55sec

(03.01 LC)
The leg of a right triangle is 2 units and the hypotenuse is 3 units. What is the length, in units, of the other leg of
the triangle? (5 points)
O√5 units
O√13 units
5 units
O 13 units

Answers

Pythagorean theorem states that for a right triangle, the sum of the squares of the legs equals the square of the hypotenuse. Therefore the other leg can be found with this formula:
2^2+b^2=3^2
4+b^2=9
b^2=5
b=sqrt(5)

So the other leg is the square root of 5 units

Solve for x.
-4> 10-7x

Answers

Answer:

x > 2

Step-by-step explanation:

-4 > 10-7x

-4 - 10 > -7x

-14 > -7x

Inequality reverses when dividing or multiplying a negative number.

-14/-7 < x

2 < x

x > 2

Evaluate 11.5x + 10.9y when x = 6 and y =7

Answers

the solution for the given expression 11.5x + 10.9y  is 145.3

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

11.5x + 10.9y

Here x = 6 and y = 7

11.5*6 + 10.9*7 = 145.3

Hence, the solution the given expression is 145.3

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write the converse inverse and contrapositive of each conditional statement. Determine the truth of each of the new statements. a. if each side of a triangle has a length of 10, then the triangles perimiter is 30 b. if an angle is acute, then it has a measure greater than 0 and less than 90

Answers

If a triangle does not have one angle greater than 90°, then it is not an obtuse triangle. Remember that you create a contrapositive by inverting and swapping both terms.

What is the triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

If a triangle lacks one angle greater than 90°, it is not an obtuse triangle. Remember that a contrapositive is formed by inverting and swapping both terms. If you have if A then B, then the contrapositive is if not B then not-A. Because you've been given "If a triangle is obtuse, then

It has one angle with a measure greater than 90°," the converse would be "If a triangle has no angles with a measure greater than 90°, it is not an obtuse triangle." So, check through the options and see what fits in intent, even if it's not phrased precisely the same. 

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Compute the reactions at A for the cantilever beam subjected to the distributed load shown. The distributed load reaches a maximum value of 2kN/m at x = 3m. Please help me, its asap tax incidence is part 2 a. the . b. the efficiency loss to the economy that results from a tax causing a reduction in the quantity of a good produced. c. the division of the tax burden between . Coffee is venezuelas main_____ a product mainly for sale Requirements for some micronutrients increase with age. Click to select the vitamins or minerals for which the RDA or AI is higher for older adults than for young adults.FolateIronVitamin DVitamin B-6CalciumZinc digby corp. ended the year carrying $16,595,000 worth of inventory. had they sold their entire inventory at their current prices, how many more dollars of contribution margin would it have brought to digby corp.? The numbers of trading cards owned by 10 middle-school students are given below.(Note that these are already ordered from least to greatest.)361, 408, 414, 417, 498, 505, 519, 520, 530, 548Send data to calculatorSuppose that the number 361 from this list changes to 401. Answer the following.(a) What happens to the mean?(b) What happens to the median?It decreases by13. It increases byIt stays the same.It decreases byIt increases byIt stays the same. What is a stagflation Mcq? What is the meaning of capital in geography the old familiar and the beehive are the only two bistros in town. each is trying to decide whether or not it should advertise in the local newspaper. the accompanying payoff table gives their weekly profits under each possible outcome. the beehive does advertise the beehive does not advertise the old familiar does advertise the old familiar earns $x in profits. the beehive earns $y in profits. the old familiar earns $3,500 in profits. the beehive earns $2,250 in profits. the old familiar does not advertise the old familiar earns $2,000 in profits. the beehive earns $4,000 in profits. the old familiar earns $2,500 in profits. the beehive earns $3,500 in profits. a. which combination or combinations of x and y would make a situation in which the old familiar does not advertise and the beehive advertises a nash equilibrium? a nash equilibrium occurs if x Which branch of the u.s. government declared some new deal legislation unconstitutional? you are managing a project and are looking at project performance. at this time, the earned value is $145, planned value is $162 and the actual cost is $138. the project has an approved budget of $200. what is the budget needed to complete the remaining tasks of this project? I need help with this asap!! I have to classify the pictures as four galaxies, either peculiar, irregular, elliptical, or spiral!! Evaluate 0.3k-4m k = 20 and m=-2 within the third step of the control process, ______ is a principle that states that managers should be informed of a situation only if data show a significant deviation from standards. Add commas where needed in the sentences below.1. Dr. Perillo a nutritionist is an expert on proper eating.2. "Students it's important to eat a well-balanced diet," she said.3. "Yes but how do we know what the right foods are?" asked one student.4. "First you need to look carefully at your eating habits," said Dr. Perillo.5. "Yes you should keep a journal of the foods you eat," she said. find the sum of all positive rational numbers that are less than 10 and that have denominator 30 when written in lowest terms. Which of the following requires treatment with both antibiotics and antitoxins?a) diphtheriab) tuberculosisc) whooping coughd) scarlet fevere) psittacosis how do you find answer to 9/35 - 1/5? What group was hit the hardest by the national origins act?