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A range of 2 reveals that the smallest and largest data values are 2 units away from each other.

Range is the difference between the highest and lowest values of a set of observations. Range is a measure of variation.

Range = highest value - lowest value

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Answer:

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We know each interior angle of an equilateral triangle is 60°, since each of three angles are of same value.

The middle triangle with two interior angles 4x and y has the missing angle also y, since it is isosceles, because both adjacent angles are equal at vertex N.

First

Measure of any angle in an equilateral triangle is 60°

So

And

Apply angle sum property

Answer:

$6.45/hour

110.26%

Step-by-step explanation:

The absolute change is the difference between salaries now ands then.

12.30 - 5.85 = 6.45

The relative change in the percent increase.

percent increase = (new number - old number)/(old number) × 100%

percent increase = (12.3 - 5.85)/(5.85) × 100%

percent increase = 110.26%

1. The z-scores corresponding to Kathy's starting salary is -1.5

2. The z-scores corresponding to Linda's starting salary is -2

z = (x - μ) / σ

Where

z = (x - μ) / σ

z = (31500 - 42000) / 7000

z-score for Kathy's starting salary = -1.5

z = (x - μ) / σ

z = (33000 - 45000) / 6000

z-score for Linda's starting salary = -2

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samples confidence intervals needed is Option C 136.

According to the Empirical rule, if data exists normally distributed then about 68% of the population lies within one standard deviation from the mean.

We assume that the mean of a normally distributed population exists at 300, and 200 simple random samples exist drawn from the population.

Number of simple random samples, n= 200

By Empirical rule, approximately 68% of 200 samples’ confidence intervals we would expect to have the population mean.

Required number of samples = 68% of 200

= 0.68 x 200 = 136

The required number of samples = 136

Therefore, the correct answer is option C) 136.

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Answer:

X = 'is the athlete injured' (X in {0,1})

Y = 'the athlete wins' (Y in {0,1})

P(Y=1|X=0) = 0.75

P(Y=1|X=1) = 0.15

P(Y=1) = 0.51

We are looking for P(X=1) - P(Y=1) = P(Y=1|X=0)*(1-P(X=1)) + P(Y=1|X=1)*P(X=1)

The above equation should provide you with the answer 0.4!

Step-by-step explanation:

Option C. The statement that describes the graph of the equation y + 2 ≥ –4(x – 3)2 is a a parabola opening down, with shading above the vertex.

To do this you have to create a graph of the equation as seen in the attachment.

From the attachment we can see that the parabola is shaped downwards while we have the shading to be at the top of the vertex.

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The slope of the line passing through the points (-4, -9) and (5, -9) is 0

The points are (-4, -9) and (5, -9).

The slope is calculated using:

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

So, we have:

Slope = (-9 + 9)/(5 + 4)

Evaluate

Slope = 0

Hence, the slope of the line passing through the points (-4, -9) and (5, -9) is 0

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The net that represents a cube is (b) net b

A cube has 6 faces

This means that the net must have 6 faces

For a net to represent a cube, there must be four adjacent faces

And 2 two adjacent faces

Where

The net that represents the above scenario is net (b)

Hence, the net that represents a cube is (b) net b

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Answer:

  (b) 27°

  (c) 34°

  ( ) 27°

Step-by-step explanation:

Angle relations involving lines, parallel lines, and triangles come into play here.

The interior angles at W and Y will be the supplement of the exterior angles at those points. The sum of interior angles is 180°.

  (180° -6x) +90° +(180° -4x) = 180°

  270° = 10x . . . . . . . . . add 10x and simplify

  27° = x

The vertical angles at S are congruent. This tells us ...

  3x +∠PSQ = 4x

  ∠PSQ = x

The sum of angles in triangle PSQ is 180°, so we have ...

  x +x +(180° -68°) = 180°

  2x = 68° . . . . . . . . add 60°-180°

  x = 34° . . . . . . . . . divide by 2

Angles BAD and EDF are corresponding angles, hence congruent. The sum of angles in triangle BAD is 180°.

  2x +2x +72° = 180°

  4x = 108° . . . . . . subtract 72°

  x = 27° . . . . . . . . divide by 4

Answer:

x = 12

Step-by-step explanation:

6x - 4 and 112 are same- side interior angles and sum to 180° , that is

6x - 4 + 112 = 180

6x + 108 = 180 ( subtract 108 from both sides )

6x = 72 ( divide both sides by 6 )

x = 12

Answer:

x = 12

Step-by-step explanation:

Consecutive Interior Angles Theorem

When a straight line intersects two parallel straight lines, the consecutive interior angles formed are are supplementary (sum to 180°).

Therefore:

⇒ 6x - 4 + 112 = 180

⇒ 6x + 108 = 180

⇒ 6x + 108 - 108 = 180 - 108

⇒ 6x = 72

⇒ 6x ÷ 6 = 72 ÷ 6

⇒ x = 12

The area of the desktop is 12. 5 feet square

The formula for area of a rectangle;

Area = length × width

Length = 2. 5 feet

Width = 5 feet

Area = 2. 5 × 5

Area = 12. 5 feet square

Thus, the area of the desktop is 12. 5 feet square

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95% men are between 165 cm and 186 cm.

What is the empirical rule?

The empirical rule is also referred to as the Three Sigma Rule or the 68-95-99.7 Rule.

z-score = (raw-score minus mean) / standard deviation.

z1 = (165-176)/5 = -2.2

z2 = (186-176)/5 = 2

The empirical rule tells us that about 95% of all values are within standard deviations of the mean,

so, 95% men are between 165 cm and 186 cm.

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95% of men are between 165 cm and 186 cm.

Given:

Find:

Solution:

The empirical rule is also referred to as the three sigma rule or the 68-95-99.7

Rule:

z - score = (raw - score minus mean) / standard deviation.

z1 = (165-176)/5 = -2.2

z2 = (186-176)/5 = 2

The empirical rule tells us that about 95% of all values are within standard deviations of the mean.

So, 95% of men are between 165 cm and 186 cm.

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Based on the various meals offered by the catering service, the ways that the order can be done is 6,930 ways..

This can be found as:

= (11! / (9!2!)) x (7! / (5!2!)) x (4! / (2!2!)

= 55 x 21 x 6

= 6,930 ways

In conclusion, the order can be made in 6,930 ways.

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Answer:

1. 30

Step-by-step explanation:

∠H + ∠T = 180

(2x+60)+(x+30)=180

3x+90=180

3x=90

x=30

Answer:switch mikes Luke’s and Alex in between each other and let winter keep her own

Step-by-step explanation:

It will take 21 days before there is another day on which he does both.

The lowest common multiple (LCM) of two or more numbers is the lowest possible number which is completely divisible by all the given numbers.

Given,

John goes for a jog every third day and every Saturday he goes to the gym.

That means he goes to the gym on every seventh day, and goes for a jog every third day.

Therefore, he goes for both on the days which are LCM of 3 and 7.

But, LCM of 3 and 7 is 21.

Hence, he goes for both in every 21 days.

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The individual-size box of cereal is a rectangular prism with a volume of 44.625 inches³.

The volume of rectangular prism of length l, width w and height h is given by:

V = lwh.

In this problem, the standard dimensions are:

The individual-size box has a 1/10 of the volume of the original box, hence:

V = 0.1 x 3.5 x 8.5 x 15 = 44.625 inches³.

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681×239 = 162,759

..... ......

162,759 is answer

happy to help

The cost given shows that the amount left is £12.

From the information given, it was stated that the person saved £60 and spent £42 on coat and £6 on scarf

The amount that the person has left will be:

= £60 - £42 - £6

= £12

In conclusion, the person has £12 left.

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Answer:

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1jwjqhwhwjmnbhokmbhiknb

Answer:

The answer is $210.

Step-by-step explanation:

60/2 = 30. 30*5= 150. 150+60=210.

well, we know Aaron received $60, and we also know that Aaron and Betty are sharing the total on a 2:5 ratio, thus

[tex]\cfrac{Aaron}{Betty}~~ = ~~\cfrac{2}{5}\implies \cfrac{60}{Betty}~~ = ~~\cfrac{2}{5}\implies (60)(5)=(Betty)(2) \\\\\\ \cfrac{(60)(5)}{2}=Betty\implies 150=Betty~\hfill \underset{\textit{total money shared}}{\stackrel{60~~ + ~~150}{210}}[/tex]

The value for x that is a double root of this function is x = -1

The function is given as:

f(x) = x^3 - 3x - 2

From the graph of the above function (see attachment), we have the following highlights:

The point that it touches the x-axis is the double root point

Hence, the value for x that is a double root of this function is x = -1

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Step-by-step explanation:

x is the number

x = 3y + 2

the square

x² = (3y + 2)² = 9y² + 12y + 4

9y² is a multiple of 3 (because of the factor 9)

12y is a multiple of 3 (because of the factor 12)

4 is 1 more than a multiple of 3 (1×3).

so, the sum of all 3 terms is 1 more than a multiple of 3.

The x-coordinates of the vertices of the hyperbola are 11 and -11

The hyperbola is given as:

[tex]\frac{x^2}{121} - \frac{y^2}{49} = 1[/tex]

A hyperbola is represented as:

[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]

Where the coordinate of the vertex is:

Vertex = (±a, 0)

By comparing the above equations, we have:

[tex]a^2= 121[/tex]

Take the square of both sides

a = 11

Substitute 11 for a in Vertex = (±a, 0)

Vertex = (±11, 0)

Hence, the x-coordinates of the vertices of the hyperbola are 11 and -11

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Similar: yes

Similarity statement: [tex]ADCB \sim SVUT[/tex]

Scale factor: 1/3

If the company sells 0 computers, they will not make a profit. They will lose $10780

The function is  given as:

P = 490n - 10780

A linear equation is represented as:

P = mn + c

Where

m represents the slope

By comparison, we have:

m = 490

This means that the slope is 490

Hence, the interpretation is

Slope; 490

The company earns $490 per computer sold

The function is  given as:

P = 490n - 10780

A linear equation is represented as:

P = mn + c

Where

c represents the vertical intercept

By comparison, we have:

c = -10780

This means that the vertical intercept is -10780

Hence, the interpretation is

Vertical intercept; -10780

If the company sells 0 computers, they will not make a profit. They will lose $10780

The function is  given as:

P = 490n - 10780

A linear equation is represented as:

P = mn + c

Where

-c/m represents the horizontal intercept

By comparison, we have:

-c/m = 10780/490

-c/m = 22

This means that the horizontal intercept is 22

Hence, the interpretation is

Horizontal intercept; 22

If the company sells 22 computers, they will break even. They will earn  $0

We have:

P = 490n - 10780

This gives

P = 490* 46 - 10780

P = 11760

If the company sells 46 computers, they will earn $11760

We have:

P = 490n - 10780

This gives

15190 = 490n - 10780

490n = 15190+10780

490n = 25970

n = 53

The company will earn $15190, if they sell 53 computers

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Step-by-step explanation:

try this option, answer is marked with red colour.

Answer:

  x/6

You're welcome! :)

Answer : 7/6

explanation is long

Answer:

Step-by-step explanation:

It would be point B. Since y-intercept is when the x is at 0, the answer would be point B.