helpp quick pleaseee

The interquartile range of the data set is 21.

Given that the heart rate of 10 adults is measured and the results are 83, 87, 90, 92, 93, 100, 104, 111, 115, 121.

The interquartile range shows the extent of the middle half of the distribution. Quartiles segment any distribution, ordered from low to high, into four equal parts. The interquartile range (IQR) contains the second and third interquartile ranges, the central half of the dataset.

The value of quartile 1 is Q₁=90

The value of quartile 3 is Q₃=111

So, the interquartile range is

IQR=Q₃-Q₁

IQR=111-90

IQR=21

Hence, the interquartile range of the data set 83, 87, 90, 92, 93, 100, 104, 111, 115, 121 is 21.

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Answer:

a1

Step-by-step explanation:

Just add the numerators if both fractions to get: a + 1 = a1

Answer:

a+1

Step-by-step explanation:

Well if you have the same denominator, which in this case you do, it's equal to b, you can simply add the numerators. This gives you the expression [tex]\frac{a+1}{b}[/tex] so the numerator is a+1

The coordinates of the circumcenter of triangle having coordinates of (0,0),(4,0),(4,-3) are (1,-17/6).

Given The coordinates of triangle are (0,0),(4,0),(4,-3).

Let the triangle be ABC.

Let the coordinates of the circumcenter be D(x, y).

We know that the length of circumcenter from the corner points are equal to each other.

In this way AD=BD=DC

AD=[tex]\sqrt{(x-0)^{2} +(y-0)^{2} }[/tex]

=[tex]\sqrt{x^{2} +y^{2} }[/tex]

DC=[tex]\sqrt{(4-x)^{2} +(-3-y)^{2} }[/tex]

BD=[tex]\sqrt{(4-x)^{2} +(0-y)^{2} }[/tex]

=[tex]\sqrt{(4-x)^{2} +y^{2} }[/tex]

AD=DC

[tex]\sqrt{x^{2} +y^{2} }[/tex]==[tex]\sqrt{(4-x)^{2} +(-3-y)^{2} }[/tex]

Squaring both sides we get

[tex]x^{2} +y^{2}=16+x^{2} -8x+9+3y+3y+y^{2}[/tex]

8x-6y=25--------------------1

DC=BD

[tex]\sqrt{(4-x)^{2} +(-3-y)^{2} } =\sqrt{(4-x)^{2} +y^{2} }[/tex]

8x+6y=-9---------------------2

Solve equation 1 and 2

Add both equations

8x-6y+8x+6y=25-9

16x=16

x=1

put the value of x in 1

8x-6y=25

8*1-6y=25

-6y=25-8

y=-17/6

Hence the coordinates of circumcenter is (1,-17/6).

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Answer:

x = -4.5

Step-by-step explanation:

Solving the equation :

[tex]\left\vert -4+\frac{5}{2} \right\vert -\left( -x\right) =-3[/tex]

[tex]\Longleftrightarrow \left\vert \frac{-8}{2} +\frac{5}{2} \right\vert +x =-3[/tex]

[tex]\Longleftrightarrow \left\vert \frac{-8+5}{2} \right\vert +x =-3[/tex]

[tex]\Longleftrightarrow \left\vert \frac{-3}{2} \right\vert +x =-3[/tex]

[tex]\Longleftrightarrow \frac{3}{2} +x =-3[/tex]

[tex]\Longleftrightarrow x =-3-\frac{3}{2}[/tex]

[tex]\Longleftrightarrow x =-\frac{6}{2} -\frac{3}{2}[/tex]

[tex]\Longleftrightarrow x = -(\frac{6}{2} +\frac{3}{2} )[/tex]

[tex]\Longleftrightarrow x =-\frac{9}{2}[/tex]

[tex]\Longleftrightarrow x =-4.5[/tex]

The solution to the equations 2/x+3/y=9/xy; and 4/x+9/y=21/xy are x = 1, and y = 3.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The complete question is:

Solve for x and y:

2/x+3/y=9/xy; and 4/x+9/y=21/xy   x ≠ 0, y ≠ 0

We have two equations:

2/x+3/y=9/xy;

4/x+9/y=21/xy

Solving substitution method:

[tex]\rm \dfrac{4}{\dfrac{9-2y}{3}}+\dfrac{9}{y}=\dfrac{21}{\dfrac{9-2y}{3}y}[/tex]

y = 3

x = 1

Thus, the solution to the equations 2/x+3/y=9/xy; and 4/x+9/y=21/xy are x = 1, and y = 3.

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Answer:

16a^2b^2

Step-by-step explanation:

An exponent that is over a whole entire fraction can be split up and put separately onto the numerator (top number) and denominator (bottom number) See image.

Then you can get rid of a negative exponent (make it positive) by moving the whole term across the fraction bar. The top moves to the bottom and the bottom moves to the top. See image.

In the term (4ab)^2, the exponent 2 can be passed out to the 4 and the a and the b. See image.

Answer: D

Step-by-step explanation:

The value of <RQZ has been calculated as 21 from the solution we have below.

We have

< PZQ= <PQZ

PQR - PRQ = 42

Let < PZQ = y⁰

PQZ = y⁰

Let PRQ = x⁰

< PQR = x + 42⁰

< QpZ + y + y = 180⁰

such that

QPZ + 2y = 180⁰

<QPZ = 180⁰ - 2y

<(QPZ + PQR + PRQ) = 180

Adding these equations, we would have

180 - 2y + x + 42 + x = 180⁰

180 would cancel out

We have

2x - 2y + 42 = 0

x- y +21 = 0

We have to add 21 to both sides of the equation

x- y + 42 = 21

(x + 42) - y = 21

(x + 42) = <PQR and y = < PQZ

Hence 21 = <RQZ

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Answer:

Step-by-step explanation:

[tex]if A+B=45\\tan(A+B)=tan(45)\\\dfrac{tanA+tanB}{1-tanA.tanB}=1\\ \implies tanA+tanB=1-tanA.tanB\\\frac{1}{cotA}+\frac{1}{cotB}=1-\frac{1}{cotA}\frac{1}{cotB}, \{tanX=\dfrac{1}{cotX} \}\\ cotA+cotB=cotA.cotB-1\\cotA.cotB-cotA-cotB=1.[/tex]

Answer: C / d=1

Step-by-step explanation:

Just did it

Answer: C

Step-by-step explanation: Just took the quiz

No, we don't have evidence to support that the mean completion time under new management has decreased but we can conclude that it remains at 15.5 minutes.

Given mean of 15.5 minutes , standard deviation of 1.7 minutes, sample size of 90 and sample mean of 15.4 minutes.

We can do the following study for conclusion:

Firstly the null hypothesis is

[tex]H_{0}: x=15.5[/tex]

The alternate hypothesis is

[tex]H_{1}: x < 15.5[/tex]

since the value is less than this is a one tailed test.

Z=x bar-x/d/[tex]\sqrt{n}[/tex]

where x is sample mean and d is standard deviation.

Z=15.4-15.5/1.7/[tex]\sqrt{90}[/tex]

=-0.1/1.7/9.4868

=-0.560

Critical value of Z at 0.1 level of significance

Z=-1.28

We fails to reject the null hypothesis since -0.560>-1,28

Hence we don't have evidence to support that the mean completion time under new management has decreased but we can conclude that it remains at 15.5 minutes.

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Question is incomplete. It should include:

mean of 15.5 minutes ,

standard deviation of 1.7 minutes,

sample size of 90

and sample mean of 15.4 minutes.

The trinomial represented by the algebraic tiles is x^2  + 4x + 3

On the horizontal axis, we have:

1 row under the big square.

This represents x + 1

On the vertical axis, we have:

3 columns beside the big square.

This represents x + 3

So, we have:

(x + 1) * (x + 3)

Expand

(x + 1) * (x + 3) = x^2  + x + 3x + 3

Evaluate

(x + 1) * (x + 3) = x^2  + 4x + 3

Hence, the trinomial represented by the algebraic tiles is x^2  + 4x + 3

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The least possible value of the expression is 2020

The expression is given as:

[tex](x + 4)(x + 5) + \frac{10^6}{x(x + 9)}[/tex]

Next, we plot the expression on a graph (see attachment)

From the attached graph, the minimum value of the expression is 2020 under the domain of x > 0

Hence, the least possible value of the expression is 2020

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Answer:

Step-by-step explanation:

1). 7x - 2y = 5 , A = 7 , B = 2 , C = 5

2). 4x - y = 1 , A = 4 , B = - 1 , C = 1

3). 5x - 2y = 3 , A = 5 , B = - 2 , C = 3

4). 4x - 3y = 3 , A = 4 , B = - 3 , C = 3

5). 2x + y = 15 , A = 2 , B = 1 , C = 15

The expression given in the task content can be evaluated and simplified to be equal to; sin²(x).

It follows from the task content that the result of the product given is to be determined.

Hence, the multiplication is as follows;

1 -cos(x) +cos(x) -cos²(x).

1 -cos²(x).

However, since sin²(x) + cos2(x) = 1; it therefore follows that;

1 -cos²(x) = sin²(x)

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True, a circle can be circumscribed about the quadrilateral described in the task content.

It follows from the task content that quadrilateral in discuss has angles; 95, 80, 85 and 100.

By convention, it follows that circles can be circumscribed about only cyclic quadrilaterals in which case their opposite angles are supplementary. Hence, since opposite angles of the quadrilateral are supplementary (i.e amount to 180). Then, True, the circle can be circumscribed about the quadrilateral.

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The equivalent expression of a + 5 is -(-a - 5)

The expression is given as:

a + 5

Multiply by 1

1 * (a + 5)

Express 1 as -1 * -1

-1 * -1 * (a + 5)

Open the bracket

-1 * (-a - 5)

This gives

-(-a - 5)

Hence, the equivalent expression of a + 5 is -(-a - 5)

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A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The length of GF is 254 units.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

Since a centroid of a triangle divides the median into a ratio of 2:1. Therefore, the ratio of AG: DG is,

AG / DG = 2/1

(19x+14)/(9x+20) = 2/1

19x + 14 = 18x + 40

19x - 18x = 40 - 14

x = 26

Assuming the triangle is an equilateral triangle, therefore, the length of GF will be,

GF = DG = 9x+20

GF = DG = 9(26) + 20

GF = 254 units

Hence, the length of GF is 254 units.

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Answer:  26 units

Step-by-step explanation:   Trust Me!!!  

The answer is correct on Edge. I just got it right!

In the beginning, they have 50 and 180 cows respectively.

The two farmers bought  a total of 230 cows .

A year later the first farmer had 10% more cows than in the beginning.

Therefore,

let

x = number of cow he has initially.

A year later the percentage increase = 0.1x

whereas the second had 20% increase. Therefore,

let

y = number of cow he has initially.

A year later percentage increase = 0.2y

Hence,

x + y = 230

1.1x + 1.2y = 263

1.1x + 1.1y = 253

1.1x + 1.2y = 263

0.2y = 10

y = 10 / 0.2

y = 50

x = 230 - 50

x = 180

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Step-by-step explanation:

sinA=sinA

sin2A

(sinA)2

Answer:

f(-3) =8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer

f(x) has the same meaning as y. So you could rewrite the question as "What value of x gives y a value of 8"

The graph tells you that x = - 3 when y = 8.

f(-3) = 8

The image of the figure under reflections in line m and then line t is shown below.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Reflection does not change the size and shape of the geometry.

The image of the figure under reflections in line m and then line t.

The reflection of the square DEFG will be given in the figure.

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Your question presented was: [tex]\frac{2}{5} (\frac{1}{3} x-\frac{15}{8} )-\frac{1}{3} (\frac{1}{2} -\frac{2}{3}x)[/tex]

Okay, lets distribute this problem and break it into two parts. We will distribute 2/5 and -1/3 to the numbers in parenthesis. This is the distributive property.

Step 1.
[tex]\frac{2}{5} (\frac{1}{3} x-\frac{15}{8} )[/tex] when distributed is [tex]\frac{2}{15} x - \frac{30}{40}[/tex]

Please note that -1/3 can be rewritten as + -1/3. So you must distribute the negative.

Step 2.
[tex]\frac{-1}{5} + \frac{2}{9} x[/tex]
So..lets put the 2 parts of the equation together

[tex]\frac{2}{15} x - \frac{30}{40}[/tex] + [tex]\frac{-1}{5} + \frac{2}{9} x[/tex] can be simplified by getting the common denominator.

You can only add like terms, so those fractions with x can only be combined with x.
Step 3.
Lets reformat while we're at it
[tex]\frac{6}{45} x + \frac{10}{45} x -\frac{30}{40} -\frac{8}{40}[/tex]

We got 45 because the LCM (Lowest Common Multiple) of 15 and 9 was 45. We multiplied both sides of the fraction by 3 for 2/15x and we multiplied by 5 on both parts of the fraction for 2/9x.

Now we combine.
Step 4.
[tex]\frac{16}{45}x-\frac{38}{40}[/tex]. We can still simplify!
Step 5.
-38/40 can be simplified by a common factor, 2! So our final answer is
[tex]\frac{16}{45}x-\frac{19}{20}[/tex]

I hope this helps you, heart if it helps.

Answer:

Choice A

Step-by-step explanation:

[tex] \rm \: a {}^{2} \{ \cdot \: \cfrac{1}{a {}^{ \frac{2}{3} } \ } \}[/tex]

Applying Distributive property;

Choice A is accurate.

Answer:

19.6ft (nearest tenth)

Step-by-step explanation:

Please refer to the attached photo for better understanding.

Given Length of Wire = BC = 22ft

Given Distance from Grounded Wire to Base of Pole = AC = 10ft

Length of Pole = AB

We can use Pythagoras' Theorem to find Length of Pole, AB.

By Pythagoras' Theorem,

[tex]c^{2} =a^{2} +b^{2} \\BC^{2} =AB^{2} + AC^{2} \\22^{2} =AB^{2} +10^{2} \\484=AB^{2} +100\\AB^{2} =484-100\\AB=\sqrt{384} ft\\=19.6ft (nearest tenth)[/tex]

The linear are said to be parallel.

Collinear points are the points that lie on the same straight line or in a single line.

Given:

slope= 3

If two non co-linear segments with a slope of 3 in a coordinate plane, which means that the two line segments are parallel to each.

So, the same slope symbolise the  concept of parallel line in same plane.

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After 6 years, the difference between owning the house and renting is $12,000.

The first step is to determine the total cost of renting the house for six years.

Total cost of renting the house = rent per month x number of years x number of months in a year

1500 x 12 x 6 = $108,000

Difference = cost of owning - cost of renting

$120,000 - $108,000  = $12,000

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If the distance is 45 miles and speed of both cyclist is 14 and 16 miles per hour then they will take time of 1.5 hour to meet.

Given First cyclist is riding at 14 miles per hour and second at 16 miles per hour. The distance is 45 miles.

We know that speed is the distance covered by an object in a particular period of time.

Speed=distance/time.

It is expressed as kilometers per hour or miles per hour, etc.

If both riders are riding towards each other then the speed will be 16+14 =30 miles per hour.

Distance=45 miles.

Time =distance/speed

=45/30

=1.5

Hence if first cyclist is riding at 14 miles per hour and second is riding at 14 miles per hour and the distance is 45 miles then they will meet after 1.5 hours.

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The equation for the trend line in the scatter plot will be Y= 5x-1. Option B is correct.

In an effort to demonstrate how much one variable is influenced by another, scatter plots are used to depict data points on a horizontal and vertical axis.

When there is no connection between two variables, it is called a zero correlation. For instance, there is no correlation between IQ level and the quantity of tea consumed.

The graphs are attached in the attachment.

The equation for the trend line in the scatter plot will be Y= 5x-1.

Hence, option B is correct.

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Triangle ABC was dilated by a scale factor to form triangle A'B'C', such that AB≠A′B′

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the increase or decrease in the size of a figure by a scale factor.

Dilation does not preserve the size of a figure, it only preserves the shape and angle.

Triangle ABC was dilated by a scale factor to form triangle A'B'C', such that AB≠A′B′

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