Find the interquartile range of the data set shown
5 8 12 12 17 18 20 22 23
what is the interquartile range

Answer:

The equation that represents the line of Paul's grade downfall is:

y = (-20)x + 130

This equation states that for every decrease of 1 in the value of x (representing the number of weeks), the value of y (representing Paul's math average) decreases by 20.

Step-by-step explanation:

To find the equation that represents the line of Paul's grade downfall, we can use the two given points to plot the line on a coordinate plane. The point (2, 90) represents the value that after 2 weeks, Paul's math average is 90, and the point (4, 50) represents the value that after 4 weeks, Paul's grade has dropped to 50. We can plot these two points on the coordinate plane as follows:

(2, 90)

(4, 50)

To find the equation of the line that passes through these two points, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the slope of the line, we can use the formula:

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

Substituting the coordinates of the two points, we get:

m = (50 - 90) / (4 - 2)

= -40 / 2

= -20

To find the y-intercept of the line, we can substitute the coordinates of one of the points and the slope into the slope-intercept form of the equation:

y = mx + b

Substituting the coordinates of the point (2, 90) and the slope of -20, we get:

90 = (-20)(2) + b

= -40 + b

= b - 40

Solving for b, we get:

b = 90 + 40

= 130

Yes the given C and D lines are parallel

How to know two lines are parallel lines?

Any two parallel lines that are crossed by a transversal can be recognized by the following characteristics.

The fundamental characteristics listed below make it simple to recognize parallel lines.

as the sum of the given angle c and d i.e. 48+132 is 180 it clearly shows that it is the Pairs of interior angles on the same side of the transversal which proves that the given lines C and D are parallel  

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Answer: read below and learn how to do it so you won’t struggle the rest of highschool college and the real world!

Step-by-step explanation:

you just plug in 2 for p and -1 for q and solve.

(4x2+3x-1)^2

4x2 =8 3x-1 =-3

(8+-3)^2

(5)^2

5x5=25

••therefore your answer is 25

it’s basic algebra. it’s not calculus:)

[tex]-\dfrac{3}{8} x\leq 24[/tex]

Multiply both sides by [tex]-\dfrac{8}{3}[/tex]:

[tex](-\dfrac{8}{3} )\times(-\dfrac{3}{8} x)\leq (-\dfrac{8}{3} )\times24[/tex]

When multiplying or dividing by negative numbers, the sign will flip.

[tex]\fbox{x}\geq \fbox{-64}[/tex]

The new pay amount Helena will earn per month after the pay increase is equal to £3575.25

What is Percentage Increase?

In the question, it is given that Helena earns a monthly pay of £3150.

Now, we have to calculate the monthly pay earned by Helena when she receives a pay increase of 13.5%.

For calculating the new monthly pay amount, first, find 13.5% of the original pay.

[tex]\implies \frac{13.5}{100} \times 3150=425.25[/tex]  -------(1)

Next, adding the original monthly pay with the increased pay calculated in (1), we get the new monthly pay.

[tex]\implies 3150+425.25=3575.25[/tex]

Therefore, the new pay amount Helena will earn after the pay increase is equal to £3575.25

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13.5m × 20.74m or 20.74m × 13.5m can be the possible dimensions.

Height, length, and width are the three dimensions that all of the places we dwell and things we utilize on a daily basis have.

Height, depth, and other dimensions are examples of dimensions.

The dimensions of a line, a square, and a cube are each one, two, and three, respectively.

However, we consider the Universe to have one temporal dimension and three spatial dimensions (north-south, east-west, and up-down).

So, we have the area (A):

A = (54 – 2x)x

A = 54x - 2x²

Differentiate to obtain: dA/dX = 54 - 4x

We shall differentiate and equate to zero for a maximum Area, so dA/dx = 0.

54 – 4x = 0

x = 54/4

x = 13.5 m

It covers 280 m². Consequently, the other potential dimension:

w = 280/13.5

w = 20.74 m

Therefore, 13.5m × 20.74m or 20.74m × 13.5m can be the possible dimensions.

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The Perimeter of the paper 11 feet and the missing data in the table is: 8, 10, 18.6, 28, 2l + 6

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.

It is given that the length of the paper is 2.5 feet, and the breadth of the paper is 3 feet.

Using the perimeter of the rectangle:

Perimeter of the paper = 2(l+w) = 2(5.5) = 11=2(l+w)=2(5.5)=11 feet.

The missing data in the table is: 8, 10, 18.6, 28, 2l + 6

Thus, the Perimeter of the paper 11 feet and the missing data in the table is: 8, 10, 18.6, 28, 2l + 6

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Answer: (x+5)(2x+10)

Step-by-step explanation: I see your comment, so try to help you fast, I am in a rush, so can't type all the work on paper yet, sorry!

The probability that the student answers exactly 1 question correctly is

                            [tex]$\frac{135}{243}=\boxed{\frac{5}{9}}$[/tex]

What is the binomial coefficient?

In combinatorics, the binomial coefficient is used to denote the number of possible ways to choose a subset of objects of a given numerosity from a larger set.

There are a total of [tex]$3^5=243$[/tex] possible ways that the student can answer the quiz. To count the number of ways that the student can answer exactly 1 question correctly, we can use the binomial coefficient formula:

      [tex]\binom{5}{1}=5[/tex]

This counts the number of ways that the student can choose which 1 question to answer correctly.

For each of these 5 ways, there are 3 ways to choose the incorrect answer for each of the other 4 questions, so the total number of ways that the student can answer exactly 1 question correctly is

[tex]$5\cdot 3^4=135$[/tex].

Therefore, the probability that the student answers exactly 1 question correctly is

              [tex]$\frac{135}{243}=\boxed{\frac{5}{9}}$[/tex]

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The given statement " All else being equal, the further the t statistic falls from 0, either in the positive or negative direction, the more likely it is that the difference between two population averages is statistically significant. " is true.

The term t statistics refers the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error.

Here we have the statement All else being equal, the further the t statistic falls from 0, either in the positive or negative direction, the more likely it is that the difference between two population averages is statistically significant.

And we need to identify whether the statement is true or not.

As per the definition of t statistics, we have identified that the t statistic falls from 0. which states that is goes on the negative direction.

Therefore, the more likely it is that the difference between two population averages is statistically significant.

So, the statement is correct.

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Answer:

16 years old

Step-by-step explanation:

2x+3=35

  -3.  -3

2x=32

/2. /2

x=16

Leon is 16 years old

Hopes this helps please mark brainliest

Answer: To write a linear equation to model the relationship between the height h of the candle and time t, we need to find the slope and y-intercept of the line that represents this relationship.

The slope of the line is given by the rise over the run, or the change in the y-value (the height of the candle) over the change in the x-value (the time). We can calculate the slope by taking the difference in the height of the candle after 5 hours and 3 hours, and dividing it by the difference in the time:

slope = (16.5 - 18) / (5 - 3) = (-1.5) / (2) = -0.75

The y-intercept of the line is the point at which the line crosses the y-axis. This is the height of the candle when the time is 0. We can use the height of the candle after 3 hours as the y-intercept, since this is the height when the time is 3:

y-intercept = 18

We can use these values to write a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.

Plugging in the values we found, we get:

h(t) = -0.75t + 18

This is the linear equation that models the relationship between the height h of the candle and time t.

To predict how tall the candle will be after burning for 8 hours, we can plug in t = 8 into the equation:

h(8) = -0.75(8) + 18 = -6 + 18 = 12 inches

This means that the candle will be 12 inches tall after burning for 8 hours.

Therefore, the correct answer is (d) h(t) = 0.75t + 20.25; 14.25 inches.

To write a linear equation to model the relationship between the height of the candle and time, we can use the information given. We know that after 3 hours, the candle is 18 inches tall, and after 5 hours, it is 16.5 inches tall.

We can set up a system of linear equations to represent this information. Let's call the height of the candle h and the time t. Then we can set up the following system:

h = 18 - 3t

h = 16.5 - 5t

To solve this system, we can set the two equations equal to each other and solve for t:

18 - 3t = 16.5 - 5t

1.5 = 2t

t = 0.75

This tells us that the height of the candle decreases by 0.75 inches per hour.

Now we can use this information to predict how tall the candle will be after 8 hours. We can plug in 8 for t in the equation h = 18 - 3t to find the height of the candle:

h = 18 - 3(8)

h = 18 - 24

h = -6 inches

So the candle will be about 6 inches shorter after burning for 8 hours. This means it will be about 10.5 inches tall.

The correct option is c, h(t) = -0.75t + 15.75; 9.75 inches.

This is because we found that the height of the candle decreases by 0.75 inches per hour, which is represented by the coefficient of t in the equation. The y-intercept, 15.75, represents the initial height of the candle, which we found to be 16.5 inches.

Happy to help!

Answer:

28

Step-by-step explanation:

Determine which integer in the solution set will make the equation true. t − 42 = −14 {−56, −28, 3, 28}

replace 28 for t:

t − 42 = −14

28 − 42 = −14

−14 = −14

Answer:

  28

Step-by-step explanation:

You want the value of t that satisfies t − 42 = −14.

The solution to this 1-step linear equation is to add the opposite of the unwanted constant (-42).

Adding 42 to both sides of the equation gives ...

  t -42 +42 = -14 +42

  t = 28

The integer that makes the equation true is 28.

The coordinates of the vertices with the base b and the height h is  O(0, 0), W(b, 0), T(b, h) and S(0,h).

What is rectangle?

An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.

The rectangle with  base b and height h.

We know that:

The point O is shown in the graph is at Origin.

So, its coordinates are O(0, 0)

Since, the height of the rectangle is h,

as S and T are h units away from the x-axis.

and the base of the rectangle is b, T and W are b units away from the y-axis.

thus the coordinates of the other vertices are:

S(0, h), T(b, h) and W(b, 0)

Therefore, the coordinates of the vertices of the following rectangle with base b and height h are:

O(0, 0), W(b, 0), T(b, h) and S(0,h)

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Answer:

y+6=(1)/(3) (x+2)

Step-by-step explanation:

substitute (-2,-6) until equality is found

y+6=(1)/(3) (x+2)

(-6)+6=(1)/(3) ((-2)+2)

0 = 1/3 (-2+2)

0 = 0

confirm it with a graph

The values of x and y are obtained as 12.99 and 7.5 respectively.

The trigonometric ratios are defined for a right angled triangle.

The example of these ratios are sin, cos, tan, cosec, sec and cot.

The trigonometric ratios are useful in determining the heights and distances of the large objects.

For the given triangle, the trigonometric ratios are used as follows,

Cos(30°) = x/15

=> √3/2 = x/15

=> x = 15√3/2

=> x = 15 × 0.866

       = 12.99

And,

Sin(30°) = y/15

=> 1/2 = y/15

=> y = 15/2

       = 7.5

Hence, for the given triangle the values of x and y are given as 12.99 and 7.5 respectively.

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Answer:

G.

8+4 / 4 = x+9 / x

8x = 36

x=4.5

BC=x+9 =13.5

Answer: 17

Step-by-step explanation:

11x - 39 = 10x - 22

11x = 10x + 17

x = 17

The equation for the circle whose endpoints are A(1,4) and B(5,4) is written in diameter form [tex]x^{2} +y^{2}[/tex] -6x -8y + 21 = 0

A circle is a closed two-dimensional object in which every point in the plane is equally spaced from a certain point known as the "center" The symmetry line of reflection is formed by each line that traverses the circle. Additionally, it is rotationally symmetric about the center for all angles. In the plane, the circle formula is as follows:

The coordinate coordinates (x,y) are equal to (x-h)2 + (y-k)2 = r2.

The centre of a circle is located at (h,k), and its radius is measured in units of r.

The equation of a circle having end points of the diameter as (x1​,y1​) and (x2​,y2​) is (x−x1​)(x−x2​)+(y−y1​)(y−y2​)=0.

we have (1,4) and (5,4) as (x1​,y1​) and (x2​,y2​)

(x−(1))(x−(5))+(y−(4))(y−(4))=0

⇒ ([tex]x^{2}[/tex] -5x -1x + 5 ) + ( [tex]y^{2}[/tex] -4y -4y + 16 ) = 0

[tex]x^{2} +y^{2}[/tex] -6x -8y + 21 = 0

The equation for the circle whose endpoints are A(1,4) and B(5,4) is written in diameter form [tex]x^{2} +y^{2}[/tex] -6x -8y + 21 = 0.

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The required value of "a" would be 3.

Perpendicular lines are two lines that cross one other and create a 90-degree angle.

As per the question, we have

Line m has the equation y = −13x − 2

Here slope of line m = -13

The slope of the given line m will be -13,

Line k passes through the points (0,4) and (9, a).

The slope of line k = (a - 4)/(9-0)

The slope of line k = (a - 4)/9

Given line m and line k are both perpendicular to each other,

We know that two lines are perpendicular if the product of their slopes is -1.

So,  -13 × (a - 4)/9 = -1

⇒ -13a + 52 = 13

⇒ 13a = 52 - 13

⇒ 13a = 39

⇒ a = 39/13

⇒ a = 3

Therefore, the required value of "a" would be 3.

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Answer:

OP/PQ

Step-by-step explanation:

You need corresponding sides in triangle OPQ.

The ratio equivalent to the given ratio is OP/PQ

Two shapes are said to be similar if their corresponding sides are in the same proportion and the corresponding angles are congruent.

Given are two triangles having two pairs of the corresponding angles equal,

So, according to the definition of the similar figures, we can say that the triangles are similar,

Also,

Their corresponding sides will be in the same proportion.

Therefore,

RS / OP = ST / QP = RT / QO

Hence, the ratio equivalent to the given ratio is OP/PQ

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Answer: S

Step-by-step explanation:

We shall therefore obtain a square as a result. Since each square is a rectangle, the same perimeter and smaller area will be produced by using length and breadth of 90 yards.

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

Here,

original length=110 yards

original width=70 yards

perimeter=2(110+70)

=2*180

=360 yards

x+y=180

y=180-x

area=xy

A=x(180-x)

A=180x-x²

A'=180-2x

A'=0

2x=180

x=90 yards

y=90 yards

We shall so receive a square as a result. Given that each square is a rectangle, a length and width of 90 yards will result in a smaller area and the same perimeter.

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100 : 110 : 121 is the ratio must they invest money at 10% per annum compounded yearly so that each gets same sum at the age of their retirement

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Let P, R and S are three persons with ages 26 years, 27 years and 28 years

We need to find the ratio must they invest money at 10% per annum compounded yearly so that each gets same sum at the age of their retirement

x(11/10)ⁿ=y(11/10)ⁿ⁻¹=3(11/10)ⁿ⁻²

x.121/100=y.11/10=3

x/100=y/110=3/121

Hence,  100 : 110 : 121 is the ratio must they invest money at 10% per annum compounded yearly so that each gets same sum at the age of their retirement

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Answer:

g(x) will be the line y=x, reflected across the y-axis and shifted down 2 units.

Step-by-step explanation:

The -x negates every x-value, which has the effect of reflecting the graph across the y-axis. The -2 moves the graph down 2 units.

In the triangle WYC, the length of the side YC is 4.76 units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know a line segment parallel to a side of a triangle divides the other two sides in the same ratio.

Given, In a ΔMRC and ΔWYC MR = 14, CR=28, WY = 6, and MW = 17.88.

Now, MR = 14 and MW = 17.88.

Therefore, (MW/MR) = 17.88/14 = 1.28.

So, If WY = 6, then WE = (1.28)(6) = 7.66.

Now, In the ΔWYC, WY = 6 and WE = 7.66.

Therefore from the Pythagoras's theorem,

WE² - WY² = YC².

YC² = (7.66)² - 6².

YC² = 22.68.

YC = 4.76.

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The length of RB of the given triangle is; RB = 54 cm

We are given that in △QRS;

Point A is between points Q and R

Point B is between points R and S

AB∥QS

QA = 23 cm

QR = 41 cm

RS = 123 cm

Let us first find the ratio between RS and QR.

Ratio = RS ÷ QR

Ratio = 123 ÷ 41 = 3

QA × 3

23 × 3 = 69

Thus;

BS = 69

Thus;

RB = RS - BS

RB = 123 - 69

RB= 54 cm

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if we have a class of 15 students and we want to choose a committee of 5 students, their order and position don't matter, 3003 many different ways are there of creating a 5-person committee among the 15 students.

The combination formula is used to determine how many options there are for choosing things from a collection so that the order in which they are chosen is irrelevant. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.

Since order and position doesn't matter in this problem, use the combination formula.

The combination formula is: n! / (n-r)! r!

where n is the total number of items (15 in this case) and r is the number of items being selected at once (5 in this case)

Plugging our numbers into the formula:

= 15! / (15-5)! 5!

= 3003 ways.

So, there are 3003 ways of picking 5 people from a group of 15.

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Answer:

5 minutes

Step-by-step explanation:

Given:
It takes five machines five minutes to make five widgets

Let's first determine how much time it takes one machine to make one widget

1 machine will take 5 times as long to make 5 widgets

Therefore for 1 machine to make 1 widget it will take 1/5th of the time

To make 100 widgets, 1 machine will take 5 x 100 minutes or 500 minutes

If we use 100 machines this time will be reduced by 100