Plot and connect the points A(-4, -1), B(6, -1), C(6, 4), D(-4, 4), and find the area of the rectangle it forms.

Answer:

16.4

Step-by-step explanation:

The interquartile range is the difference between the upper and lower quartiles.

Given the five figure summary, then

upper quartile = 28.8

lower quartile = 12.4

interquartile range = 28.8 - 12.4 = 16.4

The Interquartile range is 16.4.

When values are ranked from lowest to highest, the Interquartile range designates the middle 50% of those values.

Find the median (middle value) of the bottom half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3).

The interquartile range represents the variation between Q3 and Q1.

The interquartile range is calculated as follows:

The upper quartile is 28.8

The lower quartile is 12.4

The interquartile range is,

= 28.8 - 12.4

= 16.4

The value of the interquartile range is 16.4.

To know more about the Interquartile range

https://brainly.com/question/4135956

#SPJ1

Answer:

110

Step-by-step explanation:

the sum of straight angle is 180

the sum of angle of triangle=180

angle E=180-120=60

triangle BDE: <B=180-60-90=30

<B in triangle ACB=180-(130+30)=20)

in traingle ACB: <A = 180-(90+20)=70

angle x=180-70=110 degrees

Answer:

Step-by-step explanation:

The box encloses data between the two quartiles, namely at least half of the data.  If there are 40 schools, then half of them would be in the box, between 1 and 6.

see attached plot.

Answer:

really hard to tell what the box plot is like without an attachment so im gonna help u find it out anyway

Step-by-step explanation:

basically when u look at a  box plot and the range the line in the middle is the median  and then the max the lowest range the lower quartile and then the higher quartile you can find ur anser, simply find the median first, find where the lower quartile is and then the lowest number in the group thats in betweeen 1 and 6

Answer:

6. Unit rate = 1.3 yards per second

7. Unit rate = 0.8 page per minute

Step-by-step explanation:

The unit rate is simply the comparison of 2 quantities, whereby dividing both, the denominator must be 1.

For example, in the graph given comparing distance walked over time, when x (time in s) = 3, y (distance in yd) = 4.

Unit rate represented by the slope is the yards covered per second.

Unit rate = [tex] \frac{4}{3} = 1.33 [/tex]

Unit rate ≈ 1.3 yards per second

For the second graph given, unit rate of the slope is the number of pages read per minute.

From the graph, 4 pages is read at 5 minutes.

Thus,

Unit rate = [tex] \frac{4}{5} = 0.8 [/tex]

Unit rate = 0.8 page per minute

Answer: Center D I think

Step-by-step explanation:

Answer:

35.1

Step-by-step explanation:

There's a formula that i've linked as an image

Basically, substitute all 3 sides and the length into that formula, chuck it into the calculator and viola.

Or... we can use pythagoras' theorem and get the height of the triangle Height = [tex]3^{2}[/tex] - [tex]1.5^{2}[/tex] = 2.6

Area of triangle = (3 * 2.6) / 2 = 3.9

Volume = 3.9 * 9

Volume of prism = 35.1

Answer:

1 13/35 (mixed number) or 48/35 (simplified)

Step-by-step explanation:

6/7 times 8/5

= (6 times 8) / (7 times 5)

= 48/35 or 1 13/35

hope this helped :)

Answer:

48/35

Step-by-step explanation:

6/7*8/5=48/35

==================================================

Explanation:

Jane does the job alone and she can finish it in 5 hours. Her rate is 1/5 of a job per hour. By "job", I mean painting the entire fence. Notice that multiplying 1/5 by the number of hours she works will yield the value 1 to indicate one full job is done.

Through similar reasoning, Paul's rate is 1/6 of a job per hour.

Let x be the time, in hours, it takes Peter to get the job done if he worked alone. His rate is 1/x of a job per hour.

Combining the three individual rates gives

1/5 + 1/6 + 1/x = (6x)/(30x) + (5x)/(30x) + (30)/(30x)

1/5 + 1/6 + 1/x = (6x+5x+30)/(30x)

1/5 + 1/6 + 1/x = (11x+30)/(30x)

The expression (11x+30)/(30x) is the total rate if the three people worked together. This is assuming neither worker slows another person down.

Set this equal to 1/2 as this is the combined rate (based on the fact everyone teaming up gets the job done in 2 hours). Then solve for x

(11x+30)/(30x) = 1/2

2(11x+30) = 30x*1 .... cross multiply

22x+60 = 30x

60 = 30x-22x

60 = 8x

8x = 60

x = 60/8

x = 7.5

It takes Peter 7.5 hours, or 7 hours 30 minutes, to get the job done if he worked alone.

--------------

Here's another equation to solve though its fairly the same idea as above

1/5 + 1/6 + 1/x = 1/2

30x*(1/5 + 1/6 + 1/x) = 30x*(1/2) ... multiply both sides by LCD

30x(1/5) + 30x(1/6) + 30x(1/x) = 30x(1/2)

6x + 5x + 30 = 15x

11x + 30 = 15x

30 = 15x-11x

30 = 4x

4x = 30

x = 30/4

x = 7.5

We get the same answer

Answer:  7 . 5 hrs

Step-by-step explanation:

It takes Jane 5 hours to finish the fence so she can get  [tex]\dfrac{1}{5}[/tex] of the job done in 1 hour.

It takes Paul 6 hours to finish the fence so he can get  [tex]\dfrac{1}{6}[/tex] of the job done in 1 hour.

It takes Peter x hours to finish the fence so he can get  [tex]\dfrac{1}{x}[/tex] of the job done in 1 hour.

Together, it takes them 2 hours to finish the fence so they can get  [tex]\dfrac{1}{2}[/tex] of the job done in 1 hour.

Jane + Paul + Peter = Together

[tex]\dfrac{1}{5}\quad +\quad \dfrac{1}{6}\quad +\quad \dfrac{1}{x}\quad =\quad \dfrac{1}{2}[/tex]

Multiply everything by 30x to eliminate the denominator:

[tex]\dfrac{1}{5}(30x) + \dfrac{1}{6}(30x) +\dfrac{1}{x}(30x) =\dfrac{1}{2}(30x)[/tex]

Simplify and solve for x:

6x + 5x + 30 = 15x

      11x + 30 = 15x

              30 = 4x

              [tex]\dfrac{30}{4}=x[/tex]

              7.5 = x

Answer:

10n = d

Step-by-step explanation:

We know that

Each CD is sold for 10 dollars

The music store has sold n amount of CD's

The total number of dollars 'd' depends on how many CD's were sold

The equation is: 10n = d

Hope this helps!

Answer:

D=10n

Step-by-step explanation:

Answer: 28

Step-by-step explanation:

I can't really think of a way to explain this well without visuals and idk how to add images on my answer. But, what I normally do is draw out the shape on paper divide the shape into different sections. Solve the area of the separate sections. It simplifies the more complex figure and turns them into basic shapes. After solving each shape, add all of them together and that leaves you with the area. Hopefully you understand what I mean. I hope this sort of helped:)

Answer:  A) 1       B) [tex]\sqrt5[/tex]

Step-by-step explanation:

[tex]A)\quad \dfrac{2\sqrt3}{\sqrt{12}}=\dfrac{2\sqrt3}{2\sqrt3}=1\\\\\\\\B)\quad \dfrac{5\sqrt7}{\sqrt{35}}=\dfrac{5\sqrt7}{\sqrt5\cdot \sqrt7}=\dfrac{5}{\sqrt5}\bigg(\dfrac{\sqrt5}{\sqrt5}\bigg)=\dfrac{5\sqrt5}{5}=\sqrt5[/tex]

Answer:

C. Fertility= Nutrients * Moisture / Pollutant

Step-by-step explanation:

F=NM/P

F= Fertility of the soil

N= Amount of nutrients in the soil

M= Amount of moisture in the soil

P= Amount of pollutant in the soil

F=NM/P

Fertility of the soil

= Amount of nutrients in the soil * Amount of moisture in the soil / Amount of pollutant in the soil

Fertility= Nutrients * Moisture / Pollutant

Option C is the correct answer

Answer:

put it in a calculator, 8,000 times whatever number u need

Answer:

A.

Step-by-step explanation:

Anwer A has the following equation:

[tex]g(x)=\frac{3}{5}x^2-3[/tex]

In this equation, we can calculated the intercept replacing x by 0, as:

[tex]g(x)=\frac{3}{5}0^2-3=-3[/tex]

if this is the answer, the graph of g(x) should be through the point (0,-3) and that happens.

Additionally, the roots of the equations are calculated replacing g(x) by 0 and solving for x, so:

[tex]0=\frac{3}{5}x^2-3\\x_1=\sqrt{5}=2.236\\x_2=-\sqrt{5}=-2.236[/tex]

It means that the graph of g(x) should be through the points (2.236,0) and (-2.236,0) and that happens too.

So, the answer is A, [tex]g(x)=\frac{3}{5}x^2-3[/tex]

Divide the two numbers to find the ratio:

400 / 1200 = 1/3

The ratio is 1:3

Answer:

B

Step-by-step explanation:

Gear A has 400 teeth.

Gear B has 1200 teeth.

Write as a ratio of gear A to gear B.

400:1200

Simplify the ratio.

4:12

1:3

Answer:

260 cm^2

Step-by-step explanation:

The area of a parallelogram is given by this formula:

● A= b*h

b is the base and h is the heigth.

The heigth of this parallelogram is 13 cm and its base is 20cm.

●A= 13*20 = 260 cm^2

Answer:

B. 14

Step-by-step explanation:

22/x = 11/(21-x)

462 - 22x = 11x

462 = 33x

x = 14

Answer: The value of x is 14, answer choice B

Let y be the other line segment connected to x

Using proportions:

[tex]\dfrac{11}{22}=\dfrac{y}{x}[/tex]

Cross multiply and simplify

[tex]22y=11x[/tex]

[tex]y=\dfrac{1}{2}x[/tex]

We know that x and y add to 21, so we can create the following equation:

[tex]x+y=21[/tex]

Substitute y=(1/2)x

[tex]x+\dfrac{1}{2}x=21[/tex]

Simplify by adding like terms

[tex]\dfrac{3}{2}x=21[/tex]

Divide both sides by 3/2

[tex]x=14[/tex]

Let me know if you need any clarifications, thanks!

Answer/Step-by-step explanation:

Surface area of cylinder = 2πrh + 2πr²

Surface area of the cylinder with,

height (h) = 4 ft

radius (r) = 5 ft

Surface area = 2*3.14*5*4 + 2*3.14*5²

= 125.6 + 157

= 282.6 ft²

Surface area of the cylinder with,

height (h) = 12 yd

radius (r) = 3 yd

Surface area = 2*3.14*3*12 + 2*3.14*3²

= 282.74 yd²

Answer:

is perpendicular to line segment  

GH

. If the length of  is a units, then the length of  is  

a

units.

Step-by-step explanation:

had to do it myself.

Answer:

Blank 1-
GH

Blank 2-
a

AB is perpendicular to line segment GH. If the length of EF is a units, then the length of GH is a units.

Step-by-step explanation:

I got it correct

Answer:

See below.

Step-by-step explanation:

To find the equation, we need to find the slope and the y-intercept. Afterwards, we can put the numbers into the slope-intercept form:

[tex]y=mx+b[/tex]

From the graph, we can see that the line crosses the y-intercept at y=-6. Thus, the y-intercept (b) is -6.

Now we need to find the slope. Pick any two points where the line crosses. I'm going to pick (0,-6) and (4,-7).

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-(-6)}{4-0}= -1/4[/tex]

Therefore, the equation of the line would be:

[tex]y=mx+b\\y=-1/4x-6[/tex]

Answer:

A= 2

B=28

C=0

Step-by-step explanation:

ax2 + bx + c=0

Answer:

x = 1

Step-by-step explanation:

Given

[tex]\frac{1}{2}[/tex] : [tex]\frac{2}{3}[/tex] = [tex]\frac{3}{4}[/tex] : x

Multiply all parts by 12 to clear the fractions

6 : 8 = 9 : 12x , simplifying

3 : 4 = 3 : 4x

Thus

4x = 4 ( divide both sides by 4 )

x = 1

Answer:

The ratio of the volume of the larger sphere to the volume of the smaller sphere is

Step-by-step explanation:

Volume of a sphere is

[tex] \frac{4}{3} \pi {r}^{3} [/tex]

Where r is the radius

radius = diameter / 2

For First sphere

diameter = 8yards

radius = 8 / 2 = 4 yards

Volume of first sphere is

[tex] \frac{4}{3} \pi( {4})^{3} \\ \\ = \frac{256}{3} \pi \: {yd}^{3} [/tex]

For second sphere

diameter = 1064 yards

radius = 1064 / 2 = 532 yards

Volume of second sphere is

[tex] \frac{4}{3} \pi( {532})^{3} \\ \\ = \frac{602275072}{3} \pi \: {yd}^{3} [/tex]

Since the volume of the second sphere is the largest

Ratio of the second sphere to the first one is

[tex] \frac{602275072}{3} \pi \div \frac{256}{3} \pi \\ \\ = \frac{602275072}{3} \pi \times \frac{3}{256} \pi \\ \\ = \frac{602275072}{256} \\ \\ = \frac{ 2352637}{1} \\ \\ = 2352637: 1[/tex]

Hope this helps you

Answer:

[tex]\boxed{6\sqrt{6} }[/tex]

Step-by-step explanation:

[tex]\sqrt{12} \sqrt{18}[/tex]

Multiply square roots.

[tex]\sqrt{12 \times 18}[/tex]

[tex]\sqrt{216}[/tex]

Simplify square root.

[tex]\sqrt{36} \sqrt{6}[/tex]

[tex]6\sqrt{6}[/tex]

Answer:

x(x^2 + x + 1)

Step-by-step explanation:

x^3 + x^2 + x = x(x^2 + x + 1)

Answer:

8(6-x)

Step-by-step explanation:

Both 48 and 8 can be divisible by 8.

48 ÷ 8 = 6

8 ÷ 8 = 1

Therefore you get the answer 8(6-x)

as the simplest form.

Hope this helps.

Answer:

Option B

Step-by-step explanation:

As shown in the picture, g(x) is the red one which can be obtained by translating f(x) - the blue one toward +x-axis direction 4 units.

=> g(x) = f(x) + 4 = |x| + 4

Answer: Choice D

g(x) = |x-4|

=================================================

Explanation:

Replacing x with x-4 shifts the xy axis four units to the left. If we fix the blue V shape to not move while the xy axis does move, then it gives the illusion of the V shape moving 4 units to the right to end up producing the red curve.

You can use a table of values to compare the two functions or you could use a graphing tool to confirm the answer.

--------

Extra info:

Choice A will move the blue graph 4 units down

Choice B will move the blue graph 4 units up

Choice C will move the blue graph 4 units to the left

Answer:

∠A=123°.

Step-by-step explanation:

From the given figure it is clear the CD and CE are two tangent lines on circle with center A.

Radius is perpendicular to the tangent at the point of tangency.

[tex]\angle ADC=90^{\circ}[/tex]

[tex]\angle AEC=90^{\circ}[/tex]

Smaller arc DE = (5x-2)°

It means central angle DAE is (5x-2)°.

[tex]\angle DAE=(5x-2)^{\circ}[/tex]

Now, ADCE is a quadrilateral and sum of all angles of a quadrilateral is 360 degrees.

[tex]\angle ADC+\angle DCE+\angle AEC+\angle DAE=360^{\circ}[/tex]

[tex]90^{\circ}+(2x+7)^{\circ}+90^{\circ}+(5x-2)^{\circ}=360^{\circ}[/tex]

[tex](7x+5)^{\circ}+180^{\circ}=360^{\circ}[/tex]

[tex](7x+5)^{\circ}=360^{\circ}-180^{\circ}[/tex]

[tex](7x+5)^{\circ}=180^{\circ}[/tex]

[tex]7x+5=180[/tex]

[tex]7x=175[/tex]

[tex]x=25[/tex]

The value of x is 25.

[tex]\angle A=5x-2=5(25)-2=125-2=123^{\circ}[/tex]

Therefore, the measure of ∠A is 123°.

Answer:

  b = 17

  ∠QPS = 124°

  ∠SPT = 17°

  ∠TPR = 39°

Step-by-step explanation:

This fact can be used to write an equation:

  (8b -12)° +b° +(2b+5)° = 180°

  11b -7 = 180

  11b = 187

  b = 17

  8b -12 = 8(17) -12 = 124

  2b +5 = 2(17) +5 = 39

The value of b is 17.

The angle measures are ...

  ∠QPS = 124°

  ∠SPT = 17°

  ∠TPR = 39°

Answer:

[tex]71.63 \: \: \mathrm{cm^2 }[/tex]

Step-by-step explanation:

Once we know the diameter of the circle, we can figure out the problem.

The diameter of the circle = The diagonal of the rectangle inscribed in the circle

To find the diagonal of the rectangle, we can use a formula.

[tex]d=\sqrt{w^2 + l^2}[/tex]

The width is 10 cm and the length is 12 cm.

[tex]d=\sqrt{10^2 + 12^2}[/tex]

[tex]d \approx 15.62[/tex]

The diagonal of the rectangle inscribed in the circle is 15.62 cm.

The diameter of the circle is 15.62 cm.

Find the area of the whole circle.

[tex]A=\pi r^2[/tex]

The [tex]r[/tex] is the radius of the circle, to find radius from diameter we can divide the value by 2.

[tex]r = \frac{d}{2}[/tex]

[tex]r=\frac{15.62}{2}[/tex]

[tex]r=7.81[/tex]

Let’s find the area now.

[tex]A=\pi (7.81)^2[/tex]

[tex]A \approx 191.625[/tex]

Find the area of rectangle.

[tex]A=lw[/tex]

Length × Width.

[tex]A = 12 \times 10[/tex]

[tex]A=120[/tex]

Subtract the area of the whole circle with the area of rectangle to find area of shaded part.

[tex]191.625-120[/tex]

[tex]71.625 \approx 71.63[/tex]