PARALLEL LINES
Find x and y.
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The range is found by subtracting the smallest data value from the largest data value. Here, the smallest data value is 2.5 and the largest is 9.3. Therefore, the range is:

[tex]9.3 - 2.5 = 6.8[/tex]

Therefore, the answer is Option A.

Just for extra.

1. The steps that follow are also needed for finding the standard deviation. Start by writing the computational formula for the variance of a sample:

[tex]{s^2}= \frac{{\sum}{x^2} - \frac{({\sum}{x})^2}{n}}{n-1}[/tex]

2. Create a table of 2 columns and 14 rows. There will be a header row and a row for each data value. The header row should be labeled with x and x^2. Enter the data values in the x column, with each data value in its own row. In the second column, put the square of each of the data values, x^2.

x     y

8.2 67.24

3.1 9.61

5.9 34.81

2.5 6.25

6.2 38.44

5.1 26.01

7.6 57.76

9.3 86.49

8.1 65.61

7.4 54.76

7.8 60.84

6.5 42.25

8.7 75.69

3. Find the sum of all the values in the first column, [tex]{\sum}{x}[/tex].

[tex]\sum{x} = 86.4[/tex]

4. Square the answer from step 3, then divide that number by the size of the sample.

[tex]\frac{({\sum}{x})^2}{n} = \frac{7464.96}{13} = 574.22769230769[/tex]

5. Find the sum of all the values in the second column, [tex]{\sum}{x^2}[/tex].

[tex]{\sum}{x^2} = 625.76[/tex]

6. Subtract the answer in step 4 from the answer in step 5.

[tex]{\sum}{x^2} - \frac{({\sum}{x})^2}{n} = 625.76 - 574.22769230769 = 51.532307692308[/tex]

7. Divide the answer in step 6 by n - 1, one less than the size of the sample. This answer is the variance of the sample.

[tex]{s^2}= \frac{{\sum}{x^2} - \frac{({\sum}{x})^2}{n}}{n-1} = \frac{ 51.532307692308 }{12} = 4.294358974359[/tex]

To find the standard deviation, first write the computational formula for the standard deviation of the sample.

[tex]{s}= \sqrt{\frac{{\sum}{x^2} - \frac{({\sum}{x})^2}{n}}{n - 1}}[/tex]

Take the square root of the answer found in step 7 above. This number is the standard deviation of the sample. It is symbolized by [tex]s[/tex]. Here, we round the standard deviation to at most 4 decimal places.

[tex]{s} = \sqrt{4023.0714285714} = 63.4277[/tex]

Contain B holds 750 mL and container A holds 350 mL. Then contain B holds more amount than container A.

Conversion means to convert the same thing into different units.

Let container A contains 350 milliliters.

Let container B contains 0.75 liters.

The conversion of liters to milliliters will be given below.

1 liter = 1000 milliliters

Then we have

Container A = 350 mL

Container B = 0.75 x 1000 = 750 mL

Then the contain B holds 750 mL and the container A holds 350 mL.

Then contain B holds more amount than container A.

More about the conversion link is given below.

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Answer:

shape A is the only shape with 4 lines of symmetry.

Step-by-step explanation:

shape A is a square and a square has 4 lines of symmetry

so therefore, shape A is the only shape with 4 lines of symmetry.

Step-by-step explanation:

it depends if you use degrees or radians as angle measure.

let's assume degrees.

arcsine is the inverse function of sine.

so, when sin(x) = 1/2, arcsin(1/2) = x

when now x = 2×arcsin(1/2), we get

x = 2×30 = 60°

Answer:

B

Explanation:

There are 19 rectangles and 8 circles

19

+8

27 so it would be 27/47

Answer:

(2) B

Step-by-step explanation:

According to the graph

p(2, 3) so (-b, a) is (-3, 2)

So B is right

Answer:

[tex]B = ( - b,\: a)[/tex]

Step-by-step explanation:

Since P has the coordinates (a, b), then (a,b) would be (2, 3). Therefore:

[tex]a = 2\: and \: b = 3[/tex]

We are trying to find what point has the coordinates (-b, a). Recall:

[tex]a = 2 \: \: \: \: \: \: \: \: b = 3 \\ ( - b, \: a) = \\ ( - 3, \: 2)[/tex]

The point that is at (-3, 2) is point B.

The volume of the larger cone is equal to the total volume of the two smaller cones

From the question, we have two equal cylinders.

This means that the cylinders have equal volume.

From the complete question, a large cone is placed in one of the cylinders, while two small cones are placed in the other.

Since the cylinders have equal volumes, then the volume of the large cone equals the sum of the volumes of the smaller cones.

Hence, the volume of the larger cone is equal to the total volume of the two smaller cones

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Step-by-step explanation:

Equation to find the sum of the first n terms :

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] x (2[tex]a_{1}[/tex] + (n - 1)d)

- where n is the first n terms

- where [tex]a_{1}[/tex] is the first term in the sequence

- where d is the difference (To find the difference: [tex]a_{1}[/tex] - [tex]a_{2}[/tex])

How to find n for the given sum :

1. Using the previous equation, plug in all the numbers that you know

2. PEMDAS then combine all like terms

3. Distribute what's on the outside to the inside of the parenthesis

4. Move  [tex]S_{n}[/tex] to the other side to make a quadratic equation

5. Solve the quadratic, then use the positive number and round that number (term of numbers that isn't whole isn't possible ig??)

Question 1:

Sum of first 10 terms : [tex]S_{10}[/tex] = [tex]\frac{10}{2}[/tex] ( 2 x 2 + (10 - 1)6)

 [tex]S_{10}[/tex] = [tex]\frac{10}{2}[/tex] (4 + (9)6) = (4 + 54) = 58

 [tex]S_{10}[/tex] = [tex]\frac{10}{2}[/tex] x 58

Answer : 290

Find n for the given sum : 1704 =  [tex]\frac{n}{2}[/tex] x (2 x 2 + (n - 1)6)

distribute 6 into (n-1)

1704 =  [tex]\frac{n}{2}[/tex] x ( 4 + 6n - 6)

combine like terms

1704 =  [tex]\frac{n}{2}[/tex] x ( -2 + 6n )

Distribute  [tex]\frac{n}{2}[/tex] to ( -2 + 6n )

1704 = [tex]\frac{-2n}{2}[/tex] - [tex]\frac{6n^{2} }{2}[/tex]

Simplify fractions and move 1704 to the other side

-3[tex]n^{2}[/tex] - n + 1704 = 0

Use a quadratic calculator to find the answer and use the answer with the whole number

Answer : -24

Question 2:

(i'm just gonna show you the answers for the rest of them-)

Sum of the first 14 terms: 490

Find n for the given sum: 33.65 (I'm gonna round it to 34)

Question 3:

Sum of the first 21 terms: 483

Find n for the given sum: 11.48 (rounded: 11)

Question 4:

Sum of the first 32 terms: -1328

Find n for the given sum: -9.34 (rounded -9)

really hope this helps in any way :D

Answer:

A

Step-by-step explanation:

to find the y- intercept let x = 0 in the equation and solve for y

y = 5(0)² - 17(0) - 12 = 5(0) - 0 - 12 = 0 - 12 = - 12

then the y- intercept is (0, - 12 )

Answer:

[tex]\huge\boxed{\sf (0,-12)}[/tex]

Step-by-step explanation:

[tex]y=5x^2-17x-12[/tex]

y-intercept is the point where x = 0

Put x = 0 in the above equation.

[tex]y=5(0)^2-17(0)-12\\\\y = 0-0-12\\\\y=-12[/tex]

So, y = -12, when x = 0.

Ordered pair = (x,y) = (0,-12)

[tex]\rule[225]{225}{2}[/tex]

Answer:

11.2

Step-by-step explanation:

Answer:

26π cm

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = πd ( d is the diameter )

   = π × 26

   = 26π cm

▶︎◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◀︎

[tex]Hello[/tex] [tex]There![/tex]

 We are looking for the circumference of the circle.

It's not hard, I promise! I will take you through a few steps, and we'll find the answer.

Are you ready? Then let's begin...:)

[tex]Procedure:[/tex]

First, we need a formula for the circumference. We can't find the circumference without a formula!

· Luckily, there is a formula for the circumference:

⇒ [tex]C=\pi d}[/tex]

Whoa. What's that?!

No worries, I'll clarify everything in a moment. :)

We are looking for the circumference.

In this formula, what stands for the circumference?

That's right, [tex]C[/tex].

Now, what is this: [tex]\pi[/tex]?

This letter stands for pi - a constant in maths that comes in handy when we're searching for the circumference of a circle (or area).

It has an infinite number of digits after the decimal point, and these digits never repeat!

You might be thinking, "Oh no! Are we really going to use that infinite number?!"

The answer is "No". Mostly, we use 3.14 for [tex]\pi[/tex], because these are the first three digits of pi, but since we aren't asked to use 3.14 for pi, we just press the [tex]\boxed{\pi }[/tex] button on our calculator.

Whew!

And then last but not least, we see "d". This isn't a constant, this is the diameter.

Checking our provided information, we see that the diameter is 26 cm.

Now, we substitute 26 for d:

[tex]\bold{C=\pi (26)}[/tex]

[tex]\bold{C=\pi *26}[/tex]

And now all we have to do is type these numbers into our calculator, and find the answer:

[tex]\bold{C\approx81.7\:cm}[/tex]

Hooray! We've found the circumference!

But wait - why isn't 81.7 an option?

Because what we need to do is write it in terms of pi, which is even easier, because we just substitute 26 for d:

[tex]\bold{C=\pi *26}[/tex]  

➢ Rearrange the order of the terms:

[tex]\bold{C=26\pi \:cm}[/tex]

▲ Circumference

Now there's another thing - why are all four options with units squared?

Circumference isn't measured in units squared, the area is!

▶︎ Incase you need the area, here it is:

[tex]\bold{A=\pi r^{2}}[/tex]

A=Area (what we're looking for)

[tex]\pi[/tex] = pi

Here we have a new variable - it's r, which is the radius.

Do you see that [tex]^2[/tex] next to r? It means that r is squared, or multiplied by itself.

You might be thinking, "But we don't have the radius!"

If we have the diameter, finding the radius is a piece of cake, because we divide the diameter by 2:

[tex]\bold{26\div2}[/tex]

[tex]\bold{13}[/tex]

Now we substitute 13 for r and evaluate:

⇒ [tex]\bold{A=\pi (13)^{2}}[/tex]

13 times itself is 169:

⇒ [tex]\bold{A=169\pi \:cm^{2}}[/tex]

Whew! We're finally done!

[tex]Greetings![/tex]

--

The student with the most accurate description of the graph that represents Kate's movement is Tim

From the graph that represents Kate's distance per minute, we have the following highlights:

The student's description that matches the above highlights is Tim

Hence, the student with the most accurate description is Tim

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Based on the scenario above, the student that most accurately described Kate's motion is Tim.

Motion is defined in physics, as the way that an object alters its position over time.

Note that in the scenario above, Tim said that Kate drives at a variable speed for 2 minutes, then drives at a constant speed for 4 minutes, and finally stops at the parking area for the next 2 minutes and thus he is correct about Kate's motion.

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Answer:

$7.60

Step-by-step explanation:

If you multiply 19.0 by 4 then you get $7.60

Answer:

i had done this before so thats your answer, pls follow

The diameter of the DVD is 12 units.

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. It is the overall area that the object's surface occupies.

As per the given data:

The area of the DVD is equal to 36π cm².

We have to find out the diameter of the DVD.

As we know that a DVD is having a circular shape:

Area for a circle is given by πr², where r is the radius of the circle.

From the given data in the question:

πr² = 36π

r² = 36

r = √36

r = 6 units

The diameter of a circle is double the radius of the circle.

Diameter = 2r = 2 × 6 = 12 units

The diameter of the DVD is 12 units.

Hence, the diameter of the DVD is 12 units.

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The 16% of these students are taller than 66.7 inches and 285 students are between 61.6 and 68.4 inches tall.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have:

Mean of 65 inches and a standard deviation of 1.7.

From the graph:

P(X> 66.7) = (13.5 + 2.35 + 0.15)%

P(X> 66.7) = 16%

P(61.6 < X < 68.4) = (13.5 +34 + 34 + 13.5)%  = 95%

= (300×95)/100

= 285 students

Thus, the 16% of these students are taller than 66.7 inches and 285 students are between 61.6 and 68.4 inches tall.

Learn more about the normal distribution here:

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Answer:

The domain is all real numbers

The y - intercept is 2

The function is decreasing over its entire domain

Answer:

The area of a rectangle is 5/4

Step-by-step explanation:

Answer: 5 hours

Step-by-step explanation:

If 10% of 140 is 14. And if 14 mg of caffeine is leaving per hour then it would take 10 hours to completely leave from ones body, but for half of it to leave it would take 5.

Answer:

A) D) F)

Step-by-step explanation:

A) Since the graph is 10x10, and there are 10 seasons, it makes sense for A) to be an option

D) There is a total of 50 values that will be on the verticle axis, which seems like a fair number when the highest value is 37

F) (Season 8, 30 average points per game)

Answer:

I'd say think

Step-by-step explanation:

Do 3i =(7²)

3i=49

Answer:

see explanation

Step-by-step explanation:

given a polynomial has roots x = a and x = b , then the corresponding factors are

(x - a) and (x - b)

the polynomial is then the product of the factors , that is

f(x) = (x - a)(x - b)

note that radical and complex roots occur in conjugate pairs.

(5)

given x = - 3i is a root then x = 3i is also a root

factors then are (x - 3i) , (x + 3i) , (x - 7) , then

f(x) = (x - 7)(x - 3i)(x + 3i) ← expand 2nd pair using foil

     = (x - 7)(x² - 9i²) [ i² = - 1 ]

    = (x - 7)(x² + 9) ← distribute factors

   = x³ + 9x - 7x² - 63

f(x) = x³ - 7x² + 9x - 63

(6)

roots are x = [tex]\sqrt{5}[/tex] , x = - [tex]\sqrt{5}[/tex] , x = i , x = - i , and factors are

(x - [tex]\sqrt{5}[/tex] ) , (x + [tex]\sqrt{5}[/tex] ) , (x - i) , (x + i) and

f(x) = (x - [tex]\sqrt{5}[/tex] )(x + [tex]\sqrt{5}[/tex] )(x - i)(x + i) ← expand pairs of factors using FOIL

     = (x² - 5)(x² + 1) ← distribute factors

     = [tex]x^{4}[/tex] + x² - 5x² - 5

then

f(x) = [tex]x^{4}[/tex] - 4x² - 5

Answer:

1% and 49%

Step-by-step explanation:

0% is impossible

1%-49% is unlikely

50% is as likely as not

51%-99% is likely

100% is certain

hope this helps!

Answer:

They have the factor (8x +3) in common.

Explanation:

Factorize 1

64x² + 48x + 9

64x² + 24x +24x + 9

8x(8x +3) +3(8x +3)

(8x +3)(8x+3)

Factorize 2

64x² – 9

(8x)² – 3²

[tex]\sf {Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]

(8x-3)(8x+3)

Answer:

Step-by-step explanation:

triangle on right is the same as the triangle on the left

use pythagorean theorem

hypotenuse will give to the sides of the rectangle

a^2 + b^2 = hypotenuse squared

10.4^2 = 108.16

15.3^2 = 234.09

342.25 = hypotenuse squared

take the square root in both sides

hypotenuse = the square root of 342.25 =

18.5

add up the areas of the 2 triangles and rectangle

triangle area is 1/2 times 10.4 times 15.3 =

79.56

2 triangles areas are 159.12

rectangle area is 18.5 × 7 = 129.5

159.12 + 129.5 = 288.62

answer 1 = 288.62

second question:

to get 1 side take the

square root of 702.25 which is

26.5

to get the perimeter

multiply 26.5 by 4 which is

106

answer 2 is choice B 106

Answer:

vertical asymptotes is x = -2 and x = 1

Step-by-step explanation:

For rational functions, the vertical asymptotes are the undefined points, also known as the zeros of the denominator (below the line), of the simplified function.

This means [tex]-4x^{2} - 4x + 8[/tex] is equal to zero than solve

*image below*

Hope it helps :)

Let me know if you have any questions or anymore help lmk, happy to help with any school work!!

We are give with the function:

[tex]{\quad \qquad \longrightarrow f(x)=\dfrac{x^{2}+x-12}{-4x^{2}-4x+8}}[/tex]

Vertical asymptotes are the points, where the function is not defined, so the denominator must be equal to 0 for making f(x) not defined

[tex]{:\implies \quad \sf -4x^{2}-4x+8=0}[/tex]

Dividing both sides by -4, we have;

[tex]{:\implies \quad \sf x^{2}+x-2=0}[/tex]

Can be further written as:

[tex]{:\implies \quad \sf x^{2}-x+2x-2=0}[/tex]

[tex]{:\implies \quad \sf x(x-1)+2(x-1)=0}[/tex]

[tex]{:\implies \quad \sf (x-1)(x+2)=0}[/tex]

Using zero product rule, Equating both multiplicants to 0, we have:

[tex]{:\implies \quad \boxed{\bf{x=1\quad or\quad -2}}}[/tex]

This is the required answer

Answer:

An average test score is the sum of all the scores on an assessment divided by the number of test-takers.

Step-by-step explanation:

I forget

Answer:

$5.24 to nearest cent.

Step-by-step explanation:

Price of 2.2 pounds

= 2.38 * 2.2

= $5.236

Answer:

  D.  plain quadrilateral

Step-by-step explanation:

This is a vocabulary question.

__

A parallelogram is a quadrilateral (4-sided plane figure) with both pairs of opposite sides parallel. A rhombus is a special case of a parallelogram in which the sides have equal lengths.

A trapezoid is quadrilateral with exactly one pair of parallel sides. An isosceles trapezoid is one that has equal-length non-parallel sides.

__

The given figure has no parallel sides, so is none of the above. It is a ...

  plain quadrilateral

Answer:

E

Step-by-step explanation:

The ordered pair numbers seemed to big so I guessed and I was right.