Two classes of students took an exam.

Here is a list of the scores in Class A:
65, 70, 70, 80, 80, 85, 85, 85, 90, 90, 100

Here is a box plot that shows the scores in Class B:
Box plot from 55 to 100 by 5’s. Whisker from 60 to 70. Box from 70 to 80 with vertical line at 75. Whisker from 80 to 90.

1. Which class had better overall results on the exam?
2. Which class had greater variability in the results?

Answer + Step-by-step explanation:

a) GE = r = GM

Then GEO is an isosceles triangle

b) since GEO is an isosceles triangle  then :

m∠SEG = m∠GOM = measure of the arc GM (mGM)  (result 1)

On the other hand :

m∠SEG = m∠SEG = (1/2)×(mAS - mGM)  (it’s a formula)   (result 2)

Now ,we equate  (result 1) and  (result 2) :

m∠SEG = mGM  

m∠SEG = (1/2)×(mAS - mGM)

Then

mGM = (1/2)×(mAS - mGM)

c) mGM = (1/2)×(mAS - mGM)

⇔ 2mGM = mAS - mGM

⇔ 3mGM = mAS

⇔ 3m∠SEA = m∠SOA

Remember:

mGM = m∠GOM = m∠SEA

Answer:

7x+2y=18

The first one

Step-by-step explanation:

The equation to be perpendicular switches they numbers before the x and y. Also plugging into a graphing calculator like desmos will show you
that

Answer: The mean of the data is 278.

Step-by-step explanation:

To the the mean of the data, we’ll have to add all the numbers up and divide it by the amount of data.

275+279+279+276+278+277+280+282+284+270=2780

2780/10=278

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[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Given question:-}}}}[/tex]

         11z-6=16, what is z?

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]

We need to make sure that all variables are on the left-hand side and the numbers are on the right-hand side.

Since we have a number on the left-hand side, we need to move it to the right-hand side with the opposite operation:-

11z=16+6

[tex]\it{11z=22}[/tex]

Divide by 11 on both sides:-

[tex]\it{z=2}[/tex]

We can check our solution by replacing z with 2 and seeing whether or not we end up with a true statement:-

[tex]\it{11(2)-6=16}[/tex]

[tex]\it{22-6=16}[/tex]

[tex]\it{16=16}[/tex]

So we conclude that our solution, z=2, is correct.

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Answer:

z=2

Step-by-step explanation:

11(2)-6=16

22-6=16

[tex]\text{Given that,}~ p(x) = x^2 +3 ~ \text{and}~ h(x) = \sqrt{x-3} \\\\(p \circ h)(x)\\\\=p(h(x))\\\\=p\left(\sqrt{x-3}\right)\\\\=\left(\sqrt{x-3} \right)^2 +3\\\\=x-3 +3\\\\=x[/tex]

The integral of [tex]\int {x(25x^2 + 1)} \, dx[/tex] is [tex]\frac{25}{4}x^4 + \frac{x^2}{2} + C[/tex]

The integral expression is given as:

[tex]\int {x(25x^2 + 1)} \, dx[/tex]

Start by expanding the bracket

[tex]\int {25x^3 + x} \, dx[/tex]

Next, we integrate each term in the expression

[tex]\frac{25}{4}x^4 + \frac{x^2}{2} + C[/tex]

Hence, the integral of [tex]\int {x(25x^2 + 1)} \, dx[/tex] is [tex]\frac{25}{4}x^4 + \frac{x^2}{2} + C[/tex]

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Answer:

$0.01

Step-by-step explanation:

Family size rate (per cubic inch)

Regular size rate

Difference in price

Volume of family sized box

Price per inch

Volume of regular size

Price per in

Difference:-

|0.02-0.03|=0.01$

The attributes to each three-dimensional shape that has the cross-section is 4,16 and 4.

Any closed figure made by 4 line segments joined end to end in series is called a quadrilateral.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

Given;

Quadrilateral A: area of 16 square inches

Quadrilateral B: perimeter of 24 inches

Quadrilateral C: perimeter of 16 inches

Now,

Quadrilateral A:

a^2=16

a=4

Quadrilateral B;

4a=24

a=6

Quadrilateral C:

4a=16

a=4

Therefore, the answers of quadrilaterals will be 4,6 and 4.

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The THREE statements that would produce the truth value F when p is true and q is false are (a) p → q (b) ¬ p ∧ ¬ q (d) q ∨ ¬ p

To do this, we simply analyze each option

The given parameters are:

p = true

q = false

(a) p → q

This means that:

If p then q

So, we have:

If true then false

The above statement would return false.

(b) ¬ p ∧ ¬ q

This means that:

If not p and not q

So, we have:

If not true and not false

i.e.

If false and true

The above statement would return false.

(c) p → ¬ q

This means that:

If p then not q

So, we have:

If true then not false

i.e.

If true then true

The above statement would return true.

(d) q ∨ ¬ p

This means that:

If q and not p

So, we have:

If false and not true

i.e.

If false and false

The above statement would return false.

Hence, the THREE statements that would produce the truth value F when p is true and q is false are (a) p → q (b) ¬ p ∧ ¬ q (d) q ∨ ¬ p

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Answer:

about 2827cm^3

Step-by-step explanation:

you are looking for the area  

4*pi*r^2

4*pi*15^15

pi*4*225

pi*900

2827.43

Answer:

b) 7 option B 7 is the answer

Step-by-step explanation:

bidmas rule:

7-2×3

2×3= 6

7-6=1

7×1= 7

therefore the answer is 7.

Answer: The answer is [tex]B. 7[/tex]

Step-by-step explanation:

[tex]7(7-2[/tex] × [tex]3)[/tex]

Simplify the expression.

[tex]7-2= 5[/tex]

[tex]7[/tex] × [tex]3[/tex] = [tex]21[/tex]

[tex]21[/tex] ÷ [tex]3=7[/tex]

Answer:

Step-by-step explanation:

A scientist is working with 12 meters of gold wire. How long is the wire in millimeters?

12 meters = 12000 mm

(1m = 1000 mm)

12 * 1000 = 12000

The exponential function that represents a stretch of a decay function is given as follows:

[tex]f(x) = \frac{5}{4}\left(\frac{4}{5}\right)^x[/tex]

An exponential function is modeled by:

[tex]y = ab^x[/tex].

In which:

It represents a stretch if a > 1, and a decay function if b < 1. Researching the problem on the internet, the correct option is given as follows:

[tex]f(x) = \frac{5}{4}\left(\frac{4}{5}\right)^x[/tex]

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Answer:

the answer is C :)

Step-by-step explanation:

Answer: Choice B

It is not a valid sample because it is not a random sample of the population.

Explanation:

The researcher should have randomly selected the participants, either by picking names out of a hat, using a random number table, or some kind of computer software to pick the names. Letting the first 8 people form the sample is very likely not representative of the population at large. We have a lot of bias here. Therefore, this is not a valid sample.

Step-by-step explanation:

product=× three=3 a number is unknown =x plus=+ five=5 is=equals to 20

3×x +5=20

3x+5=20

Subtract 5 from both sides

3x+5-5=20-5

3x=15

3x/3=15/3

x=5

From the section formula, it was found that the coordinate for the point S is (12,21).

The coordinates of the point S which divides the line AB into two sections can be found from the application of the Section Formula that is presented below:

[tex]S=(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})[/tex], where

[tex]ratio=\frac{m}{n}[/tex]

[tex]x_1[/tex] and [tex]y_1[/tex] are coordinates of A

[tex]x_2[/tex] and [tex]y_2[/tex] are coordinates of  B

The question gives  r=[tex]\frac{3}{2}[/tex], A=(21,3) and B=(6,33). From the ratio, you can find m=3 and n=2.

Next step, applying the internal section formula. Then, you have:

[tex]S=(\frac{3*6+2*21}{3+2}, \frac{3*33+2*3}{3+2})\\ \\ S=(\frac{18+42}{5}, \frac{99+6}{5})\\ \\ S=(\frac{60}{5}, \frac{105}{5})\\ \\ S=(12, 21)[/tex]

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Answer:

Table B

Step-by-step explanation:

A function is present when x-value can only have a single y-value.

Answer:

The amplitude is the highest point that the curve reached

Which is in your case = 2

Builder can build 7 one bedroom houses and 5 two bedroom houses.

What is consistent Equation?

A linear or nonlinear system of equations is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, when substituted into each of the equations, they make each equation hold true as an identity.

Let x represents the number of one-bedroom houses and y represents the number of two bedroom houses.

According to Question,

Total number of houses is 12 i.e. x + y = 12..........(i)

Total we have 88 windows in which 6 windows can be use in one bedroom house and 9 windows can be used in two bedroom house so,

6x + 9y = 88 ..................(ii)

From Equation (i) and (ii), we get

x = 7 and y = 5

Thus, Builder can build 7 one bedroom houses and 5 two bedroom houses.

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Answer:

Step-by-step explanation:

you have a rotation angle of 360 °, take out the known values ​​(360 ° -90 ° -144 ° = 126), 144 ° is part of a flat angle of 180 °, from 180 ° remove 144 and you have 36 °, they are opposite angles therefore the same. therefore 360 ​​- 144 - 90 - 36 - 36 = 54.

54 is 3x, so x = 18 ° (54 : 3 = 18)

Answer and step-by-step explanation:

[tex]28v^3 +16v^2-21v-12 =[/tex] collecting [tex]4v^2[/tex] in the first two terms and [tex]-3[/tex] in the last two:

[tex]4v^2(7v+4)-3(7v+4) =[/tex] collecting the bracket

[tex](7v+4)(4v^2-3)[/tex]

Bonus stage: if you are factoring over the real numbers and not over the rational, the second brackets is a difference of squares. Else, you stop  here.

[tex](7v+4)(2v+\sqrt3)(2v-\sqrt3)[/tex]

NEXT!

[tex]49x^3-35x^2+56x-40=[/tex]As before, [tex]7x^2[/tex]in the first two, and [tex]8[/tex] in the last two:

[tex]7x^2(7x-5)-8(7x-5)[/tex] collecting the bracket again

[tex](7x-5)(7x^2-8) =[/tex]again, bonus step

[tex](7x-5)(\sqrt7 x +2\sqrt2) (\sqrt7x-2\sqrt2)[/tex]

FINALLY!

[tex]24r^3-64r^2-21r+56 =\\8r^2(3r-8) -7(3r-8)=\\(3r-8)(8r^2-7) =[/tex]Again, bonus step

[tex](3r-8)(2\sqrt2r+\sqrt7)(2\sqrt2r-\sqrt7)[/tex]

Since usually most courses talk about factorization of polynomials BEFORE talking about real numbers, I would stop at the third stage, skipping the fourth.

Answer:

2 pounds.

Step-by-step explanation:

We have been given that Luke bought 256 ounces of strawberries. He divided them evenly between 8 different pies. We are asked to find the pounds of strawberries that Luke put on each pie.

First of all, we will convert 256 ounces into pounds.

We know that 1 pound equals 16 ounces. To convert 256 ounces into pounds, we need to divide 256 by 16.

[tex]256[/tex] [tex]ounces=\frac{256}{16}[/tex] [tex]pounds=16[/tex] [tex]pounds[/tex]

Now we will divide 16 pounds by 8 to find number of strawberries put on each pie.

[tex]Pounds[/tex] [tex]of[/tex] [tex]strawberries[/tex] [tex]on[/tex] [tex]each[/tex] [tex]pie=\frac{16}{8}[/tex]

[tex]Pounds[/tex] [tex]of[/tex] [tex]strawberries[/tex] [tex]on[/tex] [tex]each[/tex] [tex]pie=2[/tex]

Therefore, Luke put 2 pounds strawberries on each pie.

The sequence converges to 5 as n goes to ∞. We can prove this rigorously:

The claim is that, for [tex]n\in\Bbb N[/tex],

[tex]\displaystyle \lim_{n\to\infty} \frac{5n-1}{n+1} = 5[/tex]

By definition of the limit, this means for any ε > 0, there exists some N such that for any n larger than N, we have

[tex]\left| \dfrac{5n-1}{n+1} - 5 \right| < \varepsilon[/tex]

In order to ensure this inequality, we work backwards to find N in terms of ε :

[tex]\left| \dfrac{5n-1}{n+1} - 5 \right| = \left| \dfrac{5n-1 - 5(n+1)}{n+1} \right| = \dfrac4{|n+1|} < \varepsilon[/tex]

n is a natural number, so n + 1 > 0 and |n + 1| = n + 1. Then

[tex]\dfrac4{n+1} < \varepsilon \implies \dfrac{n+1}4 > \dfrac1\varepsilon \implies n+1 > \dfrac4\varepsilon \implies n > \dfrac4\varepsilon - 1[/tex]

Let N be the smallest natural number greater than or equal to 4/ε - 1, i.e.

[tex]N = \left\lceil \dfrac4\varepsilon - 1 \right\rceil[/tex]

Then the proof follows: suppose

[tex]n \ge N = \left\lceil \dfrac4\varepsilon - 1 \right\rceil[/tex]

Then

[tex]n \ge \left\lceil\dfrac4\varepsilon - 1\right\rceil \implies n > \dfrac4\varepsilon - 1 \\\\ \implies n+1 > \dfrac4\varepsilon \\\\ \implies \dfrac4{n+1} < \varepsilon \\\\\implies \left|\dfrac{5n-1}{n+1}-5\right| < \varepsilon[/tex]

as required.

Or we can avoid the rigor and use some facts we know about limits:

[tex]\displaystyle \lim_{n\to\infty} \frac{5n-1}{n+1} = \lim_{n\to\infty} \frac{5-\frac1n}{1+\frac1n} = 5[/tex]

since 1/n converges to 0 as n goes to ∞.

The volume of the cone that has a radius of 8 in. and a height of 10.5 in. is: 703.7 in.³

Volume = 1/3πr²h

Given the parameters:

Volume of the cone = 1/3πr²h = 1/3π(8²)(10.5)

Volume of the cone = 1/3π(64)(10.5)

Volume of the cone = 703.7 in.³

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Answer:

224Pi inches cubed

Step-by-step explanation:

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[tex]\diamond\large\textsf{\textbf{\underline{Question:-}}}[/tex]

          ✥ 19 more than the number c is 4.

[tex]\diamond[/tex] [tex]\large\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]

◆ First, the word "more" indicates that we add.

Here we have 19 more than c, so we add c plus 19, which looks as follows:-

 ✳︎ [tex]\sf{19+c}[/tex]

This expression is equal to 4:-

✳︎[tex]\sf{19+c=4}[/tex]

If you also need to find c, subtract 19 on both sides:-

So we conclude that the value of c is -15.

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Answer:

19 + c = 4

Step-by-step explanation:

Given:

We know that:

Therefore, we can make the following replacements:

When we replace the bolded text in the statement, we get;

⇒ 19 more than the number c is 4

⇒ 19 more than the number c is 4                       ["19" ⇒ "19"]

⇒ 19 + than the number c is 4                            ["more" ⇒ "+"]

⇒ 19 + c is 4                                             ["than the number c" ⇒ "c"]

⇒ 19 + c = 4                                                            ["is" ⇒ "="]

⇒ 19 + c = 4                                                            ["4" ⇒ "4"]

Thus, the expression/equation that represents the statement is [tex]\small\text{19 + c = 4.}[/tex]

For the horizontal segment, the value of the ordinate will not change. Then the second point will be (x, 3.5).

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

The point is given as (3, 3.5).

Then name a second point so that the two points form a horizontal segment.

For the horizontal segment, the value of the ordinate will not change.

Let x be the abscissa.

Then the point will be given as (x, 3.5).

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