Solve the system of equations.
12x-5y = -20
y =x+4

Answer:

[tex]Median = 90.4[/tex]

[tex]Q_1 = 88.6[/tex]

[tex]Q_3 = 92.2[/tex]

Step-by-step explanation:

Given

The above data

Required

- A stem and leaf display

- The median

- The quartiles

First, determine the range of the data

[tex]Smallest = 83.4[/tex]

[tex]Highest = 100.3[/tex]

Next, group each dataset base on common whole numbers.

So, we have:

[tex]83.4[/tex]

[tex]84.3\ 84.3[/tex]

[tex]85.3[/tex]

[tex]86.7\ 86.7\ 86.7[/tex]

[tex]87.4\ 87.5\ 87.6\ 87.7\ 87.8\ 87.9[/tex]

[tex]88.2\ 88.3\ 88.3\ 88.3\ 88.4\ 88.5\ 88.5\ 88.6\ 88.6\ 88.7\ 88.9[/tex]

[tex]89.0\ 89.2\ 89.3\ 89.3\ 89.6\ 89.7\ 89.8\ 89.8\ 89.9\ 89.9[/tex]

[tex]90.0\ 90.1\ 90.1\ 90.1\ 90.3\ 90.4\ 90.4\ 90.4\ 90.5\ 90.6\ 90.7\ 90.8\ 90.9[/tex]

[tex]91.0\ 91.0\ 91.0\ 91.1\ 91.1\ 91.1\ 91.2\ 91.2\ 91.2\ \ 91.5\ 91.6\ 91.6\ 91.8\ 91.8[/tex]

[tex]92.2\ 92.2\ 92.2\ 92.3\ 92.6\ 92.7\ 92.7\ 92.7[/tex]

[tex]93.0\ 93.2\ 93.3\ 93.3\ 93.4\ 93.7[/tex]

[tex]94.2\ 94.2\ 94.4\ 94.7[/tex]

[tex]96.1\ 96.5[/tex]

[tex]98.8[/tex]

[tex]100.3[/tex]

Next, we construct the stem and leaf plot.

The whole numbers will be the stem while the decimal parts will be the leaf.

So, we have:

[tex]\begin{array}{ccc}{Stem} & {} & {Leaf} & {83} & {|} & {.4} & {84} & {|} & {.3\ .3} & {85} & {|} & {.3} & {86} & {|} & {.7\ .7\ .7} & {87} &{|} & {.4\ .5\ .6\ .7\ .8\ .9} & {88} & {|} & {.2\ .3\ .3\ .3\ .4\ .5\ .5\ .6\ .6\ .7\ .9} &{89} & {|} & {.0\ .2\ .3\ .3\ .6\ .7\ .8\ .8\ .9\ .9} & {90} & {|} &{.0\ .1\ .1\ .1\ .3\ .4\ .4\ .4\ .5\ .6\ .7\ .8\ .9} & {91} &{|}&{.0\ .0\ .0\ .1\ .1\ .1\ .2\ .2\ .2\ .5\ .6\ .6\ .8\ .8} &{92} &{|} &{.2\ .2\ .2\ .3\ .6\ .7\ .7\ .7} \ \end{array}[/tex]

  [tex]\begin{array}{ccc} {93} & {|} & {.0\ .2\ .3\ .3\ .4\ .7} & {94} &{|} & {.2\ .2\ .4\ .7} &{96} & {|} & {.1\ .5} & {98} & {|} & {.8} & {100} &{|} &{.3} \ \end{array}[/tex]

From the above plot,

[tex]n = 83[/tex]

The median is calculated as:

[tex]Median = \frac{n+1}{2}th[/tex]

[tex]Median = \frac{83+1}{2}th[/tex]

[tex]Median = \frac{84}{2}th[/tex]

[tex]Median = 42nd[/tex]

i.e. the median is at the 42nd position.

From the above stem and leaf plot.

The 42nd position is at stem 90 and the leaf  .4

So the median is:

[tex]Median = 90.4[/tex]

The lower quartile (Q) is calculated as:

[tex]Q_1 = \frac{n+1}{4}th[/tex]

[tex]Q_1 = \frac{83+1}{4}th[/tex]

[tex]Q_1 = \frac{84}{4}th[/tex]

[tex]Q_1 = 21st[/tex]

i.e. the lower quartile is at the 21st position.

From the above stem and leaf plot.

The 42nd position is at stem 88 and the leaf .6

So the lower quartile is:

[tex]Q_1 = 88.6[/tex]

The upper quartile (Q3) is calculated as:

[tex]Q_3 = 3 * \frac{n+1}{4}th[/tex]

[tex]Q_3 = 3 * \frac{83+1}{4}th[/tex]

[tex]Q_3 = 3 * \frac{84}{4}th[/tex]

[tex]Q_3 = 3 * 21th[/tex]

[tex]Q_3 = 63rd[/tex]

i.e. the upper quartile is at the 63rd position.

From the above stem and leaf plot.

The 63rd position is at stem 92 and the leaf .2

So the upper quartile is:

[tex]Q_3 = 92.2[/tex]

Answer:

great job

Step-by-step explanation:

Answer:

A and D

Step-by-step explanation:

for infinitely many solutions, ratio of coefficients should be equal.

since ratio = 1/4 so they will have infinitely many solutions.

Answer:

[tex]4x^{2}[/tex]

Step-by-step explanation:

Answer:

4[tex]x^{2}[/tex]

Step-by-step explanation:

Apply the product rule to 2x.

[tex]2^{2}[/tex] [tex]x^{2}[/tex]

Raise 2 to the power of 2.

[tex]4x^{2}[/tex]

Answer:

A.

1. No

2. Yes, 6*6=36

3. Yes, 7*7=49

4. No

5. Yes, 11*11=121

6. Yes, 13*13=169

7. Yes, 20*20=400

8. No

B.

1. 8

2. 10

3. 9

4. 4

5. 2

6. 0

7. 5

8. 12

C.

1. 11.4

2. 2.8

3. 9.2

4. 6.3

5. 4.9

6. 10.5

D.

1. rational

2. rational

3. irrational

4. rational

5. irrational

6. irrational

7. rational

8. rational

9. rational

10. rational

11. irrational

12. irrational?

Answer:

A1. No (4 more than 4²)

A2. Yes - 6 * 6 = 36

A3. Yes - 7 * 7 = 49

A4. No (4 more than 8²)

A5. Yes - 11 * 11 = 121

A6. Yes - 13 * 13 = 169

A7. Yes - 20 * 20 = 400

A8. No (6 more than 12²)

B1. 8

B2. 10

B3. 9

B4. 4

B5. 2

B6. 0

B7. 5

B8. 4

C1. 11.4

C2. 2.8

C3. 9.2

C4. 6.3

C5. 4.9

C6. 10.5

D1. Rational

D2. Rational

D3. Irrational (closest rational (2 decimal places) is -1.41)

D4. Rational

D5. Irrational (closest rational (2 decimal places) is 2.23)

D6. Irrational (closest rational (2 decimal places) is 3.14)

D7. Rational

D8. Rational (simplifies to 4)

D9. Rational

D10. Rational (same as 0.75)

D11. Irrational (because of the dots)

D12. Rational (5/13 pattern goes like this: 384615)

Answer:

Hi there your question was a little confusing

well I'm using a formula this [tex]X=\sqrt{Y}[/tex]

Hope this helps :)

Step-by-step explanation:

Answer:

[tex] \huge\green{ \mid{ \underline{ \overline{ \tt ♡ ANSWER ♡ }} \mid}}[/tex]

There's no specific formula to find the square root of a number, however we can find the square root of a number by the following methods:

i) By Prime Factorisation

ii) By Long Division

iii) By Repeated subtraction method

Step I: Obtain the given number.

Step II: Reduce the given number into prime factors by successive division.

Step III: Now make pairs of prime factors in such a way that both the factors in each pair are equal.

Step IV: Take one factor from each pair and find the product of these factors.

Step V: The product obtained by multiplying the factors is the required square root.

Step 1: Firstly, we place a bar on every pair of digits starting from the unit digit. If the number of digits in it is odd, we put a bar on the single-digit too.

Step 2: Now we find the largest number whose square is less than or equal to the 1st number.

Step 3: Now we bring down the next bar number.

Step 4: For new divisor, we add the divisor & quotient.

Step 5: Number taken is the product of a new divisor and this digit is equal to or less than the new dividend.

In this method, the given number is subtracted by 1, 3, 5, 7,… at every step till you get zero at the end. The number of steps in the solution is the required square root.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

Answer:

the perimeter is 30ft

Step-by-step explanation:

a square + b square = c square

so first we find your missing side

this is how we solve for that:

a square + 12 squared = 13 squared

a squared + 144 = 169

now we do 169 - 144 = 25

now to find the missing side it is 25 square root which is 5

now that we have found the missing side lengths let's find the perimeter which is: 5 + 12 + 13 = 30 ft

I hope this helped!

Answer:

115000

Step-by-step explanation:

25000 x .12 = 3000

3000 x 30 = 90000

90000 + 25000 = 115000

Answer:

0.155litre

Step-by-step explanation:

55+25+40+35=155cm

100Cm=1litre

155cm_ ?

155cm×1litre/1000cm

0.155Litre

Answer:

x≤-8

Step-by-step explanation:

Answer:

x ≤ -8

Step-by-step explanation:

Good Luck!

Answer:

7200

Step-by-step explanation:

80*90=7200

Answer:

7,200 paper clips

Step-by-step explanation:

80*90=7,200

Answer:

7 yd^3

Step-by-step explanation:

The Volume is:

V=a*b*c

a=7*(1/3) yd

b=3*(1/3) yd

c=9*(1/3) yd

So, V=7 yd^3

Answer:

Step-by-step explanation:

We see 75% of data lies in the interval 0 - 48, and the 120 is the outlier.

We wouldn't use the range as it won't be a representation of variability.

The best measure would be IQR:

Correct choice is C.

Answer:

19.44 (I think)

Step-by-step explanation:

Answer:

1436.03 m³

Step-by-step explanation:

The formula of volume of sphere

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

The volume of the sphere

[tex] = \frac{4}{3} \times 3.14 \times {(14 \div 2)}^{3} [/tex]

[tex] = \frac{4}{3} \times 3.14 \times {7}^{3} [/tex]

[tex] = \frac{4308.08}{3} [/tex]

[tex] = 1436.0266667...[/tex]

= 1436.03 m³ (rounded to the nearest hundredth)

Answer:

13.93

Step-by-step explanation:

use the Pythagorean theorem

Answer:

f(X)=2x+3

Step-by-step explanation:

f(4) = 2*4 + 3

= 8 + 3

= 11

Answer and Step-by-step explanation:

For this function, we need to plug in 4 for x to find out what the value of f(x) is when x is equal to 4.

f(4) = 2(4) + 3

= 8 + 3

= 11

The answer is 11, when the value is f(4).

#teamtrees #PAW (Plant And Water)

Answer:

Value is 2

Step-by-step explanation:

f(3)= 1/4 x  2^(3)      ------- 2 x 2 x 2= 8

1/4 x 8    = 8/4 = 2

Answer:

h=13

Step-by-step explanation:

volume=w*h*l

312=(4)(6)(X)

Answer:

3cm

Step-by-step explanation:

The formula for the volume of the cuboid is [tex]w*l*h=volume[/tex]

We already have the length, width, and volume, so we have to plug it in to the equation.

[tex]15*10*h=450[/tex] (Just a heads up in case you didn't know: the centimeters cubed is just part of the units, so you don't need to worry about it when plugging it in to the equation.)

To solve for h:

1. Multiply 15 and 10

[tex]150*h=450[/tex]

2. Divide both sides by 150

[tex]h = 450/150[/tex]

h = 3

This is in centimeters, so the final answer is 3cm.

The height of a cuboid with a volume of 450cm³ with a length of 10cm and width of 15cm is 3cm.

The volume of a cuboid can be calculated using the following formula:

Volume = length × width × height

According to this question, the volume of a cuboid is 450cm³ and has a length of 10cm and the width is 15cm. The height is as follows:

450cm³ = 15cm × 10cm × h

450cm³ = 150²h

h = 450/150

h = 3

Therefore, the height of a cuboid with a volume of 450cm³ with a length of 10cm and width of 15cm is 3cm.

Learn more about height at: https://brainly.com/question/1578538

Answer:

I'm not sure if it is the correct answer but I believe it is 14

Answer:

14 i think

Step-by-step explanation:

Answer:

y = -2x + 4

Step-by-step explanation:

To write an equation in slope-intercept form, y = mx + b, we need to find the slope (m) and the y-intercept (b).

✔️Slope (m) using two pairs of values, (0, 4) and (1, 2):

Slope (m) = change in y/change in x

m = (2 - 4)/(1 - 0) = -2/1

m = -2

✔️y-intercept is the value of y when x = 0. Therefore, fromm the table, when x = 0, y = 4.

y-intercept (b) = 4

✅Write the equation by substituting m = -2 and b = 4 into y = mx + b:

Thus,

y = -2x + 4

Answer:

3

Step-by-step explanation:

For x<=0, f is constant: f(x) =3

-4<0, so f(-4)=3

Answer:

c

Step-by-step explanation:

c is the only one containing the number three, which is shown on the graph.

Answer:

[tex]M(y)=10y+10[/tex]

Step-by-step explanation:

Answer:

D. 1.5

Step-by-step explanation:

The median number of excused absences from given data is 1.5.

We have given that,

The dot plot below shows the number of excused absences students in Mr. Beckett's class have.

We have to determine the median

The median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as the middle value.

Therefore the median number of excused absences from given data is 1.5.

Therefore option D is correct.

To learn more about the median visit:

https://brainly.com/question/26151333

#SPJ2

Answer:

x=4√−0.45068027,−4√0.45068027

Step-by-step explanation:

Answer:

None

See below under Remark.

Step-by-step explanation:

When you shift left, you think of moving in the negative direction. But it is not shown that way. You need to show what happens when you substitute a value in for x. Usually a graphing program helps to show which choice is right.

g(x) = f(x+4) = 2(x + 4)

None of the choices are this result, so we have to assume that the brackets were just omitted.  The graph below shows what the answer given is the correct one.

Remark

Look at the graph carefully. The red line is f(x) = 2x

The blue line is g(x) = f(x-4) = 2(x - 4)

Notice that g(x) has shifted 4 units to the left. The x intercept has gone from 0,0 to (-4,0) and is so labeled.

If you have an answer with brackets around (x + 4) that's the one you choose. It needs the 2 outside the brackets.