A ladder that is 6 meters long leans
against a building. The base of the
ladder is 1.5 meters from the base
of the building. To the nearest
hundredth of a meter, how far up
the building does the ladder reach?

Answer:

70

Step-by-step explanation:

Answer:

[tex]Q_3 = 56.45[/tex] --- The third quartile

[tex]Var = 370.18[/tex] -- Variance

Step-by-step explanation:

Given

[tex]Q_1 = 30.8[/tex] -- First quartile

[tex]Q_2 = 48.5[/tex] --- Median

[tex]\bar x = 42[/tex] --- Mean

[tex]Skp = -0.38[/tex] --- Coefficient of skewness

Solving (9): The third quartile [tex]Q_3[/tex]

This is calculated from

[tex]Skp = \frac{Q_1 + Q_3 - 2Q_2}{Q_3 - Q_1}[/tex]

So, we have:

[tex]-0.38 = \frac{30.8 + Q_3- 2*48.5}{Q_3 - 30.8}[/tex]

Cross Multiply

[tex]-0.38 (Q_3 - 30.8)= 30.8 + Q_3- 2*48.5[/tex]

Open bracket

[tex]-0.38Q_3 + 11.704= 30.8 + Q_3- 97.0[/tex]

Collect like terms

[tex]-0.38Q_3 -Q_3= 30.8 - 97.0- 11.704[/tex]

[tex]-1.38Q_3= -77.904[/tex]

Divide both sides -1.38

[tex]Q_3 = \frac{-77.904}{-1.38}[/tex]

[tex]Q_3 = 56.45[/tex] --- approximated

Solving (b): The variance

First, calculate the standard deviation from:

[tex]3IQR = 4SD[/tex]

[tex]IQR= Q_3 - Q_1[/tex]

So:

[tex]3IQR = 4SD[/tex]

[tex]3(Q_3 - Q_1) = 4SD[/tex]

Make SD the subject

[tex]SD = \frac{3}{4}(Q_3 - Q_1)[/tex]

[tex]SD = \frac{3}{4}(56.45 - 30.8)[/tex]

[tex]SD = \frac{3}{4}*25.65[/tex]

[tex]SD = \frac{3*25.65}{4}[/tex]

[tex]SD = \frac{76.95}{4}[/tex]

[tex]SD = 19.24[/tex]

So, the variance is:

[tex]Var = SD^2[/tex]

[tex]Var = 19.24^2[/tex]

[tex]Var = 370.18[/tex]

Answer:

The missing figure is 26 cm.

Step-by-step explanation:

The Pythagorean theorem consists of a formula [tex]a^2+b^2=c^2[/tex]

Therefore, the missing figure is 26 cm.

Answer:

It would cost $21.30 for Robert to buy 6 notebooks.

Step-by-step explanation:

find cost for each notebook:

28.40 ÷ 8 = 3.55

multiply by 6:

3.55 x 6 = 21.3

Hope this helped!

Answer:

a) 0.8

b) 0.3

c) 0.9

d) 0.95

Step-by-step explanation:

A probability always adds up to 1. It is between the scale of 0 (never likely) to 1 (very likely).

So:

1 - 0.2 = 0.8

1 - 0.7 = 0.3

1 - 0.1 = 0.9

1 - 0.05 = 0.95

Hope this helped!

Answer:

[tex] {x}^{0} y + 9 \\ = y + 9[/tex]

Answer:

Step-by-step explanation:

Full surface area:

Answer:

Surface Area = Surface Area of triangle + SA of rectangle

Surface Area = 3 × (6 × 10) + 2 × ½ × 8 × 10

Surface Area = 3 × 60 + 80

Surface Area = 180 + 80

Surface Area = 260 cm ³

[tex] \\ [/tex]

Answer:

t ≤ 210°

Step-by-step explanation:

If the temperature of the water in a coffeepot does not exceed 210°, this means that the temperature cannot be more than 210° and the required inequality sign that fits is ≤ (less than or equal to).

Since t is the temperature of the water in the coffeepot, the required inequality expression will be t ≤ 210°

Answer:

114

Step-by-step explanation:

12% of 950 is 114, so since 12% more donuts are sold this week, we sold 114 more donuts this week compared to last week.

Answer:

0.27 repeating.

Step-by-step explanation:

So to solve this we just have to use division.

1 clearly doesnt go into 3 at least one time, so we can add a decimal point and add a 0 to make it 30.

11 goes into 30 2 times, so we have:

0.2

and 30-22=8

So we can add another 0 and make it 80.

Then 11 goes into 80 7 times. So we have:

0.27

and 80-77=3

So again, add the 0, we have 30.

11 goes into 30 2 times, so:

0.272

and 30-22=8

Add another 0 we get 80.

11 goes into 80 7 times.

So finally, we have:

0.2727.

This is a repeating decimal.

This can be shown as:

0.27

So this is your answer!

I was a bit confused with which one it was on your answer key, but knowing that it is 0.27 I am guessing you can chose!

Hope this helps!

Answer:

7 gallons per minute.

Step-by-step explanation:

42 / 6 = 7

Answer:

7 gallons per minute.

Step-by-step explanation:

42 divided by  6 = 7

and if you multiply 6 and 7 you will get 42

Answer:

11/16

Step-by-step explanation:

9+2+5=16

9+2=11

11/16

Answer:

You use ratios to determine, so to find blue crayons it will be 16/2 chance of finding a blue crayon since there are 16 crayons and 2 blue crayons, and simplified it will be 8/1, you can find out the red crayon also by doing the same thing, since you are trying to get a red or blue crayon it will be 11/16 chance of finding a blue or red crayon.

Answer:

4/5

Step-by-step explanation:

for this problem you just add across so it would be 2+2= 4 but you don't add 5+5 because their the same number

Answer:

130 miles

Step-by-step explanation:

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

Actual distance = 31/4 x 40

convert 31/4 to an improper fraction

to convert to improper fraction, take the following steps :  

1. Multiply the whole number  by the denominator

2. Add the numerator to the answer gotten in the previous step

3. divide the number gotten in the previous step by the denominator  

13/4 x 40 = 130 miles

Answer:

0 remainder 19

Step-by-step explanation:

Answer:

1272.3 yd^3

Step-by-step explanation:

Radius = 9 yd

V = radius^2 x pI x height = 9^2 x 3,14 x 5 = 1272.3 yd^3

Answer:

D. 3.7 × 10⁶

Step-by-step explanation:

3.7 × 10⁶

3700000

Answer:

a) 2nd quadrant

b) 3rd quadrant

c) 2nd quadrant

d) 1st quadrant

Step-by-step explanation:

When we talk about ordinate, we mean the y axis value

abscissa is the x axis value

There are four quadrants with the following distribution of signs;

1st quadrant: positive x and positive y

2nd quadrant: negative x and positive y

3rd quadrant; negative x and negative y

4th quadrant ; positive x and negative y

a) (-3,5)

negative x and positive y; this is the 2nd quadrant

b) (-5,-3)

Negative x and negative y, this is the 3rd quadrant

c) (-5 , 3)

Negative x and positive y; 2nd quadrant

d) (5,3)

Positive x and positive y; 1st quadrant

Cubcivtiv tyk ok givyog Answer: gg

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

[tex]x^2 = 8^2 + 6^2\\x^2 = 64 + 36 = 100\\x = \sqrt{100} = 10[/tex]

Answer:

B

Step-by-step explanation:

∠ 3 and ∠ 8 are alternate angles and are congruent, then

6x + 3 = 4x + 29 ( subtract 4x from both sides )

2x + 3 = 29 ( subtract 3 from both sides )

2x = 26 ( divide both sides by 2 )

x = 13 → B

Answer:

x<6

Step-by-step explanation:

4x-36<-12

Add 36 to each side

4x-36+36<-12+36

4x < 24

Divide each side by 4

4x/4 < 24/4

x<6

Answer:

x<6

Step-by-step explanation:

Reverse order of operations SADMEP

4x<24 (add 36 to both sides)

x<6 (divide both sides by 4)

Answer:

-2x =-42+12

-2x =-30

x =15

3x=15×3

=45

Answer:

3.25"

Step-by-step explanation:

If the scale is 1/8, then the model or drawing has lengths which are 1/8 of the objects lengths.

Find 1/8 of 26.

[tex]26 \times \frac{1}{8} = \frac{26}{8}= 3.25[/tex]

Answer:

f(x) = - 2(x - 3)² + 2

Step-by-step explanation:

Given

f(x) = - 2x² + 12x - 16 ( factor out - 2 from the first 2 terms )

      = - 2(x² - 6x) - 16

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² - 6x

f(x) = - 2(x² + 2(- 3)x + 9 - 9) - 16

     = - 2(x - 3)² + 18 - 16

     = - 2(x - 3)² + 2

Step-by-step explanation:

Let b is breadth and l is length of the cuboid such that,

Length, l = 3b and l = 2h

or

h = l/2

We know that, the volume of a cuboid box is given by :

V = lbh

Put all the values,

[tex]V=l\times \dfrac{l}{3}\times \dfrac{l}{2}\\\\750=l\times \dfrac{l}{3}\times \dfrac{l}{2}\\\\750\times 6=l^3\\\\l=(750\times 6)^{1/3}\\\\l=16.5\ cm[/tex]

Breadth, b = 16.5/3 = 5.5 cm

Height, h = 16.5/2 = 8.25 cm

Hence, this is the required solution.

Answer:

[tex]y=(x-3)^2-7[/tex]

Minimum

(-3,-7)

Step-by-step explanation:

[tex]y=x^2 -6x+2[/tex]

[tex]b=-6[/tex]

[tex]\frac{b}{2} =(-3)^2=9[/tex]

[tex]y+7=x^2-6x+9[/tex]

[tex]y=(x-3)^2-7[/tex]

-7 is a minimum.

Answer:

a is correct and b is incorrect