What is the volume of the cube

9514 1404 393

Answer:

  (√17 -4√595)/102

Step-by-step explanation:

To use the sine of the angle sum formula, we need to know the sine and cosine of each of the angles.

  sin(sin^-1(1/6)) = 1/6 . . . . a first-quadrant angle

  cos(sin^-1(1/6)) = √(1 -(1/6)²) = √(35/36) = (√35)/6

  sin(tan^-1(-4)) = -4/√(1+(-4)²) = -4/√17 . . . . a 4th-quadrant angle

  cos(tan^-1(-4)) = √(1 -(-4/√17)²) = 1/√17

The sum of angles formula is ...

  sin(α+β) = sin(α)cos(β) +cos(α)sin(β)

So, our sine is ...

  [tex]\sin\left(\sin^{-1}\left(\dfrac{1}{6}\right)+\tan^{-1}(-4)\right)=\dfrac{1}{6}\cdot\dfrac{1}{\sqrt{17}}+\dfrac{\sqrt{35}}{6}\cdot\dfrac{-4}{\sqrt{17}}\\\\=\dfrac{1-4\sqrt{35}}{6\sqrt{17}}=\boxed{\dfrac{\sqrt{17}-4\sqrt{595}}{102}}[/tex]

Answer:

484 students

Step-by-step explanation:

This is simple probability. Assuming 22/80 students walk to school within a small population, and there are 1760 students at the school, there should be (22/80)*1760 students that walk to school in total. (This is just theoretical). This is 484 students.

The number of students who usually walk to school will be 484 students.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Alexis surveys a random sample of 80 students at his school and finds that 22 of them usually walk to school.

Then the number of students who usually walk to school will be

⇒ 22 / 80

⇒ 11 / 40

We know that the ratio will remain the same.

There are 1,760 students at the school.

Let x be the number of students who usually walk to school.

Then the number of students who usually walk to school will be

x / 1760 = 11 / 40

x = 484 students

Thus, the number of students who usually walk to school will be 484 students.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

#SPJ5

Answer:

I'm not 100% sure but I think its B. 1> -18

Answer:

After four years the house was worth $128,891.03

Step-by-step explanation:

170828(x)^12 = 73828

solve for x

x = 0.932 (House depreciates by 6.8% yearly)

plug in x and change into function and substitute 4 for 12 because it's 4 years

170828(0.932)^4

128891.0334

Answer:

Match the packaging type with the number of seedlings it contains.

gerbera daisy cell pack

gerbera daisy flat

standard flat

standard cell pack

Step-by-step explanation:

Answer:

A is the answer

Step-by-step explanation:

Answer:

Option C and D!

Step-by-step explanation:

When 9 is placed in the box after 7, we get:-

7 ÷ 9 = [tex]\frac{7}{9}[/tex] which is correct!

7 ÷ 9 can also be written as [tex]\frac{7}{9}[/tex]. So, this Option is right since the equation is correct when 9 is placed in the box!

When we place 9 in the box before [tex]\frac{1}{9}[/tex], we get:-

9 ÷ [tex]\frac{1}{9}[/tex] = 81

9 ÷ [tex]\frac{1}{9}[/tex]  equals 9 x 9 (take the reciprocal of [tex]\frac{1}{9}[/tex])

9 x 9 equals 81 which means the equation is correct when 9 is placed in the box!

Answer:

1109.1cm³

Step-by-step explanation:

V

=

π

r

2

h

3

3.14 ×8.7² × 14/3

Answer:

yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

The histogram shows the distribution of the newly planted trees

The dataset is given as:

3.2, 4.3, 3.5, 5.4, 3.7, 5.5, 6.2, 3.1, 6.8, 7.1, 4.8, 6.5, 4.9, 5.3, 5.9

Sort the data elements

3.1, 3.2, 3.5, 3.7, 4.3, 4.8, 4.9, 5.3, 5.4, 5.5, 5.9, 6.2, 6.5, 6.8, 7.1

Calculate the range

Range = Highest - Least

This gives

Range = 7.1 - 3.1

Range = 4

Divide by 4 to calculate the class width

Width = 4/4

Width = 1

So, the classes and the frequencies are:

Class               Frequency

3.1 - 4.0              4

4.1 - 5.0              3

5.1 - 6.0             4

6.1 - 7.0              3

7.1 - 8.0              1

See attachment for the histogram

Read more about histograms at:

https://brainly.com/question/18198700

Answer: 10 groups

Step-by-step explanation:

Since we know she is making a group of 7 sheep, we can do 37-7 to get 30 sheep left

If she wants to find how many groups she can make we have to do 30/3 which gets us to 10 which is the number of groups she can do

I hope this helps

Answer:

B) (-6,9)

Step-by-step explanation:

since it's reflecting on the x-axis, the x is gonna stay the same. the y changes though. opposite of -9 is 9.

hope this helps <3

Answer:

B, (-6, 9)

Step-by-step explanation:

this is because it's like as if it was a mirror, so that is the correct answer

48kg200g....…........

Answer:

(6*1000)g+25g=6025g

6025g*8=48200g

48kg200g. {:1000g=1kg}

Answer:

1/4

Step-by-step explanation:

To find probability, multiply the probability of one roll times the probability of the second roll.

A die usually have 6 numbers so ill assume it has that.

1/2 or 3/6 of the sides are odd. So multiply 1/2*1/2 to get 1/4.

Me either ive been stuck on a question and no one will help me

Answer:

me three

Step-by-step explanation:

you guys are awesome

Answer:

y = –5x + 5

Step-by-step explanation:

Answer:

2 1/6 ft

Step-by-step explanation:

This problem bothers on subtraction of fraction

Given data

Total length of rope 3 1/2 feet

Let's convert mixed fraction to proper fraction = 7/2ft

First piece of rope = 1 1/3ft

= 4/3ft

Hence the second piece of the rope is = 7/2-4/3= 21-8/6= 13/6

Second piece = 2 1/6 ft

Answer:

2/7

Step-by-step explanation:

There are 14 fish and 4 of them are small, red ones.

P(small red fish) = 4/14 = 2/7

Answer:

False

x=8-10=-2

Step-by-step explanation:

[tex]10 = x - 8 \\ ➡ \: x = 10 + 8 \\ ➡ \: x = 18[/tex]

[tex]\sf\red{The\:value\:of\:x\:is\:18.\:}[/tex]

[tex]\sf\pink{Hence,\:it\:is\:false.}[/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Answer. i cant answer this without a pic of the slope

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

Answer:

3:7

Step-by-step explanation:

15-8=7 green skateboards

3:7

Answer:

$1200.50

plug 5 for n

5000(.7)^4

5000*.2401

=1200.5

Answer:

the answer is b. the segment has a length of 8 units vertical.

Step-by-step explanation:

Answer:

A= ( 5 x 3 ) x [(9-5)x3 divided by 2]

15+6

=21

P= 5+5+3+9

=22

Answer:

its usAlly 9-5

Step-by-step explanation:

Answer:

[tex]g\ o\ f(1) = 2[/tex]

Step-by-step explanation:

Given

The attached tables

Required

[tex]g\ o\ f(1)[/tex]

This is calculated as:

[tex]g\ o\ f(1) = g(f(1))[/tex]

From the attached tables,

[tex]f(1) = 5[/tex]

So, we have:

[tex]g\ o\ f(1) = g(5)[/tex]

From the attached tables,

[tex]g(5) = 2[/tex]

So, we have:

[tex]g\ o\ f(1) = 2[/tex]

answer:

15

step-by-step explanation:

9, 10, 15, 17, 15, 14, 37, 45, 42, 13