There are 24 girls in a class. The ratio of girls to boys is 3:8.
How many boys are in the class?​

Answer:

84 cm²

Step-by-step explanation:

3 x 4 x 0.5 = 6

3 x 4 x 0.5 = 6

3x 6 = 18

5 x 6 = 30

4 x 6 = 24

add up = 84

Answer:

336 cm²

Step-by-step explanation:

rectangle area:

b×h = 24×7,5=180 cm²

" " = 6,5×24=156 cm²

total area: 180+156=336 cm²

Answer:

71

Step-by-step explanation:

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Answer:

[tex] \rm\displaystyle \displaystyle \displaystyle θ= {60}^{ \circ} , {300}^{ \circ} [/tex]

[tex] \rm \displaystyle a = - \frac{ \sqrt{3} }{2} - 1, \frac{\sqrt{3}}{2} - 1[/tex]

Step-by-step explanation:

we are given two coincident points

[tex] \displaystyle P( \sin(θ)+2, \tan(θ)-2) \: \text{and } \\ \displaystyle Q(4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2a \cos(θ), 3 \sin(θ)-2 \cos(θ)+a)[/tex]

since they are coincident points

[tex] \rm \displaystyle P( \sin(θ)+2, \tan(θ)-2) = \displaystyle Q(4 \sin ^{2} (θ)+4 \sin(θ )\cos(θ)+2a \cos(θ), 3 \sin(θ)-2 \cos(θ)+a)[/tex]

By order pair we obtain:

[tex] \begin{cases} \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2a \cos(θ) = \sin( \theta) + 2 \\ \\ \displaystyle 3 \sin( \theta) - 2 \cos( \theta) + a = \tan( \theta) - 2\end{cases}[/tex]

now we end up with a simultaneous equation as we have two variables

to figure out the simultaneous equation we can consider using substitution method

to do so, make a the subject of the equation.therefore from the second equation we acquire:

[tex] \begin{cases} \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sinθ \cos(θ)+2a \cos(θ )= \sin( \theta) + 2 \\ \\ \boxed{\displaystyle a = \tan( \theta) - 2 - 3 \sin( \theta) + 2 \cos( \theta) } \end{cases}[/tex]

now substitute:

[tex] \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2 \cos(θ) \{\tan( \theta) - 2 - 3 \sin( \theta) + 2 \cos( \theta) \}= \sin( \theta) + 2 [/tex]

distribute:

[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ)+4 \sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) - 6 \sin( \theta) \cos( \theta) + 4 \cos ^{2} ( \theta) = \sin( \theta) + 2 [/tex]

collect like terms:

[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ) - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) + 4 \cos ^{2} ( \theta) = \sin( \theta) + 2 [/tex]

rearrange:

[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ) + 4 \cos ^{2} ( \theta) - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) + = \sin( \theta) + 2 [/tex]

by Pythagorean theorem we obtain:

[tex]\rm\displaystyle \displaystyle 4 - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) = \sin( \theta) + 2 [/tex]

cancel 4 from both sides:

[tex]\rm\displaystyle \displaystyle - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) = \sin( \theta) - 2[/tex]

move right hand side expression to left hand side and change its sign:

[tex]\rm\displaystyle \displaystyle - 2\sin(θ) \cos(θ)+\sin(θ ) - 4\cos( \theta) + 2 = 0[/tex]

factor out sin:

[tex]\rm\displaystyle \displaystyle \sin (θ) (- 2 \cos(θ)+1) - 4\cos( \theta) + 2 = 0[/tex]

factor out 2:

[tex]\rm\displaystyle \displaystyle \sin (θ) (- 2 \cos(θ)+1) + 2(- 2\cos( \theta) + 1 ) = 0[/tex]

group:

[tex]\rm\displaystyle \displaystyle ( \sin (θ) + 2)(- 2 \cos(θ)+1) = 0[/tex]

factor out -1:

[tex]\rm\displaystyle \displaystyle - ( \sin (θ) + 2)(2 \cos(θ) - 1) = 0[/tex]

divide both sides by -1:

[tex]\rm\displaystyle \displaystyle ( \sin (θ) + 2)(2 \cos(θ) - 1) = 0[/tex]

by Zero product property we acquire:

[tex] \begin{cases}\rm\displaystyle \displaystyle \sin (θ) + 2 = 0 \\ \displaystyle2 \cos(θ) - 1= 0 \end{cases}[/tex]

cancel 2 from the first equation and add 1 to the second equation since -1≤sinθ≤1 the first equation is false for any value of theta

[tex] \begin{cases}\rm\displaystyle \displaystyle \sin (θ) \neq - 2 \\ \displaystyle2 \cos(θ) = 1\end{cases}[/tex]

divide both sides by 2:

[tex] \rm\displaystyle \displaystyle \displaystyle \cos(θ) = \frac{1}{2}[/tex]

by unit circle we get:

[tex] \rm\displaystyle \displaystyle \displaystyle θ= {60}^{ \circ} , {300}^{ \circ} [/tex]

so when θ is 60° a is:

[tex] \rm \displaystyle a = \tan( {60}^{ \circ} ) - 2 - 3 \sin( {60}^{ \circ} ) + 2 \cos( {60}^{ \circ} ) [/tex]

recall unit circle:

[tex] \rm \displaystyle a = \sqrt{3} - 2 - \frac{ 3\sqrt{3} }{2} + 2 \cdot \frac{1}{2} [/tex]

simplify which yields:

[tex] \rm \displaystyle a = - \frac{ \sqrt{3} }{2} - 1[/tex]

when θ is 300°

[tex] \rm \displaystyle a = \tan( {300}^{ \circ} ) - 2 - 3 \sin( {300}^{ \circ} ) + 2 \cos( {300}^{ \circ} ) [/tex]

remember unit circle:

[tex] \rm \displaystyle a = - \sqrt{3} - 2 + \frac{3\sqrt{ 3} }{2} + 2 \cdot \frac{1}{2} [/tex]

simplify which yields:

[tex] \rm \displaystyle a = \frac{ \sqrt{3} }{2} - 1[/tex]

and we are done!

disclaimer: also refer the attachment I did it first before answering the question

Answer:

Taking 45 degree as reference angle

Then using sine rule

sin 45=

p/h

replacing the value of sin 45 degree by 1/root 2.so

1/root 2=9/c

doing cross multiplication

9*root 2=1*c

9 root 2 =c

therefore the value of c is 9 root 2

Step-by-step explanation:

Answer:

Hi, there the answer is Graph A because the y-intercept and I did rise over run

Step-by-step explanation:

Hope this helps :)

Answer:

B 18.79

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

8 1/3 or 8.33 yards per second

Step-by-step explanation:

100/12 = 8 1/3

Answer:

Step-by-step explanation:

y=x^2-8x+14

To write in vertex form, group the two x-terms to make a complete square, adjust the constant term accordingly

y = x^2-8x+16  -2

factor the first three terms on the right hand side

y = (x-4)^2 -2

This means that the vertex is at x-4 = 0, or x=4, and y=2.

Answer:

c

Step-by-step explanation:

Answer:

Hi! The answer to your question is the range is 23

Step-by-step explanation:

Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is 62-39=23

VOCAB:

Minumum Data = Smallest Number

Maximum Data = Largest Number

Data Range = The set of y-values that a function passes through, Also the right coordinate in a coordinate pair.

In statistics, the difference between the largest number and the smallest numbers in a data set.

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Hope this helps!!

- Brooklynn Deka

Answer:answer is 2.5v+5<5v A.k.a:A

Step-by-step explanation:

Answer:

i don't know that language sorry

Step-by-step explanation:

Answer:

[tex] \frac{108}{2 } = 54[/tex]

The value of y for the given circle will be 54°.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

The diameter is the longest line that can be drawn inside a circle.

In our daily life, we always see circle objects for example our bike wheel.

Area of circle = πr² and the perimeter of circle = 2πr where r is the radius of the circle.

In the given question by the circle theorem that if a curve makes a 2x angle then the extreme point will make the angle on circle as x.

So angle y = half of angle 108°

∠Y = 108°/2 = 54°

Angle w will also same as 54° because it also satisfies the theorem of the circle.

To learn more about the circle,

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Answer:

The angle between the two blades is 120 degree.

Step-by-step explanation:

number of blades = 3

The blades are equally spaced.

The total angle around a circle is 360 degree.

So, the angle between the two blades is given by

[tex]\theta =\frac{360}{n}\\\theta =\frac{360}{3} = 120^{o}[/tex]

Answer:

There is a little over 1 gallon

Step-by-step explanation:

Answer:

x=0, y=-2

Step-by-step explanation:

6x0=0

2(-2)=-4

so, -4=-4 so it is determined true

Then 0-2(-2), -2(-2)=4

subtract 0 from 4 which is 4

so, 4=4, so it is determined true

Answer:

C. Multiply 1st equation by 3, then add together

Step-by-step explanation:

X+y=10

3(x+y)=3(10)multiply by 3

3x+3y=30 add to following equation

2x-3y=6

5x=36

Answer:

3 * (½*2*5) = x

Step-by-step explanation:

Cost of carpeting = $3 per square foot

We have a triangular section to cover having the following dimensions:

base = 2 yd

height = 5 yd

First, let's find the area of the section = area of triangle

Area of triangle = ½*base*height

Area of the triangular section of the floor = ½*2*5

If $3 will cover 1 ft², therefore,

x will cover ½*2*5

Thus:

3 * (½*2*5) = x

Answer:

The probability that all 4 units are good is 10.66%.

Step-by-step explanation:

Given that a shipement of 14 microwave ovens contains six defective units, and a vending company has ordered 4 of these units and selection will be random, to determine what is the probability that all 4 units are good the following calculation must be performed:

14 - 6 = 8

8/14 x 8/14 x 8/14 x 8/14 = X

0.5714 x 0.5714 x 0.5714 x 0.5714 = X

0.1066 = X

0.1066 x 100 = 10.66

Therefore, the probability that all 4 units are good is 10.66%.

Answer: [tex]254.94\ ft[/tex]

Step-by-step explanation:

Given

Building A is 490 feet tall and building B is 754 ft tall.

If the angle of depression from building B to the top of building A is [tex]46^{\circ}[/tex]

Difference in the height of the two buildings is [tex]754-490=264\ ft[/tex]

If the difference between them is [tex]x[/tex]

From the figure, we can write

[tex]\Rightarrow \tan 46^{\circ}=\dfrac{264}{x}\\\\\Rightarrow x=\dfrac{264}{\tan 46^{\circ}}\\\\\Rightarrow x=254.94\ ft[/tex]

Therefore, the two buildings are [tex]254.94\ ft[/tex] apart.

Answer:

What?

Step-by-step explanation:

G8ve me more info and Ill answer again

Answer:

hope this helps

Step-by-step explanation:

31 divided by 2 = 15.5 then do 15.5 x 15.5= 240.25 then you do 240.25 x 3.14 = 754.385

Answer:

Siswe

Step-by-step explanation:

[tex]\frac{1}{3} = \frac{4}{12}\\\\\frac{1}{4} = \frac{3}{12}\\\\\frac{5}{12} =\frac{5}{12}[/tex]

Answer:

siswe gets more juice

Step-by-step explanation:

i hope this helps

Answer:

B

Step-by-step explanation:

B...............................

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The statement about rectangles and rhombuses that is always true is that both figures are quadrilaterals.

A quadrilateral is a closed, two-dimensional shape which has four straight sides.

In other word, a quadrilateral is a plane figure that has four sides or edges, and also has four corners or vertices.

Quadrilateral has four sides.

Rhombuses and rectangles have four sides. Therefore, they are both quadrilaterals.

learn more on quadrilateral here: https://brainly.com/question/10388790

Answer:

∠ G ≈ 8.3°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan G = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{HI}{GI}[/tex] = [tex]\frac{1.1}{7.5}[/tex] , then

∠ G = [tex]tan^{-1}[/tex] ([tex]\frac{1.1}{7.5}[/tex] ) ≈ 8.3° ( to the nearest tenth )

The total mass of 5 x 10³ microorganisms is  1.2 x [tex]10^{-2}[/tex].

Option C is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Mass of an organism = 2.4 x [tex]10^{-6}[/tex] grams

The total mass of 5 x 10³ microorganism.

= 5 x 10³ x 2.4 x [tex]10^{-6}[/tex]

= 12.0 x [tex]10^{3 - 6}[/tex]

= 12 x [tex]10^{-3}[/tex]

= 1.2 x [tex]10^{-2}[/tex]

Thus,

The total mass is 1.2 x [tex]10^{-2}[/tex]

Learn more about expressions here:p

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