There were Math and Science books in one section of a library. Before an addition of 84 Math books, the ratio of Math books to Science books was 3 : 7. How many Science books were there if the eventual ratio of Math books to Science books was 6 : 7?

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SOH CAH TOA

sin(θ) is the ratio of the opposite side to the hypotenuse

sin(θ) = opposite/ hypotenuse

sin 50 = 0.766

sin 50 = x / 16

0.766 = x/ 16

0.766 × 16 = x

x = 12.256

Answer:

The total number of outcomes is 15.

favourable outcomes =6 (2,3,5,7,11,13)

prime number probability = 6/15

Answer: 24 cubic meters

Step-by-step explanation:

The formula for the volume of a triangular prism is  [tex]\frac{1}{2}[/tex]bhl

Where

b is the base (3 for this)

h is the height (2 for this)

and l is the length (8 for this)

Sub the values into the formula and solve

[tex]\frac{1}{2}bhl\\\frac{1}{2}(3)(2)(8)\\\frac{1}{2}(3)(16)\\\frac{1}{2}(48)\\24[/tex]

Answer:

1,512 ft cubed

Step-by-step explanation:

Volume Formula is Length times Width times Height.

Do 9ft x 14ft x 12ft = n ft cubed

**n is a variable used**

1,512 ft cubed is the correct answer.

The number of children who disliked the smoothie is 9, total children is 27, and conditional relative frequency is 33%

It is defined as the frequency that can be evaluated by the two-way frequency table. Usually, we can obtain this frequency by dividing the frequency that is not in the total frequency cell to total frequency.

From the data given in the table:

The number of children who disliked the smoothie = 9

The total number of children = 27

To find the conditional relative frequency that a customer disliked the new smoothie(if the person is a child)

It is the ratio of total number of children who disliked the smoothie to total number of children, mathematically:

= 9/27

= 0.3333

= 0.3333×100

= 33.33 ≈ 33%

Thus, the number of children who disliked the smoothie is 9, total children is 27, and conditional relative frequency is 33%

Learn more about the conditional relative frequency here:

https://brainly.com/question/8358304

Answer:

9, 27, 33

Step-by-step explanation:

Answer:

Given:-

Y = 3x² - 3x + 2

Find : - Discriminant

Y = ax² - bx + c

Discriminant is : - Y = b² - 4ac

So, Discriminant is :-

(-3²) - 4 (3) (2)

= 9-24

=-15

If b² - 4ac < 0.

The equation has no real solution but it does have complex solution.

Answer:

Option A

Step-by-step explanation:

Check out the attached photo

Answer:

I think it's A I hope this helps!!

Step-by-step explanation:

Step-by-step explanation:

4) 42

5) -9

6) 27

7) x=3,y=27

8) x=6,y=13

9) x=2,y=(-3)

I hope I have helped you

pls mention any doubts in comment

Answer:

11165

Step-by-step explanation:

77*145= 11165

Hope this helps. :D

Answer:

Step-by-step explanation:

The length of b, the base of the triangle, is

The area of the triangle is

The area of the rectangle is

The area of the irregular figure is

Answer:

[tex]b=2\frac23\:\sf ft[/tex]

Area of triangle = 4 ft²

Area of rectangle = [tex]6\frac23\: \sf ft^2[/tex]

Area of irregular figure = [tex]10\frac23\: \sf ft^2[/tex]

Step-by-step explanation:

[tex]\begin{aligned}\sf Base\:of\:triangle\:(b) & = 5-2\frac13\\\\& = \dfrac{15}{3}-\dfrac73\\\\ & = \dfrac83\\\\ & = 2\frac23\:\sf ft \end{aligned}[/tex]

[tex]\begin{aligned}\sf Area\:of\:a\:triangle & =\dfrac12 \sf \times base \times height\\\\& = \dfrac12 \times b \times 3\\\\ & = \dfrac12 \times \dfrac83 \times \dfrac31\\\\ & = \dfrac{24}{6}\\\\ & = 4\: \sf ft^2\end{aligned}[/tex]

[tex]\begin{aligned}\sf Area\:of\:rectangle& =\sf length \times width\\\\& = 5 \times 1\frac13\\\\ & = \dfrac51\times \dfrac43\\\\& = \dfrac{20}{3}\\\\ & = 6\frac23\: \sf ft^2\end{aligned}[/tex]

[tex]\begin{aligned} \sf Area\:of\:irregular\:figure & = \sf area\:of\:triangle+area\:of\:rectangle\\\\ & = 4 + 6\frac23\\\\ & = 10\frac23\: \sf ft^2\end{aligned}[/tex]

Answer:

D

Step-by-step explanation:

I and IV

Answer:

See below ~

Step-by-step explanation:

We know the sum of the interior angles is 720° for a hexagon.

Finding x

Finding m∠ABC

Answer:

  B)  When you're finished, you have a line that bisects your segment

Step-by-step explanation:

An angle bisector is a ray that divides a given angle into two congruent parts. There is no line segment involved.

__

The statement that is not true about this construction is ...

  B) When you're finished, you have a line that bisects your segment

_____

Additional comment

The construction effectively creates an arc of a circle, then creates the perpendicular bisector of the chord of that arc. The center of the circular arc is the vertex of the angle being bisected. The constructed perpendicular bisector of the chord also bisects the angle. (The chord is never actually drawn, and the "circular arc" may be two short arcs across the rays of the angle being bisected.)

Answer:

no

Step-by-step explanation:

Answer:

The area of a trapezoid = 1/2 (altitude)(base 1 + base 2)

Step-by-step explanation:

Answer:

322ft2

Step-by-step explanation:

I promise this is correct

The dot plot with the least number of sites has the least frequency

The dot plot has the least number of sites is the Shield Darter

To determine the dot plot with the least number of sites, we simply calculate the total frequency of each dot plot

So, we have:

Shield Darter = 3 + 1 + 4 + 2 + 3 + 1 + 1

Shield Darter = 15

Calico Crayfish = 1 + 1 + 3 + 4 + 1 + 2 + 4 + 2

Calico Crayfish = 18

Zebra Mussel = 1 + 3 + 2 + 5 + 1 + 1 + 2 + 3 + 2

Zebra Mussel = 20

Blue back Herring = 3 + 3 + 2 + 1 + 3 + 1 + 4

Blue back Herring = 17

From the computation above, the least frequency is

Shield Darter = 15

Hence, the dot plot has the least number of sites is the Shield Darter

Read more about dot plots at:

https://brainly.com/question/21862696

C. 2916 Mice

Step-by-step explanation:

4 x 3^6 = 2916

Because as the mice increases, you triple that amount, instead of tripling 4 & multiplying by 6.

So, you're doing this instead:

4 x 3 = 12 (1 wk)

12 x 3 = 36 (2 wk)

36 x 3 =108 (3 wk)

108 x 3 = 324 (4 wk)

324 x 3 = 972 (5 wk)

972 x 3 = 2916 (6 wk)

Hope this helps!

Step-by-step explanation:

Let the angle of triangle be x , so each angle will be 1x , 2x , 3x respectively.

We know that sum of all angles in triangle is 180°

So ,

1x + 2x + 3x = 180°

6x = 180°

x = 30°

Therefore , each angle would be 30° , 60° , 90° respectively.

The ordered pair maximizes the objective function p = 3x + 8y will be (5, 6) .Option C is correct.

The objective function is simply an equation that represents the goal production capability that relates to maximizing profits in relation to manufacturing.

On putting the values we will get the values one by one. We get;

1. (0, 0)

[tex]3 (0)+8(0) = 0[/tex]

2. (2,7)

[tex]3(2)+8(7)=62[/tex]

3. (5,6)

[tex]3(5)+8(6)=63[/tex]

4. (8,1)

[tex]3(8)+8(1)=42[/tex]

The maximum value obtained from the 63. Obtained from option C. The ordered pair maximizes the objective function p = 3x + 8y will be (5, 6)

Hence option C is correct.

To learn more about the objective function refer to the link;

https://brainly.com/question/15830007

Answer:

C

Step-by-step explanation:

let x be number of adults and y the number of underage , then

x + y = 350 → (1)

6x + 4y = 1600 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate y

- 4x - 4y = - 1400 → (3)

add (2) and (3) term by term to eliminate y

(6x - 4x) + (4y - 4y) = 1600 - 1400

2x + 0 = 200

2x = 200 ( divide both sides by 2 )

x = 100

the number of adults who attended is 100

Answer:

It is also known as E: random cause

Answer:

If x2 + 6x + c = (x + d)2, then d =What value of c makes x2 + 6x + c a perfect square trinomial? c =

Divide the x-term coefficient by 2: 6/2 = 3

Now square 3: 3^2 = 9

c = 9

If x^2 + 6x + c = (x + d)^2, then d =

x^2 + 6x + 9 = (x + 3)^2 = (x + d)^2, so d = 3

Step-by-step explanation:

Answer:

c = +9.

Step-by-step explanation:

x^2 + 6x + c.

Divide 6 by 3 then square it

- so c = 3^2 = 9.

x^2 + 6x + 9 = (x + 3)^2.

Answer:

The answer should be 14.5

Step-by-step explanation:

Hope This Helps

Have A great day

~Zero~

Answer:

I would be a diamond because diamonds are one of my favorite shapes.

Step-by-step explanation:

Diamonds are a girl's best friend

Hope it Helps

Hi There! Hope you are having a great day! As you know, you need to find the unit rate of the problem. In order to do that you must divide how much ounces there is, (52.8) and divide that integer by how much money she made (26.4) leaving you with a unit rate of 2. Hope this helps! :)

Answer:

240 cm²

Explanation:

The shape given above is a parallelogram.

Area of parallelogram = base × perpendicular height

Identify the following:

So here area = b × h = 20 × 12 = 240 cm²

Considering that the data has no outliers, the mean of 3.2 inches should be used to describe the center of the data represented in this line plot.

It depends if the data-set has outliers or not.

The dot plot gives the number of times each measure appears. Since there is no outliers, that is, all values are close, the mean should be used. It is given by:

M = (2 x 1 + 3 x 2 + 2 x 3 + 1 x 5 + 1 x 6 + 1 x 7)/(2 + 3 + 2 + 1 + 1 + 1) = 3.2 inches.

The mean of 3.2 inches should be used to describe the center of the data represented in this line plot.

More can be learned about the mean of a data-set at https://brainly.com/question/24628525

Answer: median 2.5

Step-by-step explanation:

Answer:

14130 cubic inches

Step-by-step explanation:

A = 4/3 n x rxrxr

A = 3.14 x 15x15x15

A = 3.14 x 3375

A = 10597.5

A = 4/3 10597.5

A = 14130