the following two-way table describes students after school activities. find the probability that a randomly selected is in music/drama.

Answer:

x = 58

y = 39

Step-by-step explanation:

x = 58 (Vertically opposite angles)

x + 2y + (x-14) = 180 (Angles in a straight line)

=> x + 2y + x - 14 = 180

=> 2x + 2y = 180 + 14

=> 2(58) + 2y = 194

=> 116 + 2y = 194

=> 2y = 194 - 116

=> 2y = 78

=> y = 78/2

=> y = 39

The required number will be 16

the expression will be like :

hope it helps you cap !!

Anti - Venom

Answer:

Step-by-step explanation:

1000 gallons - 940 = 60 then divide by the time which gets us 60/10=6

Now we can use this answer to help find out the amount remaining in the tank.

5 minutes = 5x6=30; 1000-30= 970 gallons

20 minutes= 20x6=120; 1000-120= 880 gallons

30 minutes=30x6=180; 1000-180= 820 gallons

27 minutes=27x6=162; 1000-162= 838 gallons

X minutes = 1000-6x

Rate of flow is 6 gallons per minute.

Hope this helps!

Answer:

X+3

Step-by-step explanation:

I did the test

Answer:

One was to write this ratio is lets say you where ordering 100 Happy Platters this mean you would get 200 corn and 300 flour.

another way is lets say you got a Happy Platter and split it in half with some one else you would get 1 corn and 1.5 flour

Answer:

8-22 is the answer ok thanks

Answer:  Choice A.  [tex]\angle T[/tex]

Explanation:

Notice how letters Q and T are in the middle of the sequences of PQR and STR respectively. This means the angles correspond.

Because the triangles are congruent, this means the corresponding pieces are congruent. Therefore, angle Q and angle T are the same measure.

As you can see, the order matters when it comes to forming congruence statements. Something like [tex]\triangle PQR \cong \triangle STR[/tex] is slightly different from [tex]\triangle PQR \cong \triangle SRT[/tex]

Congruent triangles have all corresponding measurements like angles and side lengths congruent. The completed statement would be ∠Q ≅ ∠T (Option A: ∠T)

Suppose it is given that two triangles ΔABC  ≅ ΔDEF

Then that means ΔABC  and  ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC  ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

(|AB| denotes length of line segment AB, and so on for others).

For this case, we have:  ΔPQR ≅ ΔSTR

Thus, we have:

[tex]\angle Q = \angle T[/tex]

Thus, the completed statement would be ∠Q ≅ ∠T. (Option A: ∠T)

Learn more about congruent triangles here:

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Answer:

yes you CAN you can use the descending to ascending formular but on people in which they might be a mixup of tallest and shortest

No, it is not always possible to sort the people from tallest to shortest using these moves.

Suppose there are four people in the line with heights A, B, C, and D, where A is the tallest and D is the shortest.

The initial order is A-B-C-D.

In each move, we can only exchange the positions of two people separated by one other person.

However, no matter how many moves we make, we cannot change the relative order of A and D since they are separated by two other people.

Thus, it is not possible to sort the people from tallest to shortest using these moves.

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I think you've got it, I don't know man.

Answer:

120 cm²

Step-by-step explanation:

Surface area of the pyramid = area of the 4 triangles + area of the square

✔️Area of the 4 triangles = 4(½*b*h)

b = 6 cm

h = 7 cm

Area = 4(½*6*7)

= 4(3*7)

= 4(21)

= 84 cm²

✔️Area of the square = s²

s = 6 cm

Area = 6² = 36 cm²

✅Surface area of the pyramid = 84 + 36 = 120 cm²

Answer:

{2}

or

{b}

a subset is a part of the whole set.

Answer:

hope it helps...

Answer:  Choice A

f(x) is continuous for all real numbers

=============================================================

Explanation:

The piecewise function given to us basically breaks down into these two cases:

So if we plug in x = 1, then we go for the top line and say

f(x) = x^2+4

f(1) = 1^2+4

f(1) = 5

Showing that f(1) is indeed defined. We rule out choice D because of this.

----------------

Let's see what happens when we plug x = 1 into the bottom equation

f(x) = x+4

f(1) = 1+4

f(1) = 5

Both pieces produce the same output. This tells us that as x approaches 1 from either the left or right sides, the y value approaches y = 5. Therefore, the limit at x = 1 exists. We rule out choice B because of this.

We rule out choice C as well because f(1) does equal the limiting value mentioned earlier.

----------------

The answer is choice A because no matter what x value we plug in, it's not only defined but also it's connected to the rest of the function curve as shown below.

Answer: A; f(x) is continuous for all real numbers

Answer:

The 3rd and the 5th

Step-by-step explanation:

The graphs of the 3rd and the 5th functions are straight lines

The 1st and 2nd are parabolas

The 4th is an exponential

You must look at the graph: it shall include all the real values for the y coordinate

Answer:

36x

Step-by-step explanation:

OF= 6x (given radius of circle)

OB=OF+FB

= 6x +6x(given OF=FB)

= 12x

Angle D= angle B and angle O= 60°( given arc EF is 60°)

D + B + O= 180° ( sum of angles in a triangle)

x + x + 60= 180° ( let the value of remaining angles be x and D= B)

2x= 180 -60

x = 120/2

x= 60°

now, triangle DOB is a equilateral triangle because all angles are equal.

so, OB=DB=OD= 12x ( all sides are equal in equilateral triangle)

so,

perimeter of DOB= OB+DB+OD

= 12x+12x+12x

= 36x

follow me if this was helpful

Answer:

no

Step-by-step explanation:

no

Step-by-step explanation:

there must be something missing here (I guess, the graph).

because just by looking at the 2 points, all 4 answer options could be wrong, or all 4 could be right.

just basing on the point coordinates I see the functional values (y) go from 2 to 4.

but we have no clue about what that curved function does in between these 2 points.

please provide the full information.

Answer:

The answer is = 4 - 12t + 9t^2

Step-by-step explanation:

(2-3t)^2

= 2^2 - 2*2*3t + (3t)^2

= 4 - 12t + 9t^2

Answer:

y = -1/6x - 1/2

Step-by-step explanation:

y = -1/6x + b

-1 = -1/6(3) + b

-1 = -1/2 + b

-1/2 = b

9514 1404 393

Answer:

  (c) The solution -6 is an extraneous solution

Step-by-step explanation:

If you solve the equation graphically, you can avoid extraneous solutions. The true solution is x = -1.

You can tell from the equation that the domain will be restricted to values of x that make the radical non-negative:

  x+4 ≥ 0   ⇒   x ≥ -4

Then x=-6 must be an extraneous solution. It arises when the negative square root is used.

__

The conventional solution method has you square both sides and solve the resulting quadratic.

  (x +4)² = x +10

  x² +7x +6 = 0

  (x +6)(x +1) = 0   ⇒   x = -6 or -1

The solution x=-6 is not in the domain, so is extraneous.

__

Additional comment

Graphical solution is often easier if the equation is in the form f(x) = 0. That form can be had by subtracting one side of the equation from both sides. In the attached, we subtracted √(x+10) from both sides. (We added the negative branch of the square root function to show where the extraneous root comes from.)

Step-by-step explanation:

please check you typing 5b = 3b, 2b

?????

Answer:

73

Step-by-step explanation:

3a + 5b + 2c = ?

Given:

a + b = 15

b + c = 14

now express in terms of b

a = 15 - b    equation (i)

c = 14 - b     equation (ii)

3a + 5b + 2c

substitute the values

3(15 - b) + 5b + 2(14 - b)

45 - 3b + 5b + 28 - 2b

add or subtract like terms

73 + 5b - 5b

plus 5b and minus 5b gets cancel

73

Answer:

C)

Step-by-step explanation:

Find the total sum

25+28= 53

53+31=84

Fimd the average by dividing by 3

84/3= 28

Hence, the answer is c

Answer:

c. 28kg

Step-by-step explanation:

28+25+31 = 84

84/3 = 28kg

Answer: Choice E. 4/sqrt(7)

This is the same as writing [tex]\frac{4}{\sqrt{7}}[/tex]

=================================================

Explanation:

0.75 = 3/4

Recall that cosine is the ratio of adjacent over hypotenuse.

That means if cos(theta) = 3/4, then the adjacent is 3 units and the hypotenuse is 4 units.

Through the pythagorean theorem, we would then find that

a^2+b^2 = c^2

a = sqrt(c^2 - b^2)

a = sqrt(4^2 - 3^2)

a = sqrt(7)

This is the opposite side of reference angle theta.

From here, we can say

csc(angle) = hypotenuse/opposite

csc(theta) = 4/sqrt(7)

which points to choice E as the final answer.

Answer:

Step-by-step explanation:

Độ dài vecto a= căn bậc hai của (-3)*(-3)+4*4=5

Answer:

5

Step-by-step explanation:

Answer:

TH is an element on the sample space for first rolling a die and then tossing a coin. A coin has both heads and tails.

The sample space for rolling a number cube and then tossing a coin is:

{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}

The elements can be any of the elements in the sample space.

It is the total number of possible outcomes from a given set.

We have,

The sample space for rolling a number cube and then tossing a coin consists of all possible outcomes from rolling the number cube and tossing the coin.

Each outcome is a pair consisting of a number from 1 to 6 (the possible outcome from rolling the number cube) and a head or tail (the possible outcome from tossing the coin).

Therefore, an element in the sample space can be represented as an ordered pair (n, h/t), where n is the number rolled on the number cube and h/t is the outcome of the coin toss (either head or tail).

So,

The sample space for rolling a number cube and then tossing a coin is:

{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}

For example, (3, H), (6, T), (1, H), and (4, T) are all elements in the sample space.

Thus,

The sample space for rolling a number cube and then tossing a coin is:

{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}

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Answer:

Step-by-step explanation:

LCM×HCF= Product

LCM×3=180

LCM=180/3=60

Answer:

x=4

Step-by-step explanation:

So basically first we see the angles of this triangle, and we learn that all the angles are congruent. Only a equilateral triangle can have all angles congruent, so this must be equilateral triangle. In equilateral triangles all the sides are congruent. So we just put 5x-12=3x-4. We then solve for x and get 4.

Answer:

4.35

Step-by-step explanation:

(1 * 0.35) + (2 * 0.2) + (5 * 0.1) + (8 * 0.2) + (10 * 0.15) = 4.35

Answer:D - mean>median

Step-by-step explanation:

There are no repeating variables to have a mode so median and mean are the only options. The mean of this data set is 7.4 and the median is 6. Therefore mean greater than median

Answer:

252 in^3

Step-by-step explanation:

7*3*12 = 252

252*.04 = $10.08

Answer:

13[tex]\sqrt{22}[/tex] / 44

Step-by-step explanation:

cos A = 9/13

here adjacent = 9 and hypotenuse = 13  opposite = ?

using pythagoras theorem to find opposite

a^2 + b^2 = c^2

9^2 + b^2 = 13^2

81 + b^2 = 169

b^2 = 169 - 81

b^2 = 88

b = [tex]\sqrt{88}[/tex]

b =  [tex]2\sqrt{22}[/tex]

therefore opposite =  [tex]2\sqrt{22}[/tex]

cosec A = hypotenuse/opposite

= 13/[tex]2\sqrt{22}[/tex]

rationalizing the denominator

=13/ [tex]2\sqrt{22}[/tex]  *  [tex]2\sqrt{22}[/tex] /  [tex]2\sqrt{22}[/tex]

=13 *[tex]2\sqrt{22}[/tex] /( [tex]2\sqrt{22}[/tex] )^2

=26 [tex]\sqrt{22}[/tex] / 4*22

=26 [tex]\sqrt{22}[/tex] / 88

=13[tex]\sqrt{22}[/tex] / 44

Answer:

[tex]cosec A = \frac{13}{\sqrt{88}}[/tex]

   OR

[tex]cosec A = \frac{13 \sqrt{22}}{44}[/tex]

Step-by-step explanation:

Formulas used:

[tex]cos^2 A = 1 - sin^2 A\\\\cosec A = \frac{1}{sin A}[/tex]

Given :

  [tex]cos A = \frac{9}{13}[/tex]

Find cosec A

   [tex]sin ^2 A = 1 - cos^2 A[/tex]

              [tex]= 1 - (\frac{9}{13})^2\\\\= 1 - \frac{81}{169}\\\\=\frac{169 - 81}{169}\\\\=\frac{88}{169}[/tex]

 [tex]sin A = \sqrt{\frac{88}{169}} = \frac{\sqrt{88}}{13}[/tex]

Therefore,

         [tex]cosec A = \frac{1}{sin A} = \frac{1}{ \frac{\sqrt{88}}{13}} = \frac{13}{ \sqrt{88}}[/tex]

OR In a simplified form :

[tex]cosec A = \frac{13}{\sqrt{88}} \times \frac{\sqrt{88}}{\sqrt{88}} = \frac {13 \times \sqrt{4 \times 22}}{88} = \frac{13 \times 2 \sqrt{22}} {88} = \frac{13 \sqrt{22}}{44}[/tex]