The dot plot below represents this set of data:
30, 29, 30, 28, 28, 27, 22, 28, 28, 22, 27, 26, 25, 27

Step-by-step explanation:

Disclaimer: When writing this on the paper use the theta symbol, I'm using x since I'm on mobile.

2.

i).

[tex] \sin(x) \tan(x) \sec(x) = \tan {}^{2} (x) [/tex]

[tex] \sin(x) \sec(x) \tan(x) = \tan {}^{2} (x) [/tex]

[tex] \sin(x) \frac{1}{ \cos(x) } \tan(x) = \tan {}^{2} (x) [/tex]

[tex] \frac{ \sin(x) }{ \cos(x) } \tan(x) = \tan {}^{2} (x) [/tex]

[tex] \tan( x) ) \tan(x) = \tan {}^{2} (x) [/tex]

[tex] \tan {}^{2} (x) = \tan {}^{2} (x) [/tex]

iii).

[tex] \sec {}^{2} (x) (1 - \sin {}^{2} ( x ) ) = 1[/tex]

[tex] \sec {}^{2} (x) ( \cos {}^{2} (x) ) = 1[/tex]

[tex] \frac{1}{ \cos {}^{2} (x) } \cos {}^{2} (x) = 1[/tex]

[tex]1 = 1[/tex]

v).

[tex] \cot {}^{2} (a) - \cos {}^{2} (a) = \cot {}^{2} (a) \cos {}^{2} (a) [/tex]

[tex] \frac{ \cos{}^{2} (x) }{ \sin {}^{2} (x) ) } - \cos {}^{2} (x) [/tex]

Factor out cosine

[tex] \cos {}^{2} (x) ( \frac{1}{ \sin {}^{2} (x) } - 1) [/tex]

Simplify

[tex] \cos {}^{2} (x) ( \frac{1 - \sin {}^{2} (x) }{ \sin(x) } [/tex]

[tex] \cos {}^{2} (x( \frac{ \cos {}^{2} (x) }{ \sin {}^{2} (x) } ) = [/tex]

[tex]( \cos {}^{2} ( x ) ( \cot {}^{2} (x) )[/tex]

Step-by-step explanation:

<TOS=122° [being vertically opposite angle]

Answer:

angleTOS =122°

EXPLANATION:

[ If two straight lines intersect at point O, vertically opposite angles are equal]As vertically opposite angles are equal; Hence AngleTOS=QOR=122°

Answer:

D

Step-by-step explanation:

Answer:

B847,030

Step-by-step explanation:

y=95,000(1.2)^x

2025 - 2013 = 12

y=95,000(1.2)^12

y=847029.54258

Answer:

C

Step-by-step explanation:

3(17x-6.5) =108

=17x-6.5=36

=17x =36 +6.5

= 17x=42.4

=x =2.5

Answer:

x= 2.5

Step-by-step explanation:

3(17x-6.5)=108

Divide each side by 3

3/3(17x-6.5)=108/3

17x - 6.5 = 36

Add 6.5 to each side

17x-6.5+6.5=36+6.5

17x = 42.5

Divide by 17

17x/17 = 42.5/17

x= 2.5

Answer:

0.00065104166

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: C. 6x+18

Step-by-step explanation:

Use the distributive property

First multiply 6 times x which is 6x

Then multiply 6 times 3 which is 18

Keep the sign the same

Therefore, this should give you 6x+18

Step-by-step explanation:

= 4x-x+5x+1+8-2

=8x+7

proved##

The coldest time of day in Mumbai is 5 hours after midnight.

Since the average temperature t hours after midnight in Mumbai, India, is given by:

T(t)=24.5-5.5sin((2pi(t+1))/24)

We have that

T(t) = 24.5 - 5.5sin((2π(t+1))/24)

The coldest time of day is when T(t) is minimum.

T(t)  is minimum when 5.5sin((2π(t+1))/24) is minimum where t is the coldest time of day at minimum temperature, T(t).

Since for a sine function, -1 ≤ sinФ ≤ 1, the minimum value of sinФ = -1.

So, T(t) = 24.5 - 5.5sin((2π(t+1))/24) is minimum when

5.5sin((2π(t+1))/24) is minimum.

Also, -5.5sin((2π(t+1))/24) = 5.5 × -1 at minimum temperature T(t)

So, 5.5 × -1 = 5.5 × -sin((2π(t+1))/24)

So, -sin((2π(t+1))/24) = -1

sin((2π(t+1))/24) = 1

Taking inverse sine of both sides, we have

sin⁻¹sin((2π(t+1))/24) = sin⁻¹(1)

((2π(t+1))/24) = π/2

Multiplying both sides by 24, we have

(2π(t+1))/24 × 24 = π/2 × 24

(2π(t+1)) = 12π

Dividing both sides by 2π, we have

2π(t+1)/2π = 12π/2π

t + 1 = 6

t = 6 - 1

t = 5 hours

So, the coldest time of day in Mumbai is 5 hours after midnight.

Learn more about average temperature here:

https://brainly.com/question/19388300

There are 30 possible combinations of teachers.

Given that at Tubman Middle School, there are 6 English teachers and 5 science teachers, to determine, if each student takes one English class and one science class, how many possible combinations of teachers are there, the following calculation must be performed:

To calculate possible combinations, the number of options A must be multiplied by the number of options B. Thus, the calculation would be as follows.

Therefore, there are 30 possible combinations of teachers.

Learn more about combinations in https://brainly.com/question/24180105.

Answer:

71.9

Step-by-step explanation:

Whenever you want to round a number to a particular digit, look only at the digit immediately to its right. For example, if you want to round to the nearest tenth, look to the right of the tenths place: This would be the hundredths place digit. Then, if it is 5 or higher, you get to add one to the tenths digit.

After rounding 71.916476787 to 1 decimal place we get 71.9.

We round numbers to get an approximate value of the given number in more compact form and which is easy to work with.

According to the given question we have to round 71.916476787  to 1 decimal place.

So, to round 71.916476787 to 1 decimal place we'll look at the digit of 2 decimal place here in this number it is 1 hence it is less than 5 so we can make all the digits after 1 decimal places zero and rewrite this number as

71.900000000 and we know zeroes are meaning less to the right of the decimal so this can be written as 71.9.

learn more about rounding of numbers :

https://brainly.com/question/28562556

#SPJ2

Answer:

Step-by-step explanation:

this may or may not be right but I tried my best

Answer:

-10

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

            Boys          Girls               Total

Walk      19              22                   41

Bus        23              10                   33

Cycle     40             56                   96

Total      82              88                  170

Answer:

Is E

explanation:

Answer:

The volume is multiplied by 8.

Step by step explanation:

Let the length equal l, the width equal w, and the height equal h for the original rectangular prism.

The volume of a right rectangular prism with length l, width w, and height h is V=lwh.

Therefore, the volume of the original prism is lwh.

The new rectangular prism has dimensions that are twice those of the original rectangular prism: the length equals 2l, the width equals 2w, and the height equals 2h.

To calculate the volume of the rectangular prism, substitute the doubled values into the formula for the volume of a rectangular prism.

V=2l·2w·2h

Simplify.

V=8lwh

The new volume is 8lwh.

If the length, width, and height of a right rectangular prism are doubled, the volume is multiplied by 8.

Therefore, the new volume is the original volume multiplied by 8.

Answer:

18.8

Step-by-step explanation:

Surface area=2*pi*r*(r+h)=2*pi*1*(3)=18.8

Answer:

5.41 m

Step-by-step explanation:

First, let's find a side length by taking the square root of the area.

117/64 ^ 1/2 = 1.352...

Next, we need to multiply by 4.

1.352... x 4 = 5.408...

= approximately 5.41

Answer:

hello dear...

see first of all there's a thm type thing

'' sides opposite to equal angles are equal ''

so here 45 degrees in both sides are equal which leads us that opposite sides are equal as well

so x = 6

now we got value of 2 sides, both are 6 and now applying pythogarus as it is right angle

6^2 + 6^2 = y^2

36+36 = y^2

72 = y^2

y = √72

y = √36*2

y = 6√2

brainliest plssss <33

Answer:

Here's the answers

Step-by-step explanation:

1. When two variables are in relation with a formula or a variable is related by the sum of two or more variables, then it is a partial variation. X = KY + C (where K and C are constants) is a straight line equation which is an example of partial variation.

2. The formula y=kxn y = k x n is used for direct variation. The value k is a nonzero constant greater than zero and is called the constant of variation.

Answer:

Area of parallelogram = 21

Step-by-step explanation:

A = BH

Plug in

A = 7×3

Solve

A = 21

The answer will be 21.

Answer:

56 litres

Step-by-step explanation:

let x be the amount when the container is full.

1/8x + 35 = 3/4x

-5/8x = -35

x = 56

Answer:

8 inches

Step-by-step explanation:

A rhombus is a four sides quadrilateral with the four sides equal in length

A rhombus has 4 equal sides and the diagonal bisect at right angles

Adjacent sides = 9/2 = 4.5

we are to determine the value of the hypotenuse given the adjacent side and angle (108/2) = 54

Cos 54 = adjacent / hypotenuse

0.58778 = 4.5 / hypotenuse

hypotenuse = 4.5 / 0.58778

=7.6559

= 8 inches

Answer:

No

Step-by-step explanation:

x^3• x^3•x^3

We add the exponents

x^(3+3+3) = x^9

x^3•3•3 x^3 *9

9x^3

These are not equal unless

x^9 = 9x^3

Answer:

A and B

Step-by-step explanation:

A and B are the correct options

Answer:

The alphabets Z, H, S, N and O have rotational symmetry.

Answer:

Player B.

Step-by-step explanation:

Player A has a mean score of 25.

Let's calculate Player B's mean score and compare it to Player A's.

23 + 27 + 28 + 22 + 25 / 5 = 125 / 5 = 25.

So, Player A and Player B have the same mean score.

This doesn't tell the scout which player is "better", so let's look at the variance.

The other statistic given for Player A is the standard deviation for their points. The given number is 4. Let’s calculate the standard deviation for Player B, and compare it to player A.

Recall that we add up the squares of the difference between each score and the mean, divide it by the total number of data, and square root that. So, the standard deviation for player B is sqrt(2^2 + 2^2 + 3^2 + 3^2 + 0^2 / 5) = sqrt (26/5) = sqrt (5.2) = 2.3.

Excellent. We have player A’s standard deviation, as well as player B’s standard of deviation. Since player B’s standard deviation is less than player A’s, it can be inferred that player B has more consistent results than player A, and the scout should get Player B.

Hope this helps!

Answer:

x = 40

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

x² + 30² = 50²

x² + 900 = 2500 ( subtract 900 from both sides )

x² = 1600 ( take the square root of both sides )

x = [tex]\sqrt{1600}[/tex] = 40