Question 1 of 5
Select the correct answer.
The dance committee at a local high school polled students to determine what theme they would like to have for the school dance. The
results of the poll are shown in the two-way frequency table below.
Starry Night Beach Party Masquerade Total
Girls 92
48
56 196
Boys 68
88
48 204
Total 160
136
104 400
Approximately what percentage of the total number of girls prefer the starry night theme?
57.5%
46.99
73.9%
34.7%
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Answer:

8 1/2

or 8.5

Step-by-step explanation:

Answer:

The second one, √4^9

Sorry lol i posted the answer in the questions section by accident

Answer:

x > 0

Step-by-step explanation:

Correct Question :-

If sec[tex]\theta[/tex] + tan[tex]\theta[/tex]= x , then prove that ,

[tex]\implies\sf sin\theta =\dfrac{x^2-1}{x^2+1}[/tex]

Proof :-

Here we are given that ,

[tex]\longrightarrow \sec\theta + tan\theta = x[/tex]

Firstly write everything in terms of sine and cosine .

[tex]\longrightarrow \dfrac{1}{\cos\theta}+\dfrac{\sin\theta}{\cos\theta}=x [/tex]

Add ,

[tex]\longrightarrow \dfrac{1+\sin\theta}{\cos\theta}=x [/tex]

On squaring both sides , we have ;

[tex]\longrightarrow \dfrac{(\sin\theta+1)^2}{(\cos\theta)^2}=x^2[/tex]

Simplify using identity sin²x + cos²x = 1 ,

[tex]\longrightarrow \dfrac{(1+\sin\theta)^2}{1-\sin^2\theta}=x^2 [/tex]

Simplify using identity (a+b)(a-b)=a²-b² ,

[tex]\longrightarrow \dfrac{(1+\sin\theta)^2}{(1+\sin\theta)(1-\sin\theta)}=x^2 [/tex]

Simplify,

[tex]\longrightarrow \dfrac{1+\sin\theta}{1-\sin\theta}=x^2 [/tex]

On using Componendo and Dividendo , we have ;

[tex]\longrightarrow \dfrac{1+\sin\theta+1-\sin\theta}{1+\sin\theta-1+\sin\theta}=\dfrac{x^2+1}{x^2-1}[/tex]

[tex]\longrightarrow \dfrac{2}{2\sin\theta}=\dfrac{x^2+1}{x^2-1}[/tex]

Simplify,

[tex]\longrightarrow \dfrac{1}{\sin\theta}=\dfrac{x^2+1}{x^2-1}\\[/tex]

Divide both the sides by 1 ,

[tex]\longrightarrow \underline{\underline{\sin\theta =\dfrac{x^2-1}{x^2+1}}} [/tex]

Hence proved .

And we are done !

[tex]\rule{200}4[/tex]

1) Trigonometric table :-

[tex]\small{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 60^{\circ} & \sf 90^{\circ} \\ \cline{1-6} $ \sin $ & 0 & $\dfrac{1}{2 }$ & $\dfrac{1}{ \sqrt{2} }$ & $\dfrac{ \sqrt{3}}{2}$ & 1 \\ \cline{1-6} $ \cos $ & 1 & $ \dfrac{ \sqrt{ 3 }}{2} } $ & $ \dfrac{1}{ \sqrt{2} } $ & $ \dfrac{ 1 }{ 2 } $ & 0 \\ \cline{1-6} $ \tan $ & 0 & $ \dfrac{1}{ \sqrt{3} } $ & 1 & $ \sqrt{3} $ & $ \infty $ \\ \cline{1-6} \cot & $ \infty $ &$ \sqrt{3} $ & 1 & $ \dfrac{1}{ \sqrt{3} } $ &0 \\ \cline{1 - 6} \sec & 1 & $ \dfrac{2}{ \sqrt{3}} $ & $ \sqrt{2} $ & 2 & $ \infty $ \\ \cline{1-6} \csc & $ \infty $ & 2 & $ \sqrt{2 } $ & $ \dfrac{ 2 }{ \sqrt{ 3 } } $ & 1 \\ \cline{1 - 6}\end{tabular}}[/tex]

[tex]\rule{200}4[/tex]

2) Important identities :-

[tex]\boxed{\begin{minipage}{6cm} Important Trigonometric identities :- \\ \\ $\: \: 1)\:\sin^2\theta+\cos^2\theta=1 \\ \\ 2)\:\sin^2\theta= 1-\cos^2\theta \\ \\ 3)\:\cos^2\theta=1-\sin^2\theta \\ \\ 4)\:1+\cot^2\theta=\text{cosec}^2 \, \theta \\ \\5)\: \text{cosec}^2 \, \theta-\cot^2\theta =1 \\ \\ 6)\:\text{cosec}^2 \, \theta= 1+\cot^2\theta \\\ \\ 7)\:\sec^2\theta=1+\tan^2\theta \\ \\ 8)\:\sec^2\theta-\tan^2\theta=1 \\ \\ 9)\:\tan^2\theta=\sec^2\theta-1$\end{minipage}}[/tex]

[tex]\rule{200}4[/tex]

If sec theta + tan theta equals to x then prove that:-

[tex]\longrightarrow \: sin \theta = \frac{ {x}^{2} - { \bold{1}} }{ {x}^{2} + 1 } [/tex]

Given that:

[tex]\longrightarrow \: sec \: \theta + tan \: \theta =x \: \: ..(i) [/tex]

We have to prove:

[tex]\longrightarrow \: sin \: \theta = \frac{ {x}^{2} - 1 }{ {x}^{2} + 1} [/tex]

We know that:

[tex]\longrightarrow \: { \sec}^{2} \theta \: - \: { \tan}^{2} \theta = 1[/tex]

[tex] \longrightarrow ( \sec \: \theta \: + \: \tan \: \theta)( \sec \: \theta - \tan \: \theta )[/tex]

[tex] \longrightarrow x( \sec \: \theta - \tan \: \theta) \: = 1[/tex]

[tex] \longrightarrow \: \sec \theta - \tan \: \theta = \frac{1}{x} \ ..(ii)[/tex]

Adding equation (i) and (ii), we get:

[tex] \longrightarrow \: 2\sec \theta = x + \frac{1}{x} [/tex]

[tex] \longrightarrow \: 2 \sec \: \theta = \frac{ {x}^{2} + 1}{x} [/tex]

[tex] \longrightarrow \: \sec \: \theta = \frac{ {x}^{2} + 1}{2x} [/tex]

[tex] \longrightarrow \: \cos \: \theta = \frac{2x}{ {x}^{2} + 1 } [/tex]

Now, we know that:

[tex] \longrightarrow \: { \sin}^{2} \theta + { \cos }^{2} \: \theta = 1[/tex]

Therefore,

[tex] \longrightarrow \: \sin \theta \: = \sqrt{1 - { \cos }^{2} } \: \theta[/tex]

[tex] \longrightarrow \: \sin \: \theta = {\sqrt{1 - ( \frac{2x}{ {x}^{2} + 1} } )}^{2} [/tex]

[tex] \longrightarrow \: \sin \: \theta = \sqrt{ \frac{ {({x}^{2} + 1)}^{2} - {(2x)}^{2} }{( {x}^{2} + 1)} } [/tex]

[tex] \longrightarrow \: \sin \: \theta = \sqrt{ \frac{ {x}^{4} \: + 2 {x}^{2} + 1 - \: 4 {x}^{2} }{( {x}^{2} { + 1)}^{2} } } [/tex]

[tex] \longrightarrow \: \sin \: \theta = \sqrt{ \frac{ {x}^{4} - {2x}^{2} + 1 }{( {x}^{2} { + 1)}^{2} } } [/tex]

[tex] \longrightarrow \: \sin \: \theta = \sqrt{ \frac{( {x}^{2} { - 1)}^{2} }{ {(x}^{2} + {1)}^{2} } } [/tex]

[tex] \longrightarrow \: \sin \: \theta = \frac{ {x}^{2} - 1 }{ {x}^{2} + 1} [/tex]

[tex] \: [/tex]

Answer:

29

Step-by-step explanation:

The first one is a row and the second one is a column. 1st row and 5th column.

Answer:29

Step-by-step explanation:

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

Work Shown:

A = probability of getting a yellow ball

A = (number of yellow)/(number total)

A = 7/(5+7+1)

A = 7/13

B = probability of getting a green ball after event A happens, no replacement

B = (number of green)/(number left after the yellow is picked)

B = 5/(13-1)

B = 5/12

A*B = probability of getting yellow followed by green, no replacement

A*B = (7/13)*(5/12)

A*B = (7*5)/(13*12)

A*B = 35/156

Given:

A square corner of 16 square centimeters is removed from a square paper with an area of 9x² square centimeters.

To find:

The area of the remaining paper shape in square centimeters.

Solution:

Initial area of the square paper = 9x² sq. cm

Area of square which is removed from the initial square paper = 16 sq. cm

Subtract area of removed square from the initial area, to find the area of the remaining paper shape.

[tex]9x^2-16=(3x)^2-4^2[/tex]

[tex]9x^2-16=(3x-4)(3x+4)[/tex]              [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

Therefore, the area of the remaining paper shape is (3x-4)(3x+4) sq. cm.

Hence, the correct option is C.

for the line that goes up - it cuts the y-axis at - 5  (p = -5)

when we take 2 points we go from one to the other by going to the right of 1 unit and going up of 3 units (slope m : 3/1)

=> y = 3x - 5

and

for the line which goes down - it cuts the y-axis in +2 (p=2)

when we take 2 points we go from one to the other by going to the right of 2 units and going down of 1 unit (slope m : -1/2)

=> y = -1/2x + 2

=> y + 1/2x = 2

2x + 4y = 8

=> B

isosceles triangle so angle Q = angle R

and sum of the angles of a triangle = 180

so

y + y + 84 = 180

2y = 96

y = 48

Answer:

The average change would be -3.36 degrees.

Step-by-step explanation:

We take the overall temperature change which is -16.8 and we would just simply divide that by 5. That's all to get the temperature.

Another example would be if the temperature change was 16 over the course of 4 days. In this case we would take the overall (16) and divide that by the number of days. There would be an average of 4 degree temperature change.

Step-by-step explanation:

2x*3y=36

2x*3(6)=36

2x*18=36

2x=36/18

2x=2

x=1

hope this was helpful

remember if you have any question ask me in the comment section

Step-by-step explanation:

Least common multiple of 66 and 88 is 2424. Convert -\frac{5}{6}−

6

5

and \frac{83}{8}

8

83

to fractions with denominator 2424.

-\frac{20}{24}+\frac{249}{24}−

24

20

+

24

249

Step 2

Since -\frac{20}{24}−

24

20

and \frac{249}{24}

24

249

have the same denominator, add them by adding their numerators.

\frac{-20+249}{24}

24

−20+249

Step 3

Add -20−20 and 249249 to get 229229.

\frac{229}{24}

24

229

answer:222/24 = 9.5419999967

A is the statement that is true

The equation represents the general form a circle with a center at

(–2, –3) and a diameter of 8 units is,

[tex]x^{2} +4x+y^{2} +6y-3=0[/tex]

Given that,circle with a center at (–2, –3)

diameter of circle is  8 units

To find

the equation of the circle that represents the general form of a circle with a center at (–2, –3) and a diameter of 8 units.

Radius of the Circle is,

The diameter of the circle is 8 units. therefore,

[tex]radius=\frac{d}{2}=\frac{8}{2} =4[/tex]

Equation of a circle

The equation of the circle that represents the general form of a circle with a center at (–2, –3) and a radius of 4 units.

[tex](x-h)^{2} +(y-k)^{2} =R^{2}[/tex]

Substituting the values,

[tex](x-(-2))^{2} + (y-(-3))^{2} =4^{2}[/tex]

[tex](x+2)^{2} + (y+3)^{2} =4^{2}\\[/tex]

[tex]x^{2} +4x+4+y^{2} +6y+9=0[/tex]

[tex]x^{2} +4x+y^{2} +6y-3=0[/tex]

Therefore, the option C is correct.

The equation represents the general form a circle with a center at

(–2, –3) and a diameter of 8 units is

[tex]x^{2} +4x+y^{2} +6y-3=0[/tex]

To learn more about the general form of circle visit:

https://brainly.com/question/3612143

Answer:

The shortest piece is 42

Step-by-step explanation:

168 ÷ 4 = 42 ( Shortest Piece )

42 × 3 = 126 ( Longest Piece )

168 - 126 = 42

Answer:

12/2

Step-by-step explanation:

12 halves equal 6 but 2 twelves equal 0.17 (rounded)

Answer:

10

Step-by-step explanation:

Given;

a = 2

b = 3

c =4

ab+c

Solve;

Since a = 2, b = 3, and c = 4

Substitute

(2)(3)+4

6 +4

= 10

Answer = 10

~Learn with lenvy~

Answer:

10

Step-by-step explanation:

Given the following question:

[tex]a=2[/tex]
[tex]b=3[/tex]
[tex]c=4[/tex]
[tex]ab+c[/tex]

To find the answer we need to substitute the values in for the variables and then solve using PEMDAS.

[tex]ab+c[/tex]
[tex]2\times3+4[/tex]
[tex]2\times3=6[/tex]
[tex]6+4[/tex]
[tex]6+4=10[/tex]
[tex]=10[/tex]

Your answer is "10."

Hope this helps.

Answer:109

Step-by-step explanation:41+68=109

109-68=41

Answer:

9%

Step-by-step explanation:

67 + 24 = 91%

100- 91 = 9%

This means they lost 9% of their games.

The requried football team lost 9% of their matches.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Since the football team won 67% of their matches and drew 24% of them, the percentage of matches they lost can be found by subtracting the percentage of matches they won and the percentage of matches they drew from 100%:

Percentage of matches lost = 100% - 67% - 24%

Percentage of matches lost = 9%

Therefore, the football team lost 9% of their matches.

Learn more about percentages here:

brainly.com/question/13450942

#SPJ3

Answer:

0.6 percent

Step-by-step explanation:

I did division that why

Using the definition of the floor function, it is found that the correct statement is:

Because 2 is the greatest integer not greater than 2.4, and –3 is the greatest integer not greater than –2.4.

Modeled by [x], it is the value of the greatest integer that is not greater than x.

Hence, in this problem:

Hence, the correct statement is:

Because 2 is the greatest integer not greater than 2.4, and –3 is the greatest integer not greater than –2.4.

More can be learned about the floor function at https://brainly.com/question/15457745

Answer:

a

Step-by-step explanation:

on edge

Answer:

C

Step-by-step explanation:

Pythagorean theorem

Answer: 3

Step-by-step explanation: A=1 and B=2  its like adding 1 and 2 it is 3

Answer:

No biscuits.

Step-by-step explanation:

We know that there is a total of 100 biscuits.
Let's assign variables.

X=Icing
Y=Hundreds and Thousands

Z=Cherries

X appears every 5 biscuits, y appears every 8 biscuits, and z appears every 9 biscuits. Let's start solving by finding their multiples that are less than or equal to 100.

X: 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100

Y: 8,16,24,32,40,48,56,64,72,80,88,96

Z: 9,18,27,36,45,54,63,72,81,90,99

The multiples need to be a multiple of 5,8, and 9.

The numbers that have both x and y are: 40 and 80

The numbers that have both x and z are: 45 and 90.

Seeing as the numbers never overlap, there are no biscuits that have x,y, and z.

Note: If you like my answer, please rate it a 5 and click thanks! (It helps with my leveling. If you want to be extra nice, you can also give me brainliest if you want!) If you think there is something wrong with my answer or that there is something I should improve on, please leave it in the comments.

Answer:

1. 96

2. 84

Step-by-step explanation:

I used the Circle theorems:

For 1 you use the alternate segment theory

For 2 you use the theory that opposite angles in a cyclic quadrilateral add up to 180.

I can't be asked to explain it properly I'm sorry but if no one else does it properly you can give me brainliest?

Answer:

19 or c

Step-by-step explanation:

Hi I just took the test as you can see on the chart by the x axis it goes from 10 to 11 and on the y axis it goes from 27 to a so really it’s just simple subtraction

Answer:

1,-5,10,3 are integers.

Step-by-step explanation:

1 is a natural number which is an integer. 8.666 is a repeating decimal which isnt an integer. -5 is a negative number and integer. 10 is a natural number which is an integer. 3 is a natural number which is an integer.

Hope this helped and have a great day!

(Please brainliest)

Answer:

2x + 1

Step-by-step explanation:

[tex] \frac{(2x² - 5x-3)}{(x - 3)} [/tex]

Factor out 2x² - 5x-3

[tex] \frac{(2x + 1)(x - 3)}{x - 3} [/tex]

divide x - 3 by x - 3

=> 2x + 1

Or another step

Step by Step Solution

STEP

1

:

Equation at the end of step 1

STEP

2

:

2x² - 5x - 3/ x - 3

Trying to factor by splitting the middle term

2.1 Factoring 2x² - 5x - 3

The first term is, 2x² its coefficient is 2 .

The middle term is, -5x its coefficient is -5 .

The last term, "the constant", is -3

Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6

Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -5 .

-6 + 1 = -5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 1

2x² - 6x + 1x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

2x • (x-3)

Add up the last 2 terms, pulling out common factors :

1 • (x-3)

Step-5 : Add up the four terms of step 4 :

(2x+1) • (x-3)

Which is the desired factorization

Canceling Out :

2.2 Cancel out (x-3) which appears on both sides of the fraction line.

Final result :

2x + 1

Answer:

9m

Step-by-step explanation:

A parallelogram you have listed has the following side lengths:
1.8m and 5m.

First, we need to understand the formula and simply comprehend it.
In this case, we're dealing with an area of a quadrilateral which is a four-sided shape.

The area is base times height.

You will simply need to do 1.8 x 5 = m

That is pretty simple. You need to setup a question like this:

1.8

x 5

____

 9.0

Remember you need to move the decimal point when you're done mulitplying. This case 9.0 is simply 9 by itself.

Answer:

$16.49

Step-by-step explanation:

The closest option to $16.50 is $16.49, so that is the answer. I hope this helps!