What is the probability that Annie rolls a sum of 6 and José rolls doubles?

Answer:

[tex]sin\theta = \sqrt{1-C^2}[/tex]

[tex]tan\theta = \dfrac{\sqrt{1-C^2}}{C}[/tex]

[tex]cot\theta = \dfrac{C}{\sqrt{1-C^2}}[/tex]

[tex]sec\theta = \dfrac{1}{C}}[/tex]

[tex]cosec\theta = \dfrac{1}{\sqrt{1-C^2}}[/tex]

Step-by-step explanation:

Given that:

[tex]\theta[/tex] is an angle in a right angled triangle.

and [tex]cos\theta = C[/tex]

To find:

To draw the triangle and write other five trigonometric functions in terms of C.

Solution:

We know that cosine of an angle is given by the formula:

[tex]cosx =\dfrac{Base}{Hypotenuse}[/tex]

Here, we are given that [tex]cos\theta = C[/tex] OR

[tex]cos\theta = \dfrac{C}{1}[/tex]

i.e. Base = C and Hypotenuse of triangle = 1

Please refer to the right angled triangle as per given statements.

[tex]\triangle PQR[/tex], with base PR = C units

and hypotenuse, QP = 1 unit

[tex]\angle R[/tex] is the right angle.

Let us use pythagorean theorem to find the value of perpendicular.

According to pythagorean theorem:

[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}[/tex]

[tex]1^{2} = C^{2} + QR^{2}\\\Rightarrow QR = \sqrt {1-C^2}[/tex]

[tex]sin\theta = \dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin\theta = \dfrac{\sqrt{1-C^2}}{1}\\\Rightarrow sin\theta = \sqrt{1-C^2}[/tex]

[tex]tan\theta = \dfrac{Perpendicular}{Base}\\\Rightarrow tan\theta = \dfrac{\sqrt{1-C^2}}{C}[/tex]

[tex]cot\theta = \dfrac{Base}{Perpendicular}\\\Rightarrow cot\theta = \dfrac{C}{\sqrt{1-C^2}}[/tex]

[tex]sec\theta = \dfrac{Hypotenuse}{Base}\\\Rightarrow sec\theta = \dfrac{1}{C}}[/tex]

[tex]cosec\theta = \dfrac{Hypotenuse}{Perpendicular}\\\Rightarrow cosec\theta = \dfrac{1}{\sqrt{1-C^2}}[/tex]

Answer:

? = 26 in

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

?² = 24² + 10² = 576 + 100 = 676 ( take the square root of both sides )

? = [tex]\sqrt{676}[/tex] = 26

Answer:

26 inch

Step-by-step explanation:

unknown side can be found using Pythagorean theorem

a*a+b*b=c*c

24*24+10*10=c*c

576+100=c*c

√676=c

c=26inche

Answer:

a. -17 -9n

Step-by-step explanation:

Question written clearly below:

Which answer choice is equivalent to the expression below?

-7(2+n)+1/3(-9-6n)

a.-17 -9n

b, -14-12n

c. 11+5n

d. 14+2n

Solution

-7(2+n)+1/3(-9-6n)

Open parenthesis

(-14-7n)+(-9/3-6/3n)

= -14-7n+(-3-2n)

= -14-7n-3-2n

Collect like terms

= -14-3-7n-2n

= -17-9n

The answer is option a. -17 -9n

Answer:

-17 -9n

Step-by-step explanation:

i got it right on edge

Question

If the CP of 15 articles equals to the SP of 12 articles, find the gain percent.

Answer:

gain percent = 25%

Step-by-step explanation:

To solve the question given, we will follow the steps below:

gain%  =   [tex]\frac{s.p - c.p}{c.p}[/tex]  ×    100%

But from the question;

"CP of 15 articles equals to the SP of 12 articles", this implies that

15 c.p  =  12 s.p

s.p = 15c.p  /   12

s.p  = [tex]\frac{15 c.p}{12}[/tex]       =   [tex]\frac{5c.p}{4}[/tex]

s.p  =  [tex]\frac{5c.p}{4}[/tex]

substitute  s.p  =  [tex]\frac{5c.p}{4}[/tex]   into the formula

gain%  =   [tex]\frac{s.p - c.p}{c.p}[/tex]  ×    100%

      =[tex]\frac{\frac{5c.p}{4} - c.p }{c.p}[/tex]     ×    100%

       =  [tex]\frac{\frac{5c.p - 4c.p}{4} }{c.p}[/tex]      ×    100%

  =   [tex]\frac{c.p}{4}[/tex]   ÷   c.p      ×    100%

= [tex]\frac{c.p}{4}[/tex]     ×   [tex]\frac{1}{c.p}[/tex]    ×    100%

=   [tex]\frac{1}{4}[/tex]  ×    100%

=  25 %

Answer:

The total revenue will decrease.

Step-by-step explanation:

The price elasticity of demand is 1.30 that shows that change in the quantity of tomatoes is greater than the change in the price of tomatoes. The hail storm will decrease the quantity (supply) of tomatoes. However, this decrease in supply will increase the price but the ratio of change in quantity will be more than the ratio of change in price. Thus, total revenue from tomatoes will also fall.

Answer:

Test statistic = 3.863

Step-by-step explanation:

We are told that most adults would erase all of their personal information online if they could. Since the word "most" is used, it means more than 50% or 50 percent.

So, p_o = 0.5

Also, we are told that 58 % of them would erase all of their personal information online if they could.

Thus, p^ = 0.58

Number of randomly selected adults; n = 583

The test statistic formula for hypothesis test for proportion is given by:

z = (p^ - p_o)/[√[p_o(1 - p_o)/n]

Plugging in the relevant values, we have;

z = (0.58 - 0.5)/[√[0.5(1 - 0.5)/583]

z = 0.08/0.02070788416

z = 3.863

Answer:

B. √16 × √6

C. √96

Step-by-step explanation:

4√6

4 can be written as a square root.

4 = √16

√16 × √6

The square roots are multiplied, they can be written under one whole square root.

√(16 × 6)

√96

Answer:

see explanation

Step-by-step explanation:

(1)

0.5 = [tex]\frac{5}{10}[/tex] = [tex]\frac{1}{2}[/tex]

(2)

3.8 = 3 [tex]\frac{8}{10}[/tex] = [tex]\frac{10(3)+8}{10}[/tex] = [tex]\frac{30+8}{10}[/tex] = [tex]\frac{38}{10}[/tex] = [tex]\frac{19}{5}[/tex]

Answer:

84 km... Mark me as BRAINLIEST

Step-by-step explanation:

Refer to the pic...

Hope it helped you!

Step-by-step explanation:

Since it takes 6 trips to cover 24 km -

1 trip = 24/6

Therefore 1 trip is -

4 km

Now, the distance for 21 trips is -

21*4 = 84

Therefore, Brad has walked -

84 km

HOPE YOU FIND THIS HELPFUL

Answer:

20>4

Step-by-step explanation:

12-3 forget about the x 12-3=9 . 9+11=20

(17-9)=8 . 8-4 =4

so your answer is correct

Answer:Subtract 3x from 12x

9 x + 11 > 4 x − ( 17 − 9 x )

Simplify  4 x − ( 17 − 9 x ) .

9 x + 11 > 13 x − 17

Move all terms containing  x  to the left side of the inequality.

−4 x + 11 > − 17

Move all terms not containing  x  to the right side of the inequality.

− 4 x > − 28

Divide each term by  − 4  and simplify

x < 7

Interval Notation:

( − ∞ , 7 )

Answer:

c. -1; no

Step-by-step explanation:

The inner product of 2 vector (a,b) and (c,d) is:

(a,b)(c,d) = a*c + b*d

If the inner product is equal to 0,  the vectors are perpendicular.

So, the inner product of (5,2) and (-3,7) is equal to:

 (5, 2)×(-3, 7) = 5(-3) + 2(7) = -1

The inner product is -1, it is different to 0, so the vectors are not perpendicular.

Answer:

This means volume of the larger canister is 8 times more than volume of the smaller canister.

This means surface area of the larger canister is 4 times greater than volume of the smaller canister.

Step-by-step explanation:

Smaller canister

Diameter=9cm

Radius=diameter/2

=9/2=4.5cm

Height=12cm

Larger canister (double of the smaller canister)

Radius=4.5*2=9cm

Height=12*2=24cm

Volume=πr^2h

Surface area=2πrh + 2πr^2

Volume of smaller canister=πr^2h

=3.14*(4.5)^2*12

=3.14*20.25*12

=763.02

Surface area of the smaller canister=2πrh + 2πr^2

=2*3.14*4.5*12 + 2*3*14*(4.5)^2

=339.12 + 127.17

=466.29

Volume of larger canister=πr^2h

=3.14*(9)^2*24

=3.14*81*24

=6104.16

Surface area of larger canister=2πrh + 2πr^2

=2*3*14*9*24 + 2*3.14*(9)^2

=1356.48 + 508.68

=1865.16

Compare smaller and larger volume of the canister:

Volume if larger/volume of smaller

=6104.16/763.02

=8

This means volume of the larger canister is 8 times more than volume of the smaller canister

Compare surface area of larger and smaller canister:

Surface area of larger canister/surface area of smaller canister=1865.16/466.29

=4

This means surface area of the larger canister is 4 times greater than volume of the smaller canister

Answer:

Yeah, what she said above.

Step-by-step explanation:

Answer:

[tex]\boxed{\sf \ \ YES \ \ }[/tex]

Step-by-step explanation:

Hello

let's say that the price of the book was x

the price after a 20% discount is x - 20%*x = x*(1-20%)=x*(1-.20)=0.8*x

and this is $72 so we can write that

0.8*x=72

and then divide by 0.8 both parts

x = 72/0.8=90

So the list price value of the book is $90

and we can verify as 90 - 20%*90 = 90 - 18 = 72

Hope this helps

Hi king,

Write [tex]4x^{2} + 16x - 9[/tex] in vertex form:

f(x)=[tex]4x^{2} + 16x - 9[/tex]

f(x)=[tex]4(x+2)^{2} -25[/tex]

Write [tex]5x^{2} - 10x + 4[/tex] in vertex form:

g(x)=[tex]5x^{2} - 10x + 4[/tex]

g(x)=[tex]5(x-1)^{2} -1[/tex]

Have a great day.

Answer:

3/2

Step-by-step explanation:

● (-3/8) ÷(-1/4)

Flip the second fraction by putting 1 instead 4 and vice versa.

● (-3/8)* (-4/1)

-4 over 1 is -4 since dividing by 1 gives the same number.

● (-3/8)*(-4)

Eliminate the - signs in both fractions since multiplying two negative numbers by each other gives a positive number.

●( 3/8)*4

● (3*4/8)

8 is 2 times 4

● (3*4)/(4*2)

Simplify by eliminating 4 in the fraction.

● 3/2

The result is 3/2

Answer:

TW = 3.18 yd (Approx)

Step-by-step explanation:

Given:

TV = 6 yd

∠TYW = 32°

∠TWV = 90°

Find:

TW

Computation:

Using trigonometry application.

TW / TV = Sin 32°

TW / 6 = 0.53

TW = 3.18 yd (Approx)

Answer: S = 8.9 or just 9

Step-by-step explanation:

Answer: C) Plane: 235 km/h, Wind: 24 km/h

Step-by-step explanation:

Given that :

Average Speed while flying with a tailwind = 259km/hr

Return trip = 211km/hr

Let the speed of airplane = a, and wind speed = w

Therefore ;

Average Speed while flying with a tailwind = 259km/hr

a + w = 259 - - - (1)

Return trip = 211km/hr

a - w = 211 - - - (2)

From (2)

a = 211 + w

Substitute the value of a into (1)

a + w = 259

211 + w + w = 259

211 + 2w = 259

2w = 259 - 211

2w = 48

w = 48/2

w = 24km = windspeed

Substituting w = 24 into (2)

a - 24 = 211

a = 211 + 24

a = 235km = speed of airplane

Answer:

2 triangles are possible.

Step-by-step explanation:

Given

a=6

b=10

[tex]\angle[/tex]A=33°

To find:

Number of triangles possible ?

Solution:

First of all, let us use the sine rule:

As per Sine Rule:

[tex]\dfrac{a}{sinA}=\dfrac{b}{sinB}[/tex]

And let us find the angle B.

[tex]\dfrac{6}{sin33}=\dfrac{10}{sinB}\\sinB = \dfrac{10}{6}\times sin33\\B =sin^{-1}(1.67 \times 0.545)\\B =sin^{-1}(0.9095) =65.44^\circ[/tex]

This value is in the 1st quadrant i.e. acute angle.

One more value for B is possible in the 2nd quadrant i.e. obtuse angle which is: 180 - 65.44 = [tex]114.56^\circ[/tex]

For the value of [tex]\angle B = 65.44^\circ[/tex], let us find [tex]\angle C[/tex]:

[tex]\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow 33+65.44+\angle C = 180\\\Rightarrow \angle C = 180-98.44 = 81.56^\circ[/tex]

Let us find side c using sine rule again:

[tex]\dfrac{6}{sin33}=\dfrac{c}{sin81.56^\circ}\\\Rightarrow c = 11.02 \times sin81.56^\circ = 10.89[/tex]

So, one possible triangle is:

a = 6, b = 10, c = 10.89

[tex]\angle[/tex]A=33°, [tex]\angle[/tex]A=65.44°, [tex]\angle[/tex]C=81.56°

For the value of [tex]\angle B =[/tex][tex]114.56^\circ[/tex], let us find [tex]\angle C[/tex]:

[tex]\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow 33+114.56+\angle C = 180\\\Rightarrow \angle C = 180-147.56 = 32.44^\circ[/tex]

Let us find side c using sine rule again:

[tex]\dfrac{6}{sin33}=\dfrac{c}{sin32.44^\circ}\\\Rightarrow c = 11.02 \times sin32.44^\circ = 5.91[/tex]

So, second possible triangle is:

a = 6, b = 10, c = 5.91

[tex]\angle[/tex]A=33°, [tex]\angle[/tex]A=114.56°, [tex]\angle[/tex]C=32.44°

So, answer is : 2 triangles are possible.

Answer: Option D

Step-by-step explanation:

Answer:

✔ D.

Step-by-step explanation:

E2021

Answer:

This question is about half-angle trigonometric identities, which are specific formulas that help us to solve problems with half-angles.

In this case, if you need a half-angle identity for the tangent, you could use

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

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

[tex]tan(\frac{x}{2})=\sqrt{\frac{1-cos(x)}{1+cos(x)} }[/tex]

Therefore, the right identity must satisfy the expression above.

Answer:

In picture

Step-by-step explanation:

Answer:

[tex]x >4[/tex]

Step-by-step explanation:

[tex]x+3>19-3x[/tex]

Add 3x and -3 on both parts.

[tex]x+3+3x-3>19-3x+3x-3[/tex]

Combine like terms.

[tex]x+3x>16[/tex]

[tex]4x >16[/tex]

Divide 4 on both parts.

[tex]\frac{4x}{4} > \frac{16}{4}[/tex]

[tex]x >4[/tex]

Answer:

C. 1/3

Step-by-step explanation:

Given:

Number of colors listed (Successful Outcome)

Red 1

Yellow 1

Purple 1

Total or Possible outcome= 3

Required:

What is the theoretical probability that it stops on the red sector on the last spin?

Formula:

Probability= Successful outcome ÷ Possible outcome

Solution:

Probability of the spinner stoping on red.

Probability= Successful outcome ÷ Possible outcome

Probability=1÷3

Probability=1/3

Hope it helps ;) ❤❤❤

The theoretical probability that spinner stops on the red sector on the last spin is option (C)  [tex]\frac{1}{3}[/tex]

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given,

A spinner is separated into 3 equal parts.

Then Mary spins the spinner 6 times.

What is the theoretical probability that it stops on the red sector on the last spin.  So only last spin is important, outcomes of first 5 spin is not important and it is independent.

Probability = Number of favorable outcome / Number of Total outcome

Probability (Red sector) =  [tex]\frac{1}{3}[/tex]

Hence, the theoretical probability that spinner stops on the red sector on the last spin is  option (C)  [tex]\frac{1}{3}[/tex]

Learn more about Probability here

https://brainly.com/question/11234923

#SPJ2

Answer:

The correct option is;

We cannot infer a cause and effect relationship because we do not have a control group

Step-by-step explanation:

The treatment in research involves giving stimulus known as treatment to a group or portion of the sample which are then known as the treatment group while the remaining portion of the the sample are exempted from the stimulus. A successful treatment manipulation is one where members of the treatment group perform higher in the measured metrics of the research than members of the control group.

Given that the researchers gathered data from a random sample of drivers and measurement of several variables  including the explanatory  variable of the of the research without subjecting a sample to a treatment or having a control group we cannot infer a cause and effect relationship as there are no control group

Answer: A = (1m/3)^2 or A= (1/3)^2 m

Or A= (1/3)(1/3)

Step-by-step explanation:

No choices given, but it will look like one these answers.

The area of a square that has a side length of 1/3 meter is 1/9 square meter.

I hope this helps you.

Answer:

a= (1/3)(1/3)

Step-by-step explanation:

Answer:

The answer is B.

Step-by-step explanation:

You solve it using the number line. Starting with the point at 3/5 then, you have to go backwards by 7 steps which is -4/5.

You can ignore the denorminator as all the denorminators are the same.

Answer:

-4/5

Step-by-step explanation:

The parentheses can be removed immediately since they do not affect the outcome in this problem.  

then we have:

3/5 - 7/5 = -4/5

Answer:

37.8 m

Step-by-step explanation:

The computation of the distance is shown below:

In triangle ADE

[tex]AD^2 = AE^2 + DE^2 \\\\ AD^2 = 5^2 + 3^2 \\\\ AD^2 = 34[/tex]

AD = 5.8

Now the distance walked after completing his edging is

Distance = AD + AB + BC + CD

= 5.8 + 12 + 5 + 15

= 37.8 m

We simply added these four sides so that the correct distance could arrive

Hence, the distance walked after completing his edging is 37.7

Answer:

The equation is  y = -x + 4

Step-by-step explanation:

This is a very trivial exercise:

The general equation of a line is given by:

y - y₁ = m(x - x₁)

where m = slope of the linear graph

From the given graph, it can be observed that the coordinate (x₁, y₁) and (x₂, y₂) are (0, 4) and (4, 0)

The slope, m = (y₂ - y₁)/(x₂ - x₁)

m = (0 - 4)/(4 - 0)

m = -4/4

m = -1

Substituting the values of (x₁, y₁) = (0, 4) and m = -1 into the general equation:

y - y₁ = m(x - x₁)

y - 4 = -1 (x - 0)

y - 4 = -x

y = -x + 4

Answer:

1. 7

2. 6

[tex]3. 3\sqrt{5}[/tex]

4?

5. [tex]8\sqrt{10}[/tex]

6.[tex]5\sqrt{3}[/tex]

7. [tex]-1+\sqrt{3}[/tex]

Step-by-step explanation:

1. [tex]\sqrt{7} *\sqrt{7} =\sqrt{49}=7[/tex]

2. [tex]\sqrt{18}*\sqrt{2} =\sqrt{36}=6[/tex]

3.[tex]\sqrt{45}=\sqrt{9^{2}*5 }=3\sqrt{5}[/tex]

4. here there are two cases

[tex]\sqrt{\frac{50}{5} }=\sqrt{10}[/tex]

[tex]\frac{\sqrt{50} }{5} =\frac{5\sqrt{2} }{5} =\sqrt{2}[/tex]

5. [tex]2\sqrt{2} *4\sqrt{5} =8\sqrt{10}[/tex]

6. [tex]\sqrt{48}- \sqrt{12} =4\sqrt{3} -2\sqrt{3} =2\sqrt{3}[/tex]

7. [tex](2-\sqrt{3} )(1+\sqrt{3} )=2+2\sqrt{3}-\sqrt{3} -3=-1+\sqrt{3}[/tex]