A circle has a circumference of 18. It has an arc of length 6.
What is the central angle of the arc, in degrees?
​

Answer:

6 or 9

Step-by-step explanation:

Let the number of green pens =x

There are three more red pens, therefore:

The number of red pens =x+3

Total Number of pens =x+x+3=2x+3

The probability that sheila will take two pens of the same color = [tex]\frac{17}{35}[/tex]

Therefore, we have that:

[tex]\text{P(two red pens)}=\dfrac{x+3}{2x+3} \times \dfrac{x+2}{2x+2}\\\\P(RR)=\dfrac{(x+3)(x+2)}{(2x+3)(2x+2)}[/tex]

[tex]P$(two green pens$)=\dfrac{x}{2x+3} \times \dfrac{x-1}{2x+2}\\\\P(GG)=\dfrac{x(x-1)}{(2x+3)(2x+2)}[/tex]

Therefore, the probability that sheila will take two pens of the same color

=P(RR)+P(GG)

[tex]\dfrac{(x+3)(x+2)}{(2x+3)(2x+2)}+\dfrac{x(x-1)}{(2x+3)(2x+2)}=\dfrac{17}{35}\\\dfrac{(x+3)(x+2)+x(x-1)}{(2x+3)(2x+2)}=\dfrac{17}{35}\\[/tex]

Cross multiply

[tex]35[(x+3)(x+2)+x(x-1)]=17[(2x+3)(2x+2)]\\35[x^2+3x+2x+6+x^2-x]=17[4x^2+4x+6x+6]\\35[2x^2+4x+6]=17[4x^2+10x+6]\\70x^2+140x+210=68x^2+170x+102\\70x^2-68x^2+140x-170x+210-102=0\\2x^2-30x+108=0[/tex]

Factorizing, we have:

[tex]2(x-6)(x-9)=0\\x-6=0$ or $x-9=0\\x=6$ or 9[/tex]

Therefore, the two different numbers of green pens that could be in the box are 6 or 9.

Answer:

11.11%

Step-by-step explanation:

So the question is:

$180 * (x)% = $y

Therefore $180 - $y = $160

Now:

180 - 160 = 20

Therefore; $20 is the discount

Now per cent of discount:

20/180 * 100 = 11.111111111111111111111%

therefore: per cent of discount is 11.11% (rounded to two decimal place)

Answer:

11.11 %

Step-by-step explanation:

Costing Price = Rs 180

Selling Price = Rs 160

Discount = C.P - S.P

=> 180-160

=> Rs 20

In %age:

=> [tex]\frac{20}{180} * 100[/tex]

=> 11.11 %

Answer:

Add and subtract the second term to the expression and factor by grouping .

(x-1)(x+1)(x-3)(x+2)

Answer:

(x-1)(x-3)(x+1)(x+2)

Step-by-step explanation:

x⁴-x³-7x²+x+6=

x⁴-x³-x²+x -6x²+6=

x³(x-1)-x(x-1)-6(x²-1)=

x³(x-1)-x(x-1)-6(x-1)(x+1)=

(x-1)(x³-x-6x-6)=

(x-1)(x³-3x²+3x²-9x+2x-6)=

(x-1)(x-3)(x²+3x+2)=

(x-1)(x-3)(x²+x+2x+2)=

(x-1)(x-3)(x+1)(x+2)

RIGHT SIDE

3: Simplification

4: Subtraction property of equality

LEFT SIDE

4: 6x -7 + 7 = 12 + 7

7: x=19/6

Hope this helped!

<!> Brainliest is appreciated! <!>

Simplification

[tex]6x-7+7=12+7[/tex],  addition property of equality

[tex]x =\frac{19}{6}[/tex]

According to the given question.

We have a equation

[tex]4x-7=-2x+12[/tex]

The following steps which are required to solve the above equation are

Step 1:

[tex]4x - 7 = -2x + 12[/tex]   (given)

Step 2:

[tex]4x - 7+ 2x = -2x + 12 + 2x[/tex]    (addition property of equality)

Step 3:

[tex]4x - 7 + 2x = -2x +12+2x\\\implies 6x-7 = 12[/tex] (simplification)

Step 4:

[tex]6x -7 + 7 = 12 +7[/tex]                 (addition property of equality)

Step 5:

[tex]\implies 6x = 19[/tex]                                  (simplification)

Step 6:

[tex]\frac{6x}{6} =\frac{19}{6}[/tex]                                      ( division property of equality)

Step 7:

[tex]x = \frac{19}{6}[/tex]                                            (simplification)

Hence, the value of x in [tex]4x-7 = -2x + 12[/tex] is [tex]\frac{19}{6}[/tex].

Find out more information about addition, subtraction, and division property of equality here:

https://brainly.com/question/13130806

#SPJ3

Answer:

Here we want to create a histogram of:

Number of houses Vs day.

First you need to create a rectangular coordinate axis.

In the x-axis you will divide the days as:

day 1, day2, day3 etc

in the y-axis you will measure the number of houses visited.

then, for the first day our height will be 12 units

for the second day, our height will be 28 units...

and so on.

Remember that for histograms you need to use columns.

Then, our histogram will look like:

Answer:

2 solutions:

(-2.899, 0.899) and (6.899, -8.899)

Step-by-step explanation:

x+y=2

y=-x+2

y=1/4x²+3

Graph both equations into graphing calculator

Graph in attachment shows solutions

Answer:

21

Step-by-step explanation:

Answer:

6.3

Step-by-step explanation:

If you cut a line through a rectangle diagonally, you form two right triangles.  Since you have a right triangle, you can use the Pythagorean Theorem.  The diagonal line will be the hypotenuse, and the width will be one of the legs.

a² + b² = c²

(3)² + b² = (7)²

9 + b² = 49

b² = 40

b = √40

b = 6.3

The length of the envelope is 6.3 inches.

Answer:

The probability for the dependent and the independent picky eater and not picky is similar in case of dependent variable and is different in case of independent variable.

Step-by-step explanation:

Independent variable is defined as the variables that are being manipulated, changed, or altered in a specific experiment or research in order to see its effect on the dependent variable.

The dependent variable is defined as the variable that is being measured or tested in a particular experiment or research by the investigator.

In the question above, as mentioned in the image or attachment, the probability of dog being picky or non-picky eater can be both dependent and independent in the different scenarios.

Answer:

f(2)=g(0) and f(0)=g(4)

3rd option for the second pic

Answer:

Step-by-step explanation:

Step 1: Create a Survey

Step 2: Administer the Survey

Step 3: Collect responses.

Step 4: Organize responses - Since the data is bivariate I'd like to see them explain that they would maybe use a frequency table to organize this data.  

Step 5: Analysis

Then he can look at how to explain the organization of their data - can we use a chart? If I am using a scatter plot, how do I find the line of best fit? How do I correlate data, etc?

The step to analyze the collected data include plotting the data on an histogram

From the question, we understand that the data has already been gathered.

The next step is to analyze the collected data.

This can be done in several ways.

One of them is as follows:

Read more about data analysis at:

https://brainly.com/question/15380707

#SPJ2

Answer:

The product of the polynomials is 6p³ + 29p² + 22p - 21

Step-by-step explanation:

(2p + 7)(3p² + 4p - 3)

Use the foil method to multiply.

6p³ + 8p² - 6p + 21p² + 28p - 21

Combine like terms. Make sure you put the equation in standard form. This means that the exponential numbers will be ordered in descending form.

6p³ + 29p² + 22p - 21

Hey there! :)

Answer:

x = 3.

Step-by-step explanation:

Given:

[tex](8x-8)^{\frac{3}{2} } = 64[/tex]

Rule of fractions in exponents:

Numerator- power

Denominator- root

Take the 2/3 root of both sides:

[tex](8x-8) = 64x^{\frac{2}{3} }[/tex]

Simplify [tex]64x^{\frac{2}{3} }[/tex]

Cube root of 64 = 4

4² = 16.

Therefore:

8x - 8 = 16

Add 8 to both sides:

8x = 24

Divide both sides by 8:

x = 3.

Answer:

x=3

Step-by-step explanation:

Not sure how to explain

Answer: x = 3

Step-by-step explanation:

The area of a triangle is 1/2bh.  Thus, the area of the triangle is 30.  The area of a rectangle is lw.  Thus it is 10x here.  Thus, 10x = 30 and x = 3.

Hope it helps <3

Answer:

x = 3

Step-by-step explanation:

To find the area the area of a triangle is 1/2 b×h

that will be 1/2× 5×12 = 30

since the area of the triangle is equal to the area of the rectangle, and the area of a rectangle is l×b so l= x ; b= 10 so x × 10 = 30

= 10x= 30 divide both sides by 10 = 3

so x = 3

Answer:

sequence B only

Step-by-step explanation:

Reflect around point N and then translate to the left the reflected figure from N to point B

Answer:

c≤

Step-by-step explanation:

hypotenuse=√(a²+b²)=√(5²+6²)=√(25+36)=√61

cosθ=5/√61=5/√61× (√61/√61)=5√61/61

Answer:

[tex]6 \sqrt{61} \div 61[/tex]

is ans

Step-by-step explanation:

given, a=5 and b=6

as the refrence angle is thit

p=6 and b= 5

[tex]now \: h \: = \sqrt{p {}^{2} + b {}^{2} } [/tex]

[tex] = \sqrt{6 { }^{2} + 5 {}^{2} } [/tex]

[tex] \sqrt{61} = [/tex]

therefore h

[tex] = \sqrt{61} [/tex]

now cos thita =b/h

therefore cos thita=

[tex]6 \sqrt{61} \div 61[/tex]

...is ans..

Answer:

9 metros bajo el nivel del mar

Step-by-step explanation:

Aquí, tenemos un autobús que está a 12 metros bajo el nivel del mar.

Ahora, el autobús ganó algo de altura y subió 3 metros hacia arriba Debemos entender que el autobús todavía está bajo el nivel del mar pero a un nivel más alto en relación con el fondo del mar.

Por lo tanto, la altura del autobús sería + 3 + (-12) = 3-12 = -9 Esto muestra que el autobús todavía está a 9 metros bajo el nivel del mar.

factors of 51 are  1, 3, 17,  51

Answer:

1 × 51 = 51

3 × 17 = 51

_________

1, 51, 3, 17 are all factors of 51!

51 is composite.

Answer:

Undefined

Step-by-step explanation:

Since you said to find the square root of "-25" the answer is undefined because you cannot square root a negative number.

Answer:

18-5i

Step-by-step explanation:

I can't see the answer choices but all you have to do is simplify this equation.

18-√-25

What is the square root of -25?

Well first we make the -25 into 25 because we can't do anything with a negative.

So square root of 25 is 5

Now plug 5 into the equation

18-5

Then multiply i to 5 because we're not sure what the exact value of 18-√-25 is.

Hope this Helps!

Answer:

0.24

Step-by-step explanation:

Given the points (10,2.4) (15, 3.6) (17.5, 4.2)

The unit rate is the slope of the line joining any of the two points.

Using points (10,2.4)  and (15, 3.6)

[tex]Slope, m=\dfrac{3.6-2.4}{15-10} \\=\dfrac{1.2}{5} \\\\=\dfrac{6}{25}[/tex]

=0.24

Using points (10,2.4)  and (17.5, 4.2)

[tex]Slope, m=\dfrac{4.2-2.4}{17.5-10} \\=\dfrac{1.8}{7.5} \\\\=\dfrac{6}{25}\\=0.24[/tex]

Therefore, the unit rate for each point is 0.24

Answer:

The original price is 170

Step-by-step explanation:

Let x be the original price

x* .20 is the decrease

x - .20x = new price

.80x = new price

.8x = 136

Divide each side by .8

.8x/.8 = 136/.8

x =170

The full price is represented by 100%. If this computer was decreased by 20%, so it worth 80% now.

So, we can make a rule of three: 80% value is equals to 136, how much is 100%?

80% ------------ 136

100% ----------- x

Let's multiply "making a x":

[tex]80x = 136\cdot 100\\80x = 13.600\\x = \frac{13600}{80} \\x = 170[/tex]

Therefore, the price before the decrease was £170.

Answer: in 340 million square miles there are 8.808 x 10^10 hectares

Step-by-step explanation:

Answer:

Hope this helps!

Step-by-step explanation:

Answer:

6 lions

Step-by-step explanation:

l:g:p= 3:5:11 ratio

4(3x+5x)+2*11x= 108 legs

32x+22x= 108

54x= 108

x= 2

Lions= 2*3= 6

Ratio of Giraffes : Lions : Penguins = 3 : 5 : 11

Giraffes = 3x

Lions = 5x

Penguins = 11x

Giraffes = 4 legs

Lions =  4 legs

Penguins = 2 legs

4(3x) + 4(5x) + 2(11x) = 108

12x + 20x + 22x = 108

54x = 108

x = 108 ÷ 54 = 2

Number of lions = 5x = 5(2) = 10

Answer:  10 lions

Answer:

see below

Step-by-step explanation:

$11.60 for $5

1. Find the rate.

$11.60 divided by $5= $2.32

2. 1 gemstone= $2.32

Your anwser should be 1 over $2.32 or $2.32 over 1 depending on how you want it.

Answer:

D) x/11.60= 1/5

Step-by-step explanation:

Answer:

La expresión algebraica que representa la compra de los auriculares es [tex]c = 105.6\cdot n[/tex], existe una proporcionalidad directa.

Step-by-step explanation:

Existe un proporcionalidad directa, pues el coste total de importación aumenta conforme aumenta la cantidad de auriculares a importar. Esto es:

[tex]c \propto n[/tex]

[tex]c = k\cdot n[/tex]

Donde:

[tex]n[/tex] - Cantidad de auriculares a importar, adimensional.

[tex]c[/tex] - Coste total de importación, medido en pesos.

[tex]k[/tex] - Constante de proporcionalidad, medido en pesos.

La constante de proporcionalidad es igual al coste unitario del auricular más el impuesto de arancel, es decir:

[tex]k = 1.10\cdot (\$\,96)[/tex]

[tex]k = \$\,105.6[/tex]

Entonces, la expresión algebraica que representa la compra de los auriculares es:

[tex]c = 105.6\cdot n[/tex]

Answer:

The notebooks are still hazardous because the Curies didn't use protective equipment (nor did they have it) and the close proximity of the radioactive isotopes allowed for spreading of radioactivity. Since Radium-226 was kept in bottles and drawers in the Curies' home, it was in close proximity to their items. This allowed for Radium-226 to radiate to other items. In turn, those items absorbed the radiation and become radioactive. Today, Marie Curie is buried under a lead-lined coffin and her belongings can be visited ONLY with protective gear and signing a liability form.

Step-by-step explanation:

Answer:

The answer is given below

Step-by-step explanation:

The addition postulate for line segment states that if we have points A, C and a point B on line AC, The distance between points A and C can be given as:

AC = AB + BC

Point A is at -6, point B is at -1, point C is at +2 and point D is at point 8.

Therefore using line segment postulates:

AD = AB + BC  + CD

But AB = -1 - (-6)= -1 + 6 = 5

BC = 2- (-1) = 2 +1 = 3

CD = 8 - (+2) = 8 - 2 = 6

Also AD = 8 - (-6) = 8 + 6 = 14

To prove AD = AB + BC  + CD

AD = 5 + 3 + 6 = 14

Answer:

D) 2

Step-by-step explanation:

Use the following slope formula:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Let:

(x₁ , y₁) = (4 , 1)

(x₂ , y₂) = (1 , -5)

Plug in the corresponding numbers to the corresponding variables:

m = (-5 - 1)/(1 - 4)

Simplify. Remember to follow PEMDAS. First subtract, then divide:

m = (-5 - 1)/(1 - 4)

m = (-6)/(-3)

m = 2

D) 2 is your answer.

~

Answer:

first one

Step-by-step explanation:

Answer:

From Dial it, we have plans of $16 per 2 gb.

then the ratio is (number of gb you get):price

in this case:

2:16 or we can reduce it to 1:8

this means that per each Gigabyte, you pay 8 dollars. 1:8

Ring Ring has plans of $9 per 1gb

then the ratio of gb to Dollars is 1:9

And the ratio between the prices of the companies is: 8 to 9 or 8:9

which means that in one company you get one thing for 8, while in the other company you get the same thing for 9.

Answer:

Dial it Up charges $32 for 4 gigabytes, and Ring Ring charges $36 for the same amount of data. The difference of the plan prices is $36 – $32 = $4.