There are only green pens and red pens in the box.There are three more red pens than green pens in the box.Sheila is going to take at random two pens from the box.The probability that sheila will take two pens of the same colour is 17/35.Work out the two different numbers of green pens that could be in the box.

Answers

Answer 1

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.


Related Questions

what is the answer? The 8x-1x confused me.
10+ 8x -1x ​

Answers

Answer:

7x + 10

Step-by-step explanation:

10 + 8x - 1x

Add or subtract like terms.

10 + (8 - 1)x

10 + (7)x

Rearrange.

7x + 10

Answer:

7x+10

Step-by-step explanation:

start by rewriting the problem

10+8x-1x

now, you can subtract 8x from 1x, because they are like terms

10+7x

arrange the terms

7x+10

now, that is your final answer!

Please answer it in two minutes

Answers

Answer:

21/20, or 1.05.

Step-by-step explanation:

In this case, the measure of angle R is the same as angle V.

To find the tangent of a triangle, you do opposite over adjacent.

So, the tangent of angle V is 21 / 20.

That means that tan(R) = 1.05.

Hope this helps!

This box has the same length, width, and height as the two tennis balls. Which expression gives the volume of the empty space encircling the tennis balls inside the box?

Answers

Formala : Times bottom row with side row with the height.

Example: A box has the same length, width, and height as two tennis balls.

Times the bottom row with side row with the height.

Please help me find the area of this shape

Answers

Answer:

44+50 =94 in²

Step-by-step explanation:

Trapezoid

A= 1/2h(b1+b2)

A= 1/2*4(7+15)

A=1/2*4(22)

A=44

Rectangle

A=l*w

A=5*10

A=50

44+50 =94 in²

I agree wit buddy above me

7.
2
a)
An open rectangular box measuring 28 cm by 20 cm
by 12 cm internally is made of woodcm thick. Find:
the capacity of the box in litres,
the volume of wood used in making the box,
the mass of the box if the density of the wood used is
1.25 g/cm3
b)
c)
J
28 82​

Answers

Answer:

1. Capacity of the box in Litres: 7.917L≈8L

2. Volume of wood used in making the box: 1197cm^3

3. The mass of the box: 1496.25g/cm^3

Step-by-step explanation:

1. 29×21×13=7917cm^3

7917cm^3 → 7.917dm^3→7.917L≈8L

2. Outside Volume: 29×21×13=7917cm^3

Inside Volume: 28×20×13=6720cm^3

7917-6720=1197cm^3

3. 1197×1.25=1496.25g/cm^3

which of the following sum in simplest form (radicals)

Answers

Answer:

9√2

Step-by-step explanation:

Easiest and fastest way is to plug it into a calc and calculate. If not, you will have to simplify the expressions to have a common root in order to add.

Answer:

92

Option C is the correct option.

Solution,

[tex] \sqrt{8} + 3 \sqrt{2} + \sqrt{32} \\ = \sqrt{2 \times 2 \times 2} + 3 \sqrt{2} + \sqrt{2 \times 2 \times 2 \times 2 \times 2} \\ = 2 \sqrt{2} + 3 \sqrt{2} + 2 \times 2 \sqrt{2} \\ = 2 \sqrt{2} + 3 \sqrt{2} + 4 \sqrt{2} \\ =( 2 + 3 + 4 )\sqrt{2 } \\ = 9 \sqrt{2} [/tex]

Hope this helps...

Good luck on your assignment..

if x= 3y-2/4, what is the value of y in terms of x?

Answers

Answer:

[tex]x = \frac{3y - 2}{4} [/tex]

Multiply through by 4

We have

[tex]3y - 2 = 4x[/tex]

Send 2 to the right side of the expression

That's

[tex]3y = 4x + 2[/tex]

Divide both sides by 3

That's

[tex] \frac{3y}{3} = \frac{4x + 2}{3} [/tex]

We have the final answer as

[tex] y = \frac{4x + 2}{3} [/tex]

Hope this helps you

Answer:

[tex]y = \frac{4x + 2}{3} [/tex]

Step by step explanation

[tex]x = \frac{3y - 2}{4} [/tex](Given)

Multiply by 4 on both sides:

[tex]4 \times x = \frac{3y - 2}{4} \times 4[/tex]

Calculate

[tex]4x = 3y - 2[/tex]

Add 2 on both sides

[tex]4x + 2 = 3y - 2 + 2[/tex]

[tex]4x + 2 = 3y[/tex]

[tex]3y = 4x + 2[/tex]

Divide both sides of the equation by 3

[tex] \frac{3y}{3} = \frac{4x + 2}{3} [/tex]

Calculate

[tex]y = \frac{4x + 2}{3} [/tex]

Hope this helps...

Good luck on your assignment..

The following box plot shows points awarded to dance teams that competed at a recent competition:

Answers

Answer:

top plot

Step-by-step explanation:

From the box and whisker plot, the smallest data point is 0 and the largest data point is 100

The median is 70

The only plot that has points at 0 and 100 is the first plot

Please answer ASAP! (I'll give brainliest and no need for explanation!)

Answers

Answer:

Median=3, Mean=2.333

Step-by-step explanation:

The MEDIAN is the middle number so you can either write all the values out in a row or look at the frequency of each number to find which would be in the middle.
Answer: 3

The MEAN is the average of all the numbers. To find it, add all the values together (remember to include as many of each value as the frequencies indicate) and then divide by the number of values you added together.
Answer:
0+0+1+1+1+1+1+1+1+1+2+2+2+2+3+3+3+3+3+3+3+3+3+3+4+4+4+4+4+4=70
2+8+4+10+6= 30
70/30= 2.333

OR

0x2=0
1x8=8
2x4=8
3x10=30
4x6=24
0+8+8+30+24= 70
2+8+4+10+6= 30
70/30=2.3333

Can any of y’all help me with this problem?

Answers

Answer:

90º clockwise rotation

Step-by-step explanation:

The rotation is a 270º counterclockwise rotation, since 270º rotation is

(x, y) → (y, -x)

F(1, 3) → (3, -1)

270º counterclockwise rotation is the same as a 90º clockwise rotation, so the answer is 90º clockwise rotation.  

90° clockwise rotation

Eight people rob a bank: * By what percent does the share of three robbers increase?

Answers

Answer:

Step-by-step explanation:

It increase by 2.3

Suppose you were deciding on a ticket price for a fundraiser dinner. There may be a temptation to continue to raise the ticket sales to increase the amount of money raised. Sounds like an okay idea to raise the most money possible for a charity. You may have heard of a guest speaker at a fundraising dinner where people are charged $100 a plate or more. What do you think is a realistic price for tickets? What are the consequences of raising the price $50 or $100 to $150 a plate or $200 a plate.

Answers

Answer:

$50 per ticket.

Step-by-step explanation:

Although it is tempting to keep raising the price for a higher profit, if you raise the price by too much, people will stop buying tickets and you will not gain as much money as you could have gotten with, say, $50 per plate.

The more you raise the price, the less tickets you can sell.

Hope this helps!

In a certain company, all employees are either beta employees or standard employees. In this company, 25% of the beta employees and 17% of the standard employees participate in the voluntary equity program. Let S be the number of standard employees. If there are 600 employees total, what is the value of S?

Answers

In addition to the question, the following conditions must be met:

(1) M > 100

(2) more than 130 employees participate in the voluntary equity program

Answer:

Value of A is 200

Step-by-step explanation:

In this scenario when we divide 100 by the percentage of each employee category we will get a proportion that the number of employees must obey.

This is illustrated below:

For Beta employees 100/25= 4

So the number of employees that are Beta must be divisible by 4

For Standard employees 100/17 = 5.882

Since fractions of employees cannot be obtained, in this case the number of employees must be a multiple of 100

Total employees are 600

The various combinations are:

1. Beta employees 500 and Standard employees 100

Survey participants= (0.25 * 500) + (0.17 * 100) = 142

Number of participants is okay as it is >130 but does not satisfy Standard employees being >100

2. Beta employees are 300 and Standard employees are 300

Survey participants = (0.25 * 300) + (0.17 * 300) = 126

This does not satisfy condition of survey participants >130

3. Beta employees 400 and Standard employees 200

Survey participants = (0.25 * 400) + (0.17 * 200) = 134

This satisfies conditions of >130 survey participants and Standard employees >100

So correct value of S is 200

which one is cheaper and why A bag of 3 kg potatoes for $3.49, or a bag of 5 kg potatoes for $4.99

Answers

Answer:

a bag of 5 kg potatoes for $4.99

Step-by-step explanation:

estimated $5.00 for 5 kg

5.00/5 = $1.00 per kg

Point M divides line segment AB, in the direction from A to B, in a ratio of 5 to 3. What value on the number line would indicate the location of point M? A = --6, B = 3

Answers

Answer:

The coordinates of point M is -0.375.

Step-by-step explanation:

Given that point A = -6 and point B = 3

Point M divides line segment AB in the direction from A to B in the ratio of 5 to 3 we have;

Length from A to M = 5/(5 + 3) × Length of segment AB

Given that length of segment AB = 3 - (-6) = 3 + 6 = 9, we have;

Length from A to M = 5/8 × 9 = 45/8 = [tex]5\frac{5}{8}[/tex] = 5.625

Therefore, the coordinates of M = -6 + 5.625 = -0.375 = -3/8

The coordinates of point M = -0.375.

Solve: -7 < 2x+5 < 7

Answers

Answer:

[tex] - 6 < x < 1[/tex]

Step-by-step explanation:

first things first:

[tex] - 7 < 2x + 5 \\ - 7 - 5 < 2x + 5 - 5 \\ - 12 < 2x \\ - 6 < x[/tex]

now:

[tex]2x + 5 < 7 \\ 2x + 5 - 5 < 7 - 5 \\ 2x < 2 \\ x < 1 [/tex]

now the intersection is:

[tex] - 6 < x < 1[/tex]

Write area square units answer

Answers

The rectangle is 13 units long by 6 units wide.

Area = Length x width

Area = 13 x 6  = 78 square units.

In your own words, tell how geometric sequences are related to exponential functions. Share your answer with the rest of the group.

Answers

Exponential functions are defined for all real numbers, and geometric sequences are defined only for positive integers. Another difference is that the base of a geometric sequence (the common ratio) can be negative, but the base of an exponential function must be positive.

Answer:

Geometric sequences are the long way to show an exponential function. The initial amount in both exponential functions and geometric sequences do the same thing, which is state the initial value and the value by which it is multiplied. What is called the common ratio in a geometric sequence is basically the second part of what the initial amount does in an exponential function. The nth term in a geometric sequence is the same as the power in an exponential function, that is to say that it shows how many times the sequence is repeated.

Step-by-step explanation:

What is the answer of .7 of which is 3.43

Answers

Answer:

4.9

Step-by-step explanation:

3.43/0.7

34.3/7=49

3.43/0.7=4.9

The value of x is approximately 4.9 when 0.7 (70%) of x is equal to 3.43.

We are given that 0.7 (which is the same as 70%) of a certain value (x) is equal to 3.43.

We represent "0.7 of x" as 0.7x.

So, the equation becomes:

0.7x = 3.43

To find the value of x, we need to isolate it on one side of the equation. To do this, we can divide both sides of the equation by 0.7:

(0.7x) / 0.7  = 3.43 / 0.7

The 0.7 on the numerator and denominator cancel out, leaving us with just x:

x = 3.43 / 0.7

Now, we perform the division:

x = 4.9

The value of x is approximately 4.9.

Hence, when 0.7 (70%) of 4.9 is calculated, it will be approximately equal to 3.43.

To learn more on Division click:

https://brainly.com/question/21416852

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Un ciclista debe realizar una ruta a través de una carretera para ir desde una ciudad A hasta una ciudad B en varios tramos. El primer tramo mide dos tercios del tercer tramo, el segundo tramo es dos veces mayor que el tercer tramo y el cuarto tramo tiene la medida del primero más el segundo. Si el último tramo es de 80 km, ¿cuál será la distancia total recorrida de la ciudad A hasta la ciudad B?

Answers

Respuesta:

190 km

Explicación paso a paso:

Lo primero es hacer las equivalencias, sea a el primer tramo, b el segundo tramo, c el tercer tramo y el ultimo tramo, el cuarto sería d, entonces:

a = 2/3*c

b = 2*c

d = a + b

Ahora bien sabemos que d = 80, reemplazamos y nos queda:

80 =  a + b

tanto a cómo b están en función del tercer tramo es decir de c, reemplazamos:

80 = 2/3*c + 2*c

80 = 8/3*c

c = 80*3/8

c = 30

ahora calculamos tanto a como b:

a = 2/3*30 = 20

b = 2*30 = 60

Ahora, el recorrido total es la suma de todos los tramos:

Total = a + b + c + d

Total = 20 + 60 + 30 + 80 = 190

Quiere decir que la distancia entre la ciudad A y la cuidad B es de 190 km

im having trouble with this :(

Answers

The answer is plus 4 because a positive plus a negative is a negative

Can I get the awnser to this please?

Answers

Answer:

151.320046 m^2

150 m^2

Hope it helped!!!!!

Step-by-step explanation:

Area of the circle is:

pi * r^2

Therefore:

= pi * 17^2

= 289 * pi

Now  Area of the sector:

= 289 * pi * (60/360)

= 289 * pi * 1/6

= 48.1666667 * pi

= 151.320046 m^2

= 150 m^2 (rounded)

3 sides of the triangle are distinct prime numbers. What is the smallest possible perimeter of the triangle ?

Answers

Answer:

15

Step-by-step explanation:

1 is neither prime nor composite

2 is the smallest prime

3 is the next smallest prime

5 is the next smallest

but 2,3,5 do not make a triangle

The third side must be smaller than the sum of the other two

2+3 <5 not equal to

7 is the next prime

3,5,7 are the three sides of the triangle

P = 3+5+7

P = 15

Identify the system of inequalities from the following. 3x + y > 2 and 3y 2 and 3y 2 and 3y < 9 4x + y = 2 and 3y < 2m

Answers

Answer:

The inequalities are;3x+y>2,3y<9,4x+y=2and 3y<2m

The length of the smaller rectangle at the right is 1 inch less than twice its width. Both the dimensions of the larger rectangle are 2 inches longer than the smaller rectangle. The area of the shaded region is 86 square inches. What is the area of the larger rectangle? PLEASE its important

Answers

Answer:  464 square inches is the area of the larger rectangle.

Step-by-step explanation:  Assuming that the shaded area is the part of the large rectangle outside the small rectangle, you can set up dimensions from the information given.

The small rectangle's Area = w (2w -1) which is 2w² -w

The large rectangle's Area = (w + 2)(2w + 1) which is 2w² + 5w +2

Now figure out the equation for the "shaded area" (probably outside the small rectangle)  2w² + 5w +2 -(2w² -w) = 86  (The 2w² terms cancel)

6w + 2 = 86,  so 6w = 84, w=14  

Substitute 14 for w in the dimensions of the large rectangle: (w + 2)(2w + 1)

(14+2)(2[14] + 1) = Area

16 × 29 = 464

(I think I deserve Brainliest for figuring this out, but I see the question has been red-flagged, so We'll see!)

Riley has a farm on a rectangular piece of land that is 200200200 meters wide. This area is divided into two parts: A square area where she grows avocados (whose side is the same as the length of the farm), and the remaining area where she lives.


Every week, Riley spends \$3$3dollar sign, 3 per square meter on the area where she lives, and earns \$7$7dollar sign, 7 per square meter from the area where she grows avocados. That way, she manages to save some money every week.



Write an inequality that models the situation. Use lll to represent the length of Riley's farm.

Answers

Answer:

The inequality that models the situation for her to have money to save is

7L² > 3(200L - L²)

On simplifying and solving,

L > 60 meters

Step-by-step explanation:

The length of her farm = L meters

The farm where she grows avocados is of square dimension

Area of the farm = L × L = L²

The piece of land is 200 m wide.

Total area of the piece of land = 200 × L = (200L) m²

If the area of her farm = L²

Area of the side where she lives will be

(Total area of the land) - (Area of the farm)

= (200L - L²)

= L(200 - L)

Every week, Riley spends $3 per square meter on the area where she lives, and earns $7 per square meter from the area where she grows avocados.

Total amount she earns from the side she grows the avocados = 7 × L² = 7L²

Total amount she spends on the side where she lives = 3 × (200L - L²) = 3(200L - L²)

For her to save money, the amount she earns must be greater than the amount she spends, hence the inequality had to be

(Amount she earns) > (Amount she spends)

7L² > 3(200L - L²)

To simplify,

7L² > 3L(200 - L)

Since L is always positive, we can divide both sides by L

7L > 3(200 - L)

7L > 600 - 3L

10L > 600

L > 60 meters

Hope this Helps!!!

Answer:

Answer is in attached image.

Please answer please please

Answers

Answer: T

Step-by-step explanation: The vertex is where the two lines meet at the endpoint, meaning that the vertex is always where the lines begin to spread out.

If m<1=45 then what is the measure of <2

HELP!!!

Answers

Hey there! :)

Answer:

m∠2 = 135°.

Step-by-step explanation:

∠1 and ∠2 are supplementary angles, meaning that they both sum up to 180°. Therefore:

m∠2 = 180 - m∠1

m∠2 = 180 - 45

m∠2 = 135°.

30 Points!! Vivian is at a fair in Coachella Valley, California. Much of the valley lies below sea level. Vivian has brought along an altimeter to measure her elevation at different places in the valley. Vivian’s first ride was on the Ferris wheel. When she sat on the wheel at its lowest point, her altimeter read -9.6 feet. When she reached the top of the wheel, her altimeter read 12.3 feet.



Is the change in Vivian's elevation from the bottom of the Ferris wheel to the top a positive number or a negative number? Why?

Answers

Answer:

Its a postive number

Step-by-step explanation:

If you look it says she is at sea leveal wicth is 0 and she is going up 12.3 feet so its postive.

The change in elevation from the bottom of the Ferris wheel to the top is 21.9 feet, which is a positive number.

What is subtraction?

The process of subtracting one number from another is known as subtraction.

Given that, the lowest point of the Ferris wheel is -9.6 feet, and the highest point is 12.3.

The change in elevation from the bottom of the Ferris wheel to the top of the Ferris wheel is,

12.3 - (-9.6)

=12.3 + 9.6

= 21.9

Hence, the change in elevation from the bottom of the Ferris wheel to the top is 21.9 feet, which is a positive number.

To learn more about subtraction, click here:

https://brainly.com/question/2346316

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Which of the following are identities?
1. x2 + 2xy + y2 = (x + y)2
II. 2x + 2 = 2(x + 1)
III. O + a = a

Answers

Answer:

The answer is 2 because they are similar it is just that the one at the side is factorised

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