The school store sells packs of 12 pens for $2.40.

Select the three unit rates that describe this sale.

CLEAR CHECK

$0.20 per pen


$2.40 per pack of pens


5 pens per dollar


120 pens per $24
NEXT

CLOSE
Reference
calculator
formulas
glossary

CLOSE
Language
Changes the language of the audio snippets and the glossary
ENGLISH

Answer:

8.76

Step-by-step explanation:

Simplifying

15.00 + -6.24 = b

Combine like terms: 15.00 + -6.24 = 8.76

8.76 = b

Solving

8.76 = b

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '-1b' to each side of the equation.

8.76 + -1b = b + -1b

Combine like terms: b + -1b = 0

8.76 + -1b = 0

Add '-8.76' to each side of the equation.

8.76 + -8.76 + -1b = 0 + -8.76

Combine like terms: 8.76 + -8.76 = 0.00

0.00 + -1b = 0 + -8.76

-1b = 0 + -8.76

Combine like terms: 0 + -8.76 = -8.76

-1b = -8.76

Divide each side by '-1'.

b = 8.76

Simplifying

b = 8.76

The question is incomplete. Here is the complete question:

The height of a wooden pole, h, is equal to 15 feet. A taut wire is stretched from a point on the ground to the top of the pole. The  distance from the base of the pole to this point on the ground, b. is equal to 8 feet. What is the length of the wire?

Answer:

Length of wire = 17 feet

Step-by-step explanation:

Given:

The height of the wooden pole is, [tex]h=15\ ft[/tex]

The distance from the base of the pole to this point on the ground is, [tex]b=8\ ft[/tex]

Let the length of the wire be 'l'.

Now, consider the triangle formed by the pole, the base, and the wire. The length of the wire is the slant length and hence the hypotenuse of the triangle.

Using Pythagorean theorem, we can find the hypotenuse.

[tex](Hypotenuse)^2=(height)^2+(base)^2\\l^2=h^2+b^2[/tex]

Plug in the given values and solve for 'l'. This gives,

[tex]l^2=15^2+8^2\\\\l^2=225+64\\\\l^2=289\\\\l=\sqrt{289}\\\\l=\pm17[/tex]

As length can never be negative, we ignore the negative result.

Therefore, the length of the wire is 17 feet.

Answer:

The correct answer is A. 4,818'000,000 kilowatt-hours per year and B. 481,800 households.

Step-by-step explanation:

1. Let's review the information provided to us for solving the questions:

Power capacity of the wind farms = 2,200 Megawatts or 2.2 Gigawatts

2. Let's resolve the questions A and B:

Part A

Assuming wind farms typically generate 25​% of their​ capacity, how much​ energy, in​ kilowatt-hours, can the​ region's wind farms generate in one​ year?

2,200 * 0.25 = 550 Megawatts

550 Megawatts = 550 * 1,000 Kilowatts = 550,000 Kilowatts

Now we calculate the amount of Kilowatts per hour, per day and per year:

550,000 Kw generated by the farms means that are capable of produce 550,000 kw per hour of energy

550,000 * 24 = 13'200,000 kilowatt-hours per day

13'200,000 * 365 = 4,818'000,000 kilowatt-hours per year

Part B

Given that the average household in the region uses about​ 10,000 kilowatt-hours of energy each​ year, how many households can be powered by these wind​ farms?

For calculating the amount of households we divide the total amount of energy the wind farms can generate (4,818'000,000 kilowatt-hours) and we divide it by the average household consumption (10,000 kilowatt-hours)

Amount of households =  4,818'000,000/10,000 = 481,800

Answer:

Solutions are -10 and 26

Step-by-step explanation:

( - the abolute sign I'm using

( x - 8 ) + 2 = 20

( x - 8 ) = 18

x - 8 = 18 (postive case)

x - 8 + 8 = 18 + 8

x = 26

( x - 8 ) = 18

x - 8 = -18 (negative case)

x - 8 + 8 = -18 + 8

x = -10

Answer:

The amount of tax paid is C. $3.20

Step-by-step explanation:

If we take $50.00 and give a 20% discount, we're taking 20% of 50 and then subtracting it from the origional price (50) which brings us down to 40, because 20% of 50 is 10 and we subtract.

Now that we have $40.00, sales tax comes in at a whopping 8%. To calculate the solution of a price with sales tax, we need to find what 8% of $40 is, which after calculations will be 3.20.

Since this question is asking on tax only, our answer is $3.200, C.

Answer:

x = 40 + -1.5y

Step-by-step explanation:

Simplifying

2x + 3y = 80

Solving

2x + 3y = 80

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3y' to each side of the equation.

2x + 3y + -3y = 80 + -3y

Combine like terms: 3y + -3y = 0

2x + 0 = 80 + -3y

2x = 80 + -3y

Divide each side by '2'.

x = 40 + -1.5y

Simplifying

x = 40 + -1.5y

Answer:

Step-by-step explanation:

Curved surface Area = 2πrh

Area of its bases = 2πr²

6* Area of its bases = 4 * Curved surface Area

6 * 2πr² = 4 *2πrh

r²  / r = 4 * 2* π*12 / 6 * 2 * π   { substituting h =12 cm}

r = 4*2

r = 8 cm

Curved surface Area = 2πrh

= 2 * 3.14 * 12 * 8

= 602.88 Sq. cm

Answer:

603.42

Step-by-step explanation:

Curved Surface Area = 2πrh sq.cm

Area of the base = πr² sq. cm

Sum area of the base = πr² + πr² = 2πr² sq.cm

                               A.T.Q

4(2πrh) = 6x2πr²

8πrh = 12πr²

2h = 3r

r = 8 cm

Curved Surface Area = 2πrh

2x22/7x8x12

4224/7

603.42

Answer:

It is B.   (36√5 + 36) ft^2.

Step-by-step explanation:

Total area = area of the base +  4 * area of the triangular side.

The slant height of a triangular side =  √(6^2 + 3^2)

= √45

= 3√5

The area of this side = 3 * 3 √5

= 9√5.

Therefore the total area of the pyramid

=  6^2 + 4*9√5

= (36 + 36√5) ft^2.

Answer:

y = 90°

Step-by-step explanation:

You do 110° + 80° which is 180 divides by two because there is a straight line in the middle of it. I don't know how to explain it.

Answer:

90 degrees

Step-by-step explanation:

you have angles of 110 and 70 on the sides. The triangle altogether equals 180 but that doesn't matter in this equation. Since y is directly between the two angles that are given, it is 90.

110-70=40/2=20 so add 20 to 70 and subtract 20 from 110 so you get 90.

Answer: Option B.

Step-by-step explanation:

For this exercise it is important to remember that, by definition, a relation is a function if and only if each input value has an unique output value.

The input values are the values of the variable "x" and the output values are the values of the variable "y".

You can observe in the table shown in the picture, that the input value -2 has two different output values:

[tex]x=-2,y=3\\\\x=-2,y=-13[/tex]

Notice that the input vale -1 has two different output values too:

[tex]x=-1,y=-1\\\\x=-1,y=-9[/tex]

Therefore, based on this, you can conclude that the information given in the table is a relation but not a function.

The graph of y = x is transformed by a reflection about the x-axis, a horizontal translation to the left by 2 units, and a vertical translation upward by 3 units to produce the graph of y = -(x + 2)^2 + 3.

The given equation is y = -(x + 2)^2 + 3, and we need to describe the transformations of the graph of y = x that will produce this graph.

The first transformation is the reflection about the x-axis, which is indicated by the negative sign in front of the original equation. This flips the graph upside down.

The second transformation is the horizontal translation to the left by 2 units, which is indicated by the addition of 2 inside the parentheses. This shifts the graph 2 units to the left.

The third transformation is the vertical translation upward by 3 units, which is indicated by the addition of 3 to the entire equation. This moves the graph 3 units up.

Answer:

Step-by-step explanation:

The vertex is of the form (h, k).  The general equation of a quadratic in vertex form is

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

where h is the x coordinate of the vertex and k is the y coordinate of the vertex.  The important thing to remember is that the "x -" part of the formula is constant, it doesn't change.  So if our expression inside the parenthesis is

(x + 3), it is understood to be (x - (-3)) which indicates movement to the left.  The "+ k" part is not taken literally.  If we have a + 2 at the end of our equation we are moving up 2; if we have a -1 at the end, we are moving down 1.  Our vertex then is located at (-3, -1)

Answer:

0.55 would be the decimal form

Step-by-step explanation:

Answer:

x>9

Step-by-step explanation:

Open parenthesis:

6x-30>3x-3

Move all like terms to one side:

6x-3x>30-3

3x>27

x>9

Answer:

the answer is x=2

I used math-way

Answer:

this should be correct.

Both Henry and Colin have a ratio of 4, so Colin gets the same amount as Henry, so we know Colin has 56.

Brian's ratio is 5, so for every 4 Colin gets, brian gets 5 ( 1 more).

Divide Colin's quantity by 4 :

56/4 = 14

Brain gets 14 more.

36km per hour

Step-by-step explanation:

The new mean is 11

Step-by-step explanation:

The mean = sum of the numbers ÷ numbers

∵ The set has 5 numbers

∵ The mean of the 5 numbers is 12

- Substitute these values in the rule of the mean above

∴ 12 = sum of the numbers ÷ 5

- Multiply both sides by 5

∴ 60 = sum of the numbers

∵ One of the number is 16

∵ 16 is removed from the set of the number

- Subtract 16 from the sum and the numbers will be four numbers

∵ The new sum = 60 - 16

∴ The new sum = 44

∵ The set has 4 numbers

∴ The new mean = 44 ÷ 4 = 11

The new mean is 11

Learn more:

You can learn more about the mean in brainly.com/question/5069437

#LearnwithBrainly

Liza is driving to her sister's house 360 miles away. After 4 hours, Liza is 2/3 of the way there.   How many more hours  does Liza have to drive?

Answer:

Liza need to drive 2 more hours to reach her sister house

Solution:

Given that Liza is driving to her sister's house 360 miles away

So total distance = 360 miles

After 4 hours, Liza is 2/3 of the way there.

[tex]\frac{2}{3} r d \text { of total distance }=\frac{2}{3} \times 360=240[/tex]

So Liza has covered 240 miles in 4 hours

Let us find the speed

The relation between distance and speed is given as:

[tex]speed = \frac{distance}{time}[/tex]

[tex]speed = \frac{240}{4} = 60[/tex]

Thus speed = 60 miles per hour

Assuming speed is same throughout the journey, let us calculate the time taken to complete remaining distance

Remaining distance = 360 - 240 = 120 miles

Now distance = 120 miles and speed = 60 miles per hour

[tex]time taken = \frac{distance}{speed}\\\\time taken = \frac{120}{60} = 2[/tex]

Thus Liza need to drive 2 more hours to reach her sister house

Answer:

2

Step-by-step explanation:

Answer:

It would take approximately 6.50 second for the cannonball to strike the ground.

Step-by-step explanation:

Consider the provided function.

[tex]h(t)=-4.9t^2+30.5t+8.8[/tex]

We need to find the time takes for the cannonball to strike the ground.

Substitute h(t) = 0 in above function.

[tex]-4.9t^2+30.5t+8.8=0[/tex]

Multiply both sides by 10.

[tex]-49t^2+305t+88=0[/tex]

For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are: [tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Substitute a = -49, b = 305 and c=88

[tex]t=\frac{-305+\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}=-\frac{-305+\sqrt{110273}}{98}\\t = \frac{-305-\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}= \frac{305+\sqrt{110273}}{98}[/tex]

Ignore the negative value of t as time can't be a negative number.

Thus,

[tex]t=\frac{305+\sqrt{110273}}{98}\approx6.50[/tex]

Hence, it would take approximately 6.50 second for the cannonball to strike the ground.

Answer:

Yes, because there are no repeated input values.

Step-by-step explanation:

*This would not be a function IF any input value (x-value) was repeated. In functions, x-values CANNOT be repeated, but y-values CAN be repeated.

I hope this helps!

- sincerelynini

Answer:

Step-by-step explanation:

You would require the table with the number of males and females who prefer either pink or yellow lemonade at the state fair.

                      Pink Lemonade         Yellow Lemonade       TOTAL

Male                    156                                104                          260

Female                  72                               48                          120

TOTAL                 228                               152                         380

P(pink lemonade | female) = 72 / (48 + 72) = 72 / 120 = 0.6

P(pink lemonade) = (156 + 72) / (156 + 72 + 104 + 48) = 228 / 380 = 0.6

Therefore, The event "prefers pink lemonade" and "female" are independent because P(pink lemonade | female) = P(pink lemonade) = 0.6

Answer:

P(pink lemonade | female) = P(pink lemonade) = 0.6.

Step-by-step explanation:

Answer:

-1/16

Step-by-step explanation:

There is no graph, so it is impossible to answer this question. I apologise.

Grant needs to ride at least 13.33 miles to male at least $ 15.00 a day

Solution:

Given that Grant has an agreement with Brian to rent the bike for $35.00 a night

He charges customers $3.75 for every mile he transports them

Grant needs to make at least $15.00 a day

To find: miles needed to ride

From given question, He charges customers $3.75 for every mile he transports them

So if he transports for "x" miles he would get,

[tex]\$ 3.75 \times x = \$ 3.75x[/tex]

So the profit he gets is $ 3.75 and initial cost invested to rent bike is $ 35. Also, Grant needs to make at least $15.00 a day

So we can frame a inequality as:

[tex]3.75x - 35 \geq 15\\\\3.75x\geq 35 + 15\\\\3.75x\geq 50\\\\x \geq 13.33[/tex]

So he needs to ride atleast 13.33 miles to male atleast $ 15.00 a day

Answer:

$37.33 dollars

Step-by-step explanation:

16 x 7/3= 112/3

d=37.33