A store selling art supplies finds that they can sell x sketch pads each week at a price of p dollars each, according to the formula x = 1000 − 400 p. What price should they charge (in interval notation and rounded to the nearest cent) if they want to sell

a . At least 625 pads each week? b . More than 300 pads each week?

c . Less than 200 pads each week? d . At most 475 pads each week?

Answers

Answer 1

Answer:

c and b and a

Step-by-step explanation:

Answer 2

The store should charge a price between ($0, $0.94] to sell at least 625 pads each week. The store should charge a price between ($0, $1.75) to sell more than 300 pads each week. The store should charge a price between ($2.00, $2.50) to sell less than 200 pads each week. The store should charge a price between [$1.31, $2.50) to sell at most 475 pads each week.

a)

In order to solve part a of the problem, we need to set our equation as an inequality. Part a asks us to find the price the store should charge to sell at least 625 pads each week. The word at least gives us a clue on what symbol to use. In this case we should use the [tex]\leq[/tex] symbol, like this:

[tex]625\leq 1000-400p[/tex]

and now we can solve the inequality, we can start by switching places between the 625 and the 400p so we get:

[tex]400p\leq 1000-625[/tex]

[tex]400p\leq 375[/tex]

and we divide both sides into 400, so we get:

[tex]p\leq \frac{375}{400}[/tex]

[tex]p\leq $0.94[/tex]

So this can be rewritten in interval notation like this:

($0, $0.94] The price they should charge can be located between those two values.

b)

In order to solve part b of the problem, we need to set our equation as an inequality. Part b asks us to find the price the store should charge to sell at more than 300 pads each week. The word more than gives us a clue on what symbol to use. In this case we should use the < symbol, like this:

[tex]300< 1000-400p[/tex]

and now we can solve the equation, we can start by switching places between the 300 and the 400p so we get:

[tex]400p< 1000-300[/tex]

[tex]400p< 700[/tex]

and we divide both sides into 400, so we get:

[tex]p< \frac{700}{400}[/tex]

[tex]p< $1.75[/tex]

So this can be rewritten in interval notation like this:

($0, $1.75) The price they should charge can be located between those two values.

c)

In order to solve part c of the problem, we need to set our equation as an inequality. Part c asks us to find the price the store should charge to sell less than 200 pads each week. The word less than gives us a clue on what symbol to use. In this case we should use the > symbol, like this:

[tex]200> 1000-400p[/tex]

and now we can solve the inequality, we can start by switching places between the 200 and the 400p so we get:

[tex]400p> 1000-200[/tex]

[tex]400p> 800[/tex]

and we divide both sides into 400, so we get:

[tex]p> \frac{800}{400}[/tex]

[tex]p> $2.00[/tex]

at this point we need to know what the maximum price the store can charge is. We can do so by setting the equation equal to zero and solve for p, so we get:

0<1000-400p

so we can now move the 400p to the other side of the equation, so we get:

400p<1000

and divide both sides into 400 so we get:

[tex]p<\frac{1000}{400}[/tex]

which simplifies to:

p<$2.50

if the store charges more than $2.50 they will not sell any item at all.

So this can be rewritten in interval notation like this:

($2.00, $2.50) The price they should charge can be located between those two values to sell less than 200 pads each week.

d)

In order to solve part d of the problem, we need to set our equation as an inequality. Part d asks us to find the price the store should charge to sell at most 475 pads each week. The word at most gives us a clue on what symbol to use. In this case we should use the [tex]\geq[/tex] symbol, like this:

[tex]475\geq 1000-400p[/tex]

and now we can solve the inequality, we can start by switching places between the 475 and the 400p so we get:

[tex]400p\geq 1000-475[/tex]

[tex]400p\geq 525[/tex]

and we divide both sides into 400, so we get:

[tex]p\geq \frac{525}{400}[/tex]

[tex]p\geq $1.31[/tex]

So this can be rewritten in interval notation like this:

[$1.31, $2.50) The price they should charge can be located between those two values to sell 475 pads at most each week.

You can check the following link for further information.

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Related Questions

Which graph represents the function f(x)=-|x|-2?

Answers

Answer:

ind the absolute value vertex. In this case, the vertex for y=−|x|−2 is (0,−2).

(0,−2)

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

(−∞,∞)

Set-Builder Notation:  {x|x ∈ R}

For each x value, there is one y value. Select few x values from the domain. It would be more useful to select the values so that they are around the x value of the absolute value vertex.

 x     y

−2   −4

−1    −3

 0   −2

 1    −3

 2   −4

Step-by-step explanation:

Answer:

The answer is C.

I hope this helps you!

Find the ratio (red to blue) of the perimeters of the similar triangles. Write your answer in simplest form.

Answers

Answer:

I think the answer is 9/2

Find the locus of a point such that the sum of its distance from the point ( 0 , 2 ) and ( 0 , -2 ) is 6.
~Thanks in advance ! ​

Answers

Answer:

[tex]\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1[/tex]

Step-by-step explanation:

We want to find the locus of a point such that the sum of the distance from any point P on the locus to (0, 2) and (0, -2) is 6.

First, we will need the distance formula, given by:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let the point on the locus be P(x, y).

So, the distance from P to (0, 2) will be:

[tex]\begin{aligned} d_1&=\sqrt{(x-0)^2+(y-2)^2}\\\\ &=\sqrt{x^2+(y-2)^2}\end{aligned}[/tex]

And, the distance from P to (0, -2) will be:

[tex]\displaystyle \begin{aligned} d_2&=\sqrt{(x-0)^2+(y-(-2))^2}\\\\ &=\sqrt{x^2+(y+2)^2}\end{aligned}[/tex]

So sum of the two distances must be 6. Therefore:

[tex]d_1+d_2=6[/tex]

Now, by substitution:

[tex](\sqrt{x^2+(y-2)^2})+(\sqrt{x^2+(y+2)^2})=6[/tex]

Simplify. We can subtract the second term from the left:

[tex]\sqrt{x^2+(y-2)^2}=6-\sqrt{x^2+(y+2)^2}[/tex]

Square both sides:

[tex](x^2+(y-2)^2)=36-12\sqrt{x^2+(y+2)^2}+(x^2+(y+2)^2)[/tex]

We can cancel the x² terms and continue squaring:

[tex]y^2-4y+4=36-12\sqrt{x^2+(y+2)^2}+y^2+4y+4[/tex]

We can cancel the y² and 4 from both sides. We can also subtract 4y from both sides. This leaves us with:

[tex]-8y=36-12\sqrt{x^2+(y+2)^2}[/tex]

We can divide both sides by -4:

[tex]2y=-9+3\sqrt{x^2+(y+2)^2}[/tex]

Adding 9 to both sides yields:

[tex]2y+9=3\sqrt{x^2+(y+2)^2}[/tex]

And, we will square both sides one final time.

[tex]4y^2+36y+81=9(x^2+(y^2+4y+4))[/tex]

Distribute:

[tex]4y^2+36y+81=9x^2+9y^2+36y+36[/tex]

The 36y will cancel. So:

[tex]4y^2+81=9x^2+9y^2+36[/tex]

Subtracting 4y² and 36 from both sides yields:

[tex]9x^2+5y^2=45[/tex]

And dividing both sides by 45 produces:

[tex]\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1[/tex]

Therefore, the equation for the locus of a point such that the sum of its distance to (0, 2) and (0, -2) is 6 is given by a vertical ellipse with a major axis length of 3 and a minor axis length of √5, centered on the origin.

Seth is two-thirds as tall as his father. If Seth is 54 inches tall, how tall is his father?

Answers

Answer:

81 inches tall

pls mark me brainliest

What is the value of 20+6•5/-2

Answers

Answer:

The answer is 25

Step-by-step explanation:

6•5=30

30+20=50

50/-2=25

help for last one please

Answers

Answer:

the slope is one since the line rises once and runs once

Last Friday Kali had $22.62. Over the weekend she received some money for cleaning the attic. She now has $33.99. How much money did she receive?

Answers

The answer is $11.37.

To find the answer, all you need to do is subtract 22.62 from 33.99. Remember that you need to line up the decimals, or else you will not get the right answer.

33.99
22.62
———
11.37

Write each percent as a fraction in simplest form.
12%

Answers

12% as a fraction is 12/100 but it’s simplest form is 3/25

A store purchases baseball hats from two different manufacturers in 3 different colors, summarized
below. One hat is chosen at random. Give your answer as a decimal out to at least 4 places.
Black Blue Red Total
Manufacturer A 23 21 29 73
Manufacturer B 27 17 10 54
Total 50 38 39 127
х
a) Find the probability that the hat was was Black or was from Manufacturer A. 0.3150
O 0.78740157480315
b) Find P(Red).
c) Find P(Manufacturer B and Red),
d) Find P(Manufacturer B or Red).

Answers

Answer:

See below

Step-by-step explanation:

a)

P(A or Black) = (73 + 27)/127 = 100/127 =  0.7874015748

b)  

P(Red) = red/total = 39/127 = 0.30708661417

c)

P(Manufacturer B and Red) = (B and red)/total = 10/ 127 = 0.0787401575

d)

P(Manufacturer B or Red) = (B or red)/total = (54 + 29)/127 = 0.65354330708

Find the surface area of the cuboid shown below

Answers

Answer:

Surface area of cuboid = 352 cm

Step-by-step explanation:

Given that:

Height of cuboid = 8 cm

Length of cuboid = 12 cm

Width of cuboid = 4 cm

Surface area = 2lw + 2lh + 2hw

Putting all the values;

Surface area = 2*12*4 + 2*12*8 + 2*8*4

Surface area = 96 + 192 + 64

Surface area = 352 cm

Hence,

Surface area of cuboid = 352 cm

Tanner is picking three varieties of apples at an orchard: Gala, Fuji, and Jazz. Each type of apple has a different cost per pound. He knows that 1 pound of each apple variety would cost a total of $5.16, and that the cost per pound of Jazz apples is the same as the combined cost per pound of the Gala and Fuji apples. Tanner picks 12 pounds of apples, including 3 pounds of Gala and 5 pounds of Fuji, for a total cost of $21.24.


If g represents the cost per pound of Gala apples, f the cost per pound of Fuji apples, and j the cost per pound of Jazz apples, which system of equations represents this situation?

Answers

Answer:

2g + 2f = 5.16

7g + 9f = 21.24

Step-by-step explanation:

Let

Gala = g ; Fuji = f ; jazz = j

g + f + j = 5.16 - - - (1)

j = g + f - - - (2)

From (1):

g + f + g + f = 5.16

2g + 2f = 5.16 - - - (3)

Total pound picked by Tanner = 12

3 Pounds of g ; 5 pounds of f

j = 12 - (5 +3) = 4 pounds

3g + 5f + 4j = 21.24 - - - (4)

3g + 5f + 4(g + f) = 21.24

3g + 5f + 4g + 4f = 21.24

7g + 9f = 21.24 - - - - - (5)

this should be the answer for this question!

x-3y=7
2х-6у=12
Solve the following systems

Answers

Answer:

Step-by-step explanation:

this system doesnt have any solutions

if you multiply the first equation by 2 you will get

2x-6y=14

second equation is

2x-6y=12

the result will -12=14

no solutions

Stella wnats to buy an atlas that costs 510, a novel that costs $8, and a comc that costs $6. She saved 516 from her pocket money. How much
more money does she need to save? What equation is correct?

Answers

Answer:

where are the equations

Step-by-step explanation:

m is how much more she needs to save

510+8+6=516+m

m=8

Find the angle of this sector.
6 cm
NEED ASAP
5 cm

Answers

Answer:

x ≈ 68.8°

Step-by-step explanation:

The length of the arc of a sector is calculated as

arc = circumference × fraction of circle , that is

6 = 2πr × [tex]\frac{x}{360}[/tex] = 2π × 5 × [tex]\frac{x}{360}[/tex]  = 10π × [tex]\frac{x}{360}[/tex] ( multiply both sides by 360 )

2160 = 10πx ( divide both sides by 10π )

68.7549... = x , that is

x ≈ 68.8° ( to 1 dec. place )

Raul is 75 ft from the world's tallest totem pole in Alert Bay, Canada. It is 173 ft tall. Raul's eyes are 5 ft from the ground, what is the angle of elevation from his line of sight to the top of the totem pole? Round the the nearest degree.

Answers

Answer:

65.9

Step-by-step explanation:

Plz help this one is the last one of the day plz help

Answers

we know 20% is 15
and now we find 80%

since 20% x 4 = 80%, we can multiply 15 by 4 to get 80% of 75

15 x 4 = 60

80% of 75 = 60

Module 11 and 12 Exam On Level
winst vatue of x make this equation true?
-90 = -100 +x

Answers

10=x
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if 10% of a group of children are girls, what is the ratio of girls to boys​

Answers

Answer:

9 boys to 1 girl

Step-by-step explanation:

Helppppp please. I am stumped..

Answers

Answer:

D

Step-by-step explanation:

w = width

length = w + 0.6

A = l · w

A = w (w + 0.6)

A = w² +.6w

Answer:

D

Step-by-step explanation:

w = width

l = length = w + 0.6

Area = ( l ) * ( w )

Area = ( w + 0.6 ) ( w )

Area = w^2 + 0.6w


Work out the percentage change to 2 decimal places when a price of £110 is
decreased to £98.

Answers

Answer:

10.91% decrease

Step-by-step explanation:

98/110 x 100 = 89.090909

100 - 89.0909 = 10.909090 to 2dp is 10.91%


Given right triangle XYZ with altitude WZ, let WY = 10 cm and XY = 13 cm. Find the
length of WZ.
A.5.4
B.11.4
C.7.3
D.3

Answers

.........The answer is B

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Answers

Answer:

-2 -4

Step-by-step explanation:

saying to use 20 letters lol hope that helps

miriam's house is 232 feet above the sea level, and silvia's house is 29 feet above sea level. about how many time's higher than sea level is miriam's house than silvia's?

Answers

Answer:

Step-by-step explanation:

about 9 because

The blue dot is at what value on the number line?

Answers

The blue dot is at 4

Part 1
Washington, DC, was warmer in February (4.3°F)than in December (44°F). Write an inequality for this relationship.

Answers

Because December is really cold

Answer:

Step-by-step explanation:

4.3 °F > 4 1/4 °F

Can someone help please

Answers

Answer:

B

Step-by-step explanation:

A parachutist's speed during a free fall reaches 135 miles per hour. What is this speed in feet per second? At this speed, how many feet will the parachutist fall during 5 seconds of free fall? In your computations, use the fact that I mile is equal to 5280 feet. Do not round your answers.​

Answers

Answer:

198 ft/s speed

99 ft distance

Step-by-step explanation:

Answer:

7.33333ft

Step-by-step explanation:

the measure of the angles in a heptagon measure 95 107 132 138 145 and 158 what is the measure of the 7th angle

Answers

Answer:

ANSWER:123

Step-by-step  its  very simple its puttin x+11 is how u get ur answer by adding the numbers close to that one angle

The measure of the seventh angle in the heptagon is 125 degrees.

What is Polygon?

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

We are given the measures of six angles in the heptagon, which are:

95, 107, 132, 138, 145, and 158 degrees

Sum of angles in Heptagon is 900 degrees.

To find the measure of the seventh angle, we can subtract the sum of the six known angles from the sum of all the angles in the heptagon:

Measure of the seventh angle = Sum of angles - Sum of known angles

Measure of the seventh angle = 900 degrees - (95 + 107 + 132 + 138 + 145 + 158) degrees

Measure of the seventh angle = 900 degrees - 775 degrees

Measure of the seventh angle = 125 degrees

Therefore, the measure of the seventh angle in the heptagon is 125 degrees.

To learn more on Polygons click:

https://brainly.com/question/28276384

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Solve the system of equations using elimination, or write “no solutions” or “infinite solutions” where applicable

4x-y = 7

Answers

Answer:

no solutions

Step-by-step explanation:

i guess   im

which expression are equivalent to this exponential expression

Answers

Answer:To create an equivalent expression, you simply need to move the base and exponent to the other side of the fraction line and change the exponent to positive: 1/(24)

Step-by-step explanation:

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