3. If pencils cost 15 cents each, and notebooks cost 85 cents each, find the number of pencils
purchased if 50 items cost $18.00.

Answers

Answer 1

Answer:

Pencils = 35

Notebooks = 15

Step-by-step explanation:

15 cents = 15/100 = $0.15

85 cents = 85/100 = $0.85

p + n = 50                    Eq. 1

0.15p + 0.85n = 18       Eq. 2

p = number of pencils

n = number of notebooks

From Eq. 1

p = 50 - n               Eq. 3

Replacing Eq. 3 in Eq. 2:

0.15(50-n) + 0.85n = 18

(0.15*50 + 0.15*-n) + 0.85n = 18

(7.5 - 0.15n) + 0.85n = 18

7.5 + 0.7n = 18

0.7n = 18 - 7.5

0.7n = 10.5

n = 10.5 / 0.7

n = 15

From Eq. 3:

p = 50 - n

p = 50 - 15

p = 35

Check:

From Eq. 2

0.15p + 0.85n = 18

0.15*35 + 0.85*15 = 18

5.25 + 12.75 = 18

e

Answer 2
if a pencils is 15 cents each and a notebook is 85 so .85+.15= one

Related Questions

x decreased by 13 is at least 15

Answers

Answer:

x [tex]\leq[/tex] 28

Step-by-step explanation:

lets say you chose 27 . 27 - 13 = 14 . thats not enough . but everything 28 and above would work for x . so x would be equal to or greater than 28 . hope this helps :)

What are the cooridinates of the point that partitions segment HE in the ratio of 2:3?​

Answers

Using proportions, the coordinates of the point C that partitions segment HE in the ratio of 2:3 are found according to the following equation:

C - H = 2/5(E - H).

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For this problem, we have point C that partitions segment HE in the ratio of 2:3, hence it is 2/5 of the way from H to E, and the rule is given by:

C - H = 2/5(E - H).

Then:

Replacing the x-coordinates of H and E, we find the x-coordinate of C.Replacing the y-coordinates of H and E, we find the y-coordinate of C.

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5/8 divided by 5/16?

Answers

Answer:

2

Step-by-step explanation:

[tex] \: \: \: \: \: \: \: \large{\frac{5}{8}} \: \div \large{\frac{5}{16}} \\ \\ = \frac{5}{8} \times \frac{16}{5} \\ \\ = \green 2 \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Answer:

2

Step-by-step explanation:

(5/8) ÷ (5/16)

= (5*16) ÷ (8*5)

= 80 ÷ 40

= 2

At its peak, an online shopping site was selling about 420 items per second. At this rate, how many items would it sell in 30 minutes (1,800 seconds)?

The online site would sell
items in 30 minutes.

Answers

Step-by-step explanation:

420x1800=756000

so 756k items in 30 minutes

simplify with the steps

Answers

By algebraic simplification, the expression [(3 · a · b²) / (5 · b²)] ÷ √[(9 · a²) / (100 · b²)] is equivalent to the expression 2 · b.

How to simplify an algebraic expression

In this question we need to simplify the division of two expressions that comprises powers and square roots, the complete procedure requires the use of algebra properties:

[(3 · a · b²) / (5 · b²)] ÷ √[(9 · a²) / (100 · b²)]          Given[(3 · a · b²) / (5 · b²)] ÷ [√(9 · a²) / √(100 · b²)]       Square root of a division[(3 · a · b²) / (5 · b²)] ÷ [(√9 · √a²) / (√100 · √b²)]  Square root of a product[(3 · a · b²) / (5 · b²)] ÷ [(3 · a) / (10 · b)]                   Definition of square root[(3 · a · b²) · (10 · b)] / [(5 · b²) · (3 · a)]                    Division of fractions(30 · a · b³) / (15 · a · b²)                                         Associative and commutative properties / Definition of multiplication / Multiplication of powers of equal base2 · b                                                                        Associative and commutative properties / Definition of division / Result

The expression [(3 · a · b²) / (5 · b²)] ÷ √[(9 · a²) / (100 · b²)] is equivalent to 2 · b.

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Write an inequality for the given scenario.

For safety, all dogs at a dog park who weigh, w, more than 50 pounds must play in Area 2.

Answers

Answer:   w > 50

This is because we are focusing on weights (w) that are larger than 50

We won't have an "or equal to" as part of this.

An inequality for the given scenario is;

⇒ w > 50

Here,

The given scenario is;

For safety, all dogs at a dog park who weigh, w, more than 50 pounds must play in Area 2.

We have to find the inequality.

What is Inequality?

An inequality compares two values, showing if one is less than, greater than.

Now,

Weight of all dogs = w

And, Weight of all dogs w is more than 50 pounds.

Hence, An inequality for the given scenario is;

⇒ w > 50

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Mrs. Chavez put $8,000.00 in her IRA savings account that offers 8.62% interest compounded annually. She makes no additional deposits or withdrawals. Which amount is closest to the interest Mrs. Chavez will have earned at the end of 4 years?

Answers

If Mrs. Chavez put $8,000.00 in her IRA savings account that offers 8.62% interest compounded annually, then she will earn $3136 interest at the end of the 4 years

Total invested amount = $8000

Interest rate = 8.62%

The interest is compounded annually

Time period = 4 years

We know

[tex]A=P(1+\frac{r}{100})^{t}[/tex]

Where,

A = Final amount

P = Principal

r = Interest rate

t = Time period

Substitute the values in the equation

A= [tex]8000(1+\frac{8.62}{100})^{4}[/tex]

A= $11136

Compounded interest = 11136-8000

=$3136

Hence, If Mrs. Chavez put $8,000.00 in her IRA savings account that offers 8.62% interest compounded annually, then she will earn $3136 interest at the end of the 4 years

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A standard 1 kilogram weight is a cylinder 54.5 mm in height and 53.0 mm in diameter. what is the density of the material?

Answers

The density of the material is  0.4 kg/cubic cm.

Given that:-

Height of the cylinder = 54.5 mm

Diameter of the cylinder = 53.0 mm

Weight of the cylinder = 1 kg

We have to find the density of the cylinder.

We know that,

Density  = mass/volume

Here, mass = 1 kg

We know that,

Volume of a cylinder = [tex]\frac{1}{3} \pi r^2 h[/tex]

Where,

r is the radius of the cylinder, and

h is the height of the cylinder

Here, h = 54.5 mm, and

r = 53/2 = 26.5 mm

Hence,

Volume of cylinder = (1/3)*(22/7)*(26.5)(26.5)*54.5 ≈ 2566.088 ≈ 2566 cubic mm. = 2566/(10*10*10) cubic cm = 2.566 cubic cm

Density of cylinder = 1kg/2.566 cubic cm  ≈ 0.3897  ≈ 0.4 kg/cubic cm.

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i need an answer for this math equation please
like now
Simplify 3^2*5*2*3
thx
(heres the picture on the link of the equation)

Answers

Power of a number 3⁶⁰ is the simplest form of math equation.

What is the power of a number?

A power is a phrase that depicts the same component being multiplied repeatedly. The exponent, 2, and base, 5, respectively, are both numbers. The number of times the base is employed as a factor is represented by the exponent.

What are power and exponent?

The term "exponent" describes how many times a number is multiplied. Power is the result of multiplying a number by itself a predetermined number of times. A number's exponent is the number raised in order to specify its power as a full expression.

3^2*5*2*3 = 3⁶⁰

               

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How many atoms of carbon (C) are present in the reactants of the following chemical equation?
C7H16+O2
CO₂ + H₂O
(1 point)
7 atoms
16 atoms
1 atom
23 atoms

Answers

The reactants in the chemical equation C7H16 + O2 = CO2 + H2O have a total of 7 atoms in them.

How to count the number of atoms?

The chemical formula of a compound indicates how many atoms are present in the substance.

The number of atoms of each element present in a molecule is noted in a chemical formula.

The answer to this query provides the following description of the chemical interaction between heptane and oxygen:

O2 + C7H16 = CO2 + H2O

Hexane's chemical composition reveals that the reactant side of the reaction has 7 carbon atoms.

Therefore, there are 7 atoms total in the reactants of the chemical equation C7H16 + O2 = CO2 + H2O.

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Write and solve an equation to answer the question.

The area of the postcard is 24 square inches. What is the width b of the message (in inches)?

Equation: __ =24

Answers

The width of the message as shown in the image attached is 3 inches.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let b represent the width of the message. The area of the postcard is 24 square inches, hence:

(b + 3)4 = 24

4b + 12 = 24

b = 3

The width of the message as shown in the image attached is 3 inches.

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If (44)x = 432, what is the value of x?

4
7
8
28

Answers

Answer:

9.81....

Step-by-step explanation:

x = 432/44

x = 9.81...

Solve the differential equation dpdt=5p a. assume a is a non-zero constant, and use c for any constant of integration that you may have in your answer. p=

Answers

The solution of the differential equation as given in the task content is; ln(5p +a)/5 + C = t

What is the solution of the differential equation as in the task content?

It follows from the task content that the solution of the differential equation is required.

Given;

dp/dt=5p +a

To find; solution to the differential equation;

By variable separation; the resulting equation is;

dp/(5p +a) = dt

By integrating both sides of the equation; we have;

ln(5p +a)/5 + C = t

Ultimately, although both sides of the equation integrated yield a constant of integration as the integral is indefinite, the two constants have been combined into constant, C as in the equation above.

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if h(t)=1248-160t+16t

Answers

Answer: 816

Step-by-step explanation:

h(3) = 1248 - 160(3) + 16(3)

h(3)= 1248 - 480 + 48

h(3)= 816

A rectangular field is 250m by 190m. How far is it across diagonally?

Answers

Answer:

314.0063694

Step-by-step explanation:

You will have to use the pythogoras. triple to solve the equation

Answer:

314 m

Step-by-step explanation:

the diagonal is the hypotenuse of the two triangles that form the rectangle (see figure) we solve with Pythagoras

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

a² = b²+ c²

a² = 250² + 190²

a² = 62500 + 36100

a² = 98600

a = √98600

a = 314 m

9+4y=-5x+7y solve for x

Answers

Answer:

x=3/5y-9/5

Step-by-step explanation:

Answer:

5x=7y-4y-9

5x=9-3y

[tex]\frac{5x}{5}[/tex]=[tex]\frac{9-3y}{5}[/tex]

[tex]x=\frac{9-3y}{5}[/tex]

me nu elin.
Joan had 174 dollars to spend on 7 books. After
buying them she had 13 dollars. How much did
pas
each book cost?
vab 199
Weit
ration
angiario
new
for this situation

Answers

Answer:

23 dollars.

Step-by-step explanation:

She spent a total of 174 - 13 = 161 dollars.

So, the cost of each book = 161/7

= 23 dollars.

Which graph shows the inverse of y = 3x - 12?

Answers

Answer:

graph B would be the answer.

Step-by-step explanation:

-

B
Check out the attached photo

here are 2 points in the plane. Explain how to construct a line segment that is half the length of AB

Answers

Making a perpendicular bisector on the segment that gives the half length of AB

Given that,
here are 2 points in the plane. Explain how to construct a line segment that is half the length of AB is to explain.

What is a Line?

A line can be defined by the shortest distance between two points is called as a line.


Here,
Two points are given on the plane,
Draw line segment joining these two points on the plane,
Now with help of a compass draw a perpendicular bisector on the line, that bisects the segment into two equal halfs.

Thus, making a perpendicular bisector on the segment that gives the half length of AB

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A regulation volleyball has a circumference of about 66 centimeters. The ratio of the surface area of that ball to the surface area of a children's ball is approximately 1.6: 1 . What is the circumference of the children's ball? Round to the nearest centimeter.

Answers

The circumference of the children's ball to the nearest centimeter is 52 centimeters.

If a regulation volleyball has a circumference of about 66 centimeters, solve for its radius using the formula for the circumference of a circle given by:

C = 2πr

66 centimeters = 2πr

r = 33/π centimeters

Then, solve for the surface area of this regulation volleyball using the formula given by:

A = 4πr^2

A = 4π(33/π centimeters)^2

A = 4356/π square centimeters

If the ratio of the surface area of that ball to the surface area of a children's ball is approximately 1.6 : 1, then

surface area of regulation volleyball : surface area of a children's ball = 1.6 : 1

surface area of a children's ball = 4356/π square centimeters/1.6

surface area of a children's ball = 2722.5/π square centimeters

If  the children's ball has a surface area of 2722.5/π square centimeters, solve for its radius using the formula for the surface area given by:

A = 4πr^2

2722.5/π square centimeters = 4πr^2

r = 26.0887907/π centimeters

Solving for the circumference:

C = 2πr

C = 2π(26.0887907/π centimeters)

C = 52.17758139 centimeters

Rounding off to the nearest centimeter.

C = 52 centimeters

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My little sister, Savannah, is three years old and has a piggy bank that she wants to fill. She
started with five pennies and each day when I come home from school, she is excited when I give her three pennies that are left over from my lunch money. How much money will Savannah have after 10 days? How many days will it take for her to have at least $1.50? Justify your answer with a mathematical model of the problem situation.

Answers

Answer:

after 10days savannah will have 31 pennies

Step-by-step explanation:

arithmetic progression (AP)

(a1) started with, 5 pennies

common difference (d), 3 pennies

formula: Tn = a + (n-1)d

after 10 days, T10 = 5 + (10- 1)(3)

T10 =5 + 27

T10= 31

therefore after ten days savannah has 31 pennies

Canon borrows $3,000 at a yearly simple interest rates of 1.6% for 2 years how much does he owe in interest and how much does he need to pay back in all

Answers

Interest is Rs.96  and Total amount payback is Rs.3096.

Principal (P) = Rs.3000

Rate of  interest (R) = 1.6%

Number of years (N) = 2 yrs

Simple interest = PNR/100

= (3000*1.6*2)/100

=(9600/100

=96Rs

Total Amount (A) = P+I

=3000+96

=3096Rs

The principal, or initial balance of your account, is where interest is calculated. This could be the initial sum of a loan or an investment. The simplest way to compute interest is as a percentage of the principal .Only relatively short-term loans frequently include one-time basic interest charges. Interest is frequently paid on a daily, monthly, quarterly, or annual basis for loans with longer terms. In that scenario, interest would be consistently earned.

Hence, the interest for the above principle is 96Rs and the total amount to be payback is 3096Rs.

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Anna's cars can travel to 8 miles on 6 gallons of gas write an equation to represent the distance y and mild and car driven on x gallons of gas

Answers

Answer:

a. [tex]y=38x[/tex].

Step-by-step explanation:

Let y represent distance in miles and x represent gallons of gas.    

a. First of all, we will find mileage of Ann's car by dividing total distance traveled by total fuel consumed.

Mileage of Ann's Car: [tex]=\frac{228 miles}{6 gallons}[/tex]Mileage of Ann's Car:[tex]=\frac{38 miles}{gallon}[/tex]

Since Ann's can travels 38 miles per gallon, so distance covered by using x gallons on gas would be [tex]38x[/tex] .

Therefore, our required equation would be [tex]y=38x[/tex].

Can you guys help me please

Answers

The shortest length of fabric, in inches, that Kirk could use to make the tablecloth without putting any separate pieces of fabric together is 30 inches

How to solve for the shortest length of fabric required to make the table cloth

Given data

diameter of the table = 3 feet

hang down dimension = 5 inches

sew down dimension = 1 inch

width of rectangular fabric = 60 inches

The question seeks for area of the table cloth, for a circular table area of a circle = pi * r^2

required radius of cloth

= radius of the table + hang down dimension + sew down dimension

= 3 feet / 2 + 5 inches + 1 inch

= 1.5 * 12 inches + 5 inches + 1 inch

= 18 + 5 + 1

= 24 inches

Area of required cloth

= pi * 24^2

= 1809.557 square inches

Area of fabric =  Area of required cloth

length * wide = 1809.557 square inches

length * 60 = 1809.557 square inches

length = 1809.557 / 60 square inches

length = 30.159 inches ≈ 30 inches

Therefore option H which is 30 inches is the answer

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Solve |x-5| + 7 = 13.
A. x= -11 and x = 1
B. x= -11 and x = -1
C. x 11 and x = -1
D. x= 11 and x = -11

Answers

|x-5| + 7 = 13 is equal to x= -11 and x = 1.

[tex]|x-5|+7=13[/tex]

Subtract 7 from both sides

[tex]|x-5|+7-7=13-7[/tex]

Simplify

[tex]|x-5|=6[/tex]

Apply absolute rule: If [tex]$|u|=a, a > 0$[/tex] then [tex]$u=a$[/tex] or [tex]$u=-a$[/tex] [tex]$x-5=-6$[/tex] or [tex]$x-5=6$[/tex]

[tex]$$x-5=-6 \text { or } x-5=6$$[/tex]

[tex]$$x=-1 \text { or } x=11$$[/tex]

Making something simpler is making it less intricate or crowded. When you describe a complex mathematical idea to a youngster in words they can easily comprehend, you are simplifying. When you eliminate many of the tasks that were keeping you occupied and stressed out, you have simplified.

Making something simpler refers to making it simpler to accomplish or comprehend. Therefore, when we reduce or simplify a fraction, we aim for maximum simplicity. In order to do this, we divide both the numerator and the denominator by the biggest integer that can be divided precisely into both numbers.

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Coventry Estates sells houses.
In February they sold twice as many houses as in January.
In March they sold 10 more houses than in February.
In April they sold half as many houses as in March.
Coventry Estates sold a minimum of 123 houses from 1st January to 30th April.
Find the least number of houses sold in January.

Answers

The total number of houses sold in January by Coventry Estates are 18.

How to do the twice of number? This suggests that the amount of A is twice as large as the quantity of anything else, which in this case is B. So, if you have a dozen B items, you have twice a certain number for A, which is 24.

As per the given question;

Let the total sales of the houses in January be 'x'.

In February they sold twice as many houses as in January.

February = 2x.

In March they sold 10 more houses than in February.

March  = February + 10

March  = 2x + 10

In April they sold half as many houses as in March.

April = March/2

April = (2x + 10)/2 = x + 5

The total sold houses = 123.

Add all the sold houses;

x + 2x + 2x + 10 + x + 5 = 123

6x + 15 = 123

On simplification;

x = 18

Thus, the total number of houses sold in January by Coventry Estates are 18.

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Can someone help me find the value of x

Answers

Answer:

25

Step-by-step explanation:

180 - 25 = 155

180 - 155 = 25

180 - 25 = 155

180 - 155 = 25

25 is the answer

PLS HELP ME WITH THIS

Answers

How do you find equivalent expressions?

Image result for what is equivalent to (5x/6)

Combine any like terms on each side of the equation: x-terms with x-terms and constants with constants. Arrange the terms in the same order, usually x-term before constants. If all of the terms in the two expressions are identical, then the two expressions are equivalent.


Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
∠1 and ∠5

Answers

The relationship between the ∠1 and ∠5 is that both are corresponding angles

Given,

The angles = ∠1 and ∠5

Here,

∠1 and ∠5 are lies on the same side of the two lines and on the same side of the transversal

So, ∠1 and ∠5 are corresponding angles

Hence, The relationship between the ∠1 and ∠5 is that both are corresponding angles

The complete question is:

Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

∠1 and ∠5

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positive & negative functions & the end behavior

Answers

Step-by-step explanation:

f(x) = 5|x - 1| - 5

f(x) will be positive that means >= 0, if

5|x - 1| - 5 >= 0

5|x - 1| >= 5

|x - 1| >= 1

that will be true for x <= 0 or x >= 2

f(x) will be negative for the other cases.

so, 0 < x < 2

f(x) is increasing in

[1, infinity)

the value "1" is for sure included, as it starts the increasing part.

f(x) is decreasing in

(-infinity, 1]

"1" is again included, because it ends the decreasing part.

end behavior means for x going to infinity and -infinity : in both cases f(x) goes to infinity.

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From the grocery store you need to purchase 1/4 lb cheese, 2.5 lbs sliced ham, 4 loaves of bread, 5 bags of potato chips, and 3 containers of salsa. Prices are listed below. ItemCostCheese$2.49/ lbSliced Ham$3.29/ lbBread$2.89/ loafPotato Chips$1.95/ ea OR 2 for $3.00Salsa$4.15/ containerUse the space below to calculate the initial cost of your purchases. Historyyy Questionn (Civil War) Which president led the United States through the end of the Cold War? An unbiased coin is tossed 14 times. in how many ways can the coin land tails either exactly 8 times or exactly 2 times? Round 3387 to the nearest hundred Write an equation of each line in standard form with integer coefficients.the line through (-4,2) with slope 3 Determine whether the underlined verb in the following sentence is an action, linking, or helping verb.The cat sneezed, and it was funny. An angle is measured 9 more than two times the measure of its supplement. find the measure of both angles. A circular dwelling has a diameter of 24 feet. What is the area inside of the home? Use 3.14 for TT (pi). A zebra can run at a constant speed of 0.6 miles per minute. How far can a zebra run in 30 minutes? Choose the equation that could be used to answer this question.Ad = (0.6)(0.5)B30 = 0.6tCd = (0.6)(30)D0.6 = 30r Which phrase In this excerpt from The Redeemed Captive by John Williams demonstrates a Puritan Influence?My master took hold of my hand to force me to cross myself; but I struggled with him, and would not suffer him to gulde my hand; upon this,he pulled off a crucifix from his own neck, and bade me kiss It; but I refused once and again; he told me he would dash out my brains with hishatchet If I refused. When two valley glaciers join together, they form a ________ at the point at which they merge. Find the next two terms in each sequence. Write a formula for the n th term. Identify each formula as explicit or recursive. 5,8,11,14,17, ........ How can I draw this problem? What is the main function of phospholipids in a cell? A. form the cell membraneB. produce energy for the cellC. contain genetic informationD. increase the rate of reactions Find each sum. -8+6 The Roman engineering achievement that made large public structures possible wasA the development of advanced math concepts B the development of organized laborC the development of measuring devices D the development of concrete ? which of these measurements would not be used to measure relative distance?A. HoursB. EffortC. DollarsD. MilesE. Minutes Find the circumference of circle described. Round to the nearest hundredth.b. diameter =16 feet 50 POINTS HELP QUICK For each scenario below, identify the opposite reaction force. 1) A baseball bat hits a ball. 2) A bowling ball pushes up against the pins. 3) Air particles push outward against a balloon. 4) During an earthquake, tectonic plates move