Johanna bought 17 items at the college bookstore. The items cost a total of $41.50. The pens cost $0.50 each, the notebooks were $4.00 each, and the highlighters cost $1.50 each. She bought 3 more notebooks than highlighters. How many of each item did she buy?
The answer to the given word problem is as follows. From the calculations: Johanna purchased
4 pens, 8 notebooks, and 5 highlighters.What is a word problem?A word problem is a few phrases that describe a real-life scenario in which an issue must be solved using a mathematical computation.
The calculations is given as follows:
Step 1 - First, let's define the variables to represent the unknowns.
Let p = number of pens
Let n = number of notebooks
Let h = number of highlighters
p + n + h = 17 ......................... 1 (purchased 17 items)
.5p + 4n + 1.5h = 41.5 ...................2 (total cost $41.50)
n = h+3 ................................3 (3 more notebooks than highlighters)
Step 2...............Solve for P in equation 1
P = 17 - n - h..................4
Recall that in equation 3,
n = h + 2
If we make n the subject of the expression, we have:
n = h+ 3
Substituting that into equation 4, we have
p = 17 - (h+3) - h
p = 17 -2h - 3 ..................5
Going back to equation 2, let's substitute n with h+3 and replace p with 17 -2h - 3
.5(17 -2h - 3) + 4 (h+3) + 1.5h = 41.5
To remove all decimals, we can multiply all with 10 to get:
5(170-20h -30) + 40(10h +30) + 15h = 415
Expand all brackets and we have:
850 - 100h - 150 + 400h + 1200 + 15h = 415
Collect like terms
-100h + 400h + 15h = 415-850+150-1200
315h = -1485
h = -1485/315
h = -4.71
Since a physical item cannot be negative, we utilize the absolute value which is:
h = 4.71
h [tex]\approx[/tex] 5 highlighter
Recall that
n = h + 3
Hence
n = 5 +3 = 8 notebooks
Recall that
p + n + h = 17
Hence we have
p + 8 + 5 = 17
p = 17 -8 - 5
p = 17 - 13
P = 4 pens.
Hence Johanna purchased
4 pens, 8 notebooks and 5 highlighters.
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If the family’s monthly income is $3,286, what is the amount the Wren family budgets for entertainment each month?
If the family’s monthly income is $3,286, Wren family budgets for entertainment each month is $328.60.
What do you mean by an income?Income, which is typically stated in the monetary terms, is the spending and saving opportunity acquired by an entity within a given duration. Conceptually, income is hard to define, and different fields may have the distinct definitions. For instance, a person's income may differ from their income as defined by law and in an economic sense.
Haig-Simons income, which defines income as Consumption + Change in Net Worth and is commonly applied in economics, is a very significant definition of income.
Income is a total that includes any wages, salaries, profits, interest payments, rent, or other forms of earnings received in a calendar year for families and individuals in the United States, as defined by tax law. Gross income less taxes and other deductions (such as required pension payments) is a common definition of discretionary income and is frequently used as a benchmark to assess the wellbeing of taxpayers.
The idea may include the accumulation of both monetary and non-monetary consumption capacity, with the former (monetary) serving as a stand-in for total income in the field of public economics.
Gross income for a business is the total revenue less the cost of items sold. Costs are subtracted from revenue by cost of goods sold, expenses, depreciation, interest, and taxes to arrive at net income.
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Choose a rational number expressed as an infinite periodic decimal greater than 0.6(3) and less than 0.64.
Answer:
0.635
Step-by-step explanation:
This is half way between 0.63 and 0.64.
Hope this helps!
If a space rover has a mass of 3900 kg, then what is its weight on Earth?
N=?
Use g-9.81m/s? and do not include units in your answer.
If a space rover has a mass of 3900 kg, then its weight on Earth N will be 38220 N.
What is a weight?Weight can be described as the body's relative mass which can be regarded as the quantity of matter that can be found in the particles of the object and the unit can be written as Newton.
To calculate the weight of a particular particles, we can use the formular (mg) which is that product of the mass of the object to that of the gravity.
from the question, the gravity is been given as g-9.81m/s
Then the weight = (3900 kg* 9.8) = 38220 N
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A case of 24 pairs of the same kind of switches cost a little more than $800 explain whether $28 per pair with tax included is a good estimate of the price
If a case of 24 pairs of the same kind of switches cost a little more than $800. $28 per pair with tax included is not good estimate of the price but $33.33 is the good estimate for the price .
Estimated priceAssuming that the cost per pair is the amount of $28. Hence, cost of 24 pairs is calculated as:
Cost= $28x24
Cost = $672.
Based on the above calculation for the cost of 25 pairs we can see that that the 24 pairs of the same kind of switches does not cost more than $800 which implies that $28 is not good estimate for the price.
Now let determine the best estimate of the price with tax included :
Cost = $800/24
Cost = $33.33
Therefore the good estimate for the price with the tax included is $33.33.
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Need help on this geometry problem, solving for x.
Answer:
A.) 30 degrees
Step-by-step explanation:
Brainly pls :)
Please give at least 2 examples of real life word problems using a proportional relationship. Will give Brainly, please and thank you!!!
Step-by-step explanation:
when we put gasoline in a car that will depend on how much it will cost us, also for example if we are going to buy popcorn depending on how many we buy will be the price
Ivanna makes 9 dollars for each hour of work. Write an equation to represent her total pay p after working h hours.
Answer:
9h=p
9 times the number of hours worked equals the total pay.
write a algebraic expression 4 less than the sum of a number and 7
The representation of the expression is 4 < x + 7
How to translate the algebraic expression?The mathematical statement is given as
"4 less than the sum of a number and 7"
Sum means Plus
So, we have the following representation
"4 less than the sum of a number and 7" ⇒ 4 less than a number + 7"
Let the number be x
So, we have
"4 less than the sum of a number and 7" ⇒ 4 less than x + 7"
Less than as used here means <
So, we have
"4 less than the sum of a number and 7" ⇒ 4 < x + 7"
Hence, the expression represented by "4 less than the sum of a number and 7" is 4 < x + 7
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A certain illness is spreading
at a rate of 10% per hour.
How long will it take to
spread to 1,200 people if 3
people are initially exposed?
Round to the nearest hour.
The illness is spreading at a rate of 10% per hour -> it is spreading 1.1x faster per hour as 10% more people are infected each time.
Therefore, we can write the amount of people infected as 3 x [tex]1.1^{n}[/tex], where n is the hour. So, if n equals 1, the amount of people infected is 3 x 1.1 = 3.3 (so when this mark surpasses the 1200 limit, we round up to the nearest whole number)
It will take 1200 : 3 : 1.1 = 363.636364.. (hours)
If it's only 363 hours, the number of people infected will not have reached 1200, as we have .636364 hours left. So, it will take 364 hours.
HELP ASAP NEEDS TO BE DONE BEFORE TONIGHT
Answer:
y=x/4
Step-by-step explanation:
if the line is perpendicular (m2)=-1/(m1)
m2=1/4
y=x/4+c
sub in 8,2
2=8/4+c
c=0
equation is therefore y=x/4
Hey there! I am having trouble on a quiz so I'll be asking some questions. Look at my profile if you are looking to earn points and help someone out! ( 25 Points For Each Question Answered Correctly - Do Not Comment Silly Stuff Or Your Points Will Be Removed.)
1st Question:
The simplified form of the expression 4(4y-[tex]7y^{2}[/tex])-9(5y+2) is -28[tex]y^{2}[/tex]-29y-18
The given the expression is 4(4y-[tex]7y^{2}[/tex])-9(5y+2)
To solve this problem first we have to use the distributive property
The distributive property states that multiplying the sum of two or more variables by a number gives the same result as when each variable is multiplied individually by the number and the products are added together
The distributive property of addition
A(B+C) = AB + AC
The distributive property of subtraction
A(B-C) = AB - AC
The given equation is 4(4y-[tex]7y^{2}[/tex])-9(5y+2)
Apply distributive property
4(4y-[tex]7y^{2}[/tex])-9(5y+2) = 16y -28[tex]y^{2}[/tex]-45y-18
Rearrange the terms
-28[tex]y^{2}[/tex]-45y+16y-18 = -28[tex]y^{2}[/tex]-29y-18
Hence, the simplified form of the expression 4(4y-[tex]7y^{2}[/tex])-9(5y+2) is -28[tex]y^{2}[/tex]-29y-18
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Fill in the missing number.
20% of
= 3
Answer:0.6
Step-by-step explanation:
20/3 is 6
HELP
25 POINTS!!!!!!!!!!!!!!!!!!!!!!11
Answer:
8/9 cups is the correct answer
point F is on line segment EG. given FG = 8, EF = 2x + 4, and EG = 4x - 10, determine the numerical length of EF
Step-by-step explanation:
equate the two small distances to the total distance and solve for x
In 2014, the global revenues for digital music were reported as $6.85 billion. Select the option that best describes the accuracy of the report.
Based on the report that digital music had led to a global revenue of $6.85 billion, the option that describes the accuracy of this report is that B. The report is probably accurate because the number is not very specific.
Why might the report be accurate?Digital music revenue recognition might vary from country to country. This means that what constitutes revenue for one country, might not be revenue in another. For that reason, we cannot say that businesses measure revenue accurately.
The report can however be very accurate even if it isn't completely accurate. This shown by the number not being specific to the last cent.
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3. Find the number of volunteers in the group if each volunteer cleans up a section of the following lengths. Be prepared to explain or show your reasoning.
a. 0.4 mile
b. 2/7 mile
c. 0.125 mile
d. 6/45 mile
The number of volunteers needed for each case is given as follows:
a. 0.4 miles: 5.
b. 2/7 miles: 7.
c. 0.125 miles: 16.
d. 6/45 miles: 15.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the unit rates of the context of the problem along with basic arithmetic operations, especially multiplication and division.
In this problem, a two mile section will be cleaned, hence the number of volunteers needed is calculated as follows:
n = 2/s.
In which s is the section cleaned by each volunteer.
In item a, the section is of 0.4 miles, hence the number of volunteers is given as follows:
n = 2/0.4 = 5 volunteers.
In item b, the section is of 2/7 miles, hence the number of volunteers is given as follows:
n = 2/(2/7) = 2 x 7/2 = 7 volunteers.
In item c, the section is of 0.125 miles, hence the number of volunteers is given as follows:
n = 2/0.125 = 2/(1/8) = 2 x 8 = 16 volunteers.
In item d, the section is of 6/45 miles, hence the number of volunteers is given as follows:
n = 2/(6/45) = 2 x 45/6 = 90/6 = 15 volunteers.
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Write the quadratic equation that has roots [tex]\frac{(-1-\sqrt{2})}{3}[/tex] and [tex]\frac{(-1+\sqrt{2})}{3}[/tex] if its coefficient with [tex]x^{2}[/tex] is equal to 1.
The quadratic equation that has roots (-1 - √2)/3 and (-1 + √2)/3 is:
x² + (2/3)x - 1/9 = 0
We have been given the roots of quadratic equation.
(-1 - √2)/3 and (-1 + √2)/3
We need to find the quadratic equation.
Since (-1 - √2)/3 and (-1 + √2)/3 are roots, (x - (-1 - √2)/3) and (x - (-1 + √2)/3) must be the factors of the quadratic equation.
So, the required quadratic equation would be,
(x - (-1 - √2)/3) * (x - (-1 + √2)/3) = 0
x[x - (-1 + √2)/3) ] - ( (-1 - √2)/3) [x - (-1 + √2)/3] = 0
x² - x(-1 + √2)/3 - x(-1 - √2)/3 + [(-1 - √2)(-1 + √2)]/9 = 0
x² - x(-2/3) + (1 - 2)/9 = 0
x² + (2/3)x - 1/9 = 0
Therefore, the quadratic equation that has roots (-1 - √2)/3 and (-1 + √2)/3 is: x² + (2/3)x - 1/9 = 0
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help pass due asap!!!
Add (7x³ - 2x² - 5x+6) and (2x³ + 3x² − x − 1)
a) 9x³ + x² - 6x +5
b) 9x6 + x4 + 5x² − 6
c) 9x³x² - 6x + 5
d) 14x³ - 6x² – 5x - 6
What is the opposite of 6?
Answer:
1
Step-by-step explanation:
The opposite of a number is the number on the other side of 0 number line, and the same distance from 0.
what is the SURFACE AREA
Answer:
164 cm
Step-by-step explanation:
(4x6) / 2= 12
12x2=24 because there are 2 triangles
10x6=60 for the rectangle
(4x10) x 2=80 for the sides
80+60=140
140+24=164
is each pair of lines parallel, perpendicular, or neither?
Answer:
1. perpendicular
2. parallel
3. neither
Step-by-step explanation:
The first set of lines are perpendicular because they intersect each other at a right angle.
The second set of lines are parallel because they never cross.
The first pair forms a 90° angle therefore the lines are perpendicular.
The second lines are straight that it's obviously clear they will never meet meaning they are parallel
the third lines are neither perpendicular nor parallel.
Simplify the expression.
2x(x + 3) - (12x - 4)
Step-by-step explanation:
I hope this will be helpful for you.
[tex]2x(x+3)-(12x-4)\\=2x^{2} +6x-12x+4\\=2x^{2} -6x+4[/tex]
I hope this helps.
I am GROUNDED AND NEED A BETTER GRADE BLEASE HELP
A lawnmower with a 3-gallon gas tank uses an average of 0.6 gallons per hour.
A function modeling this situation, where x represents the amount of gas in the tank, has a domain described by which inequality?
A. 0 ≤ x ≤ 5
B. 0 < x < 5
C. 0 < x < 3
D. 0 ≤ x ≤ 3
The inequality that describes the domain is 0 ≤ x ≤ 5
How to determine the domain of the situation?The given parameters are
Size of tank = 3 gallons
Rate = 0.6 gallons per hour
The highest number of time is calculated as
Time = Size of tank/Rate
Substitute the known values in the above equation
So, we have the following equation
Time = 3/0.6
Evaluate
Time = 5
The domain is then represented as
0 ≤ x ≤ Time
This gives
0 ≤ x ≤ 5
Hence, the domain of the situation is 0 ≤ x ≤ 5
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Making a equation with the slope: 2/3 and the y intersept:2
Answer:
Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.
Equation of line is y = 2/3x + 2
Graph a line with a slope of 1/4 that contains the point (6,3) khan academy
4y = x + 6 is the equation of the line using the slope value.
What is a line's slope?The steepness of a line segment is explained by the slope of the line. It is a ratio of the vertical x-axis coordinates and the y-axis coordinates. The classification of whether two lines are parallel or perpendicular depends on the slope value.
The parameters for the line segment are as follows, in accordance with the question:
The coordinate points (6, 3) and the slope of a line (1/4) are as follows: (x = 6; y = 3)
Using the line segment's standard equation now: y = mx + c
If (x, y) are coordinates, "m" is the slope, "c" is the y-intercept,
The following results are obtained by replacing the slope and y-intercept values in the formula:
y = mx + c
⇒ 3 = (1/4)(6) + c
⇒ c = 3 - 3/2 = 3/2
Consequently, c = (3/2) is the y-value. intercept's
by changing the slope value and y-intercept value in the line's equation:
y = (1/4)x + (3/2) = 4y = x +6
Consequently, 4y = x + 6 is the equation of the line using the slope value.
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Rewrite 0.00518 in scientific notation.
Answer: 5.18 x 10^-3
Step-by-step explanation:
0.00518
**Move the decimal 3 spaces to the right**
5.18
**Since it goes like 0.00, you want to make sure the exponent is negative**
5.18 x 10^-3
Hope this helped <3
A farmer has 220 bushels of wheat to sell at her roadside stand. She sells an average of 15 5/8 bushels each day. Represent the total change in the number of bushels she has for sale after 7 days
Based on the number of bushels that the farmer has to sell, the equation that represents the total change in the number of bushels after seven days is 220 - 15⁵/₈(7).
How to represent the total change?The farmer has a total of 220 bushels of wheat to sell and then sells about 15⁵/₈ every day.
After 7 days, the total change in the number of bushels would be:
= Total bushels to be sold - Bushels of wheat already sold
= Total bushels to be sold - (Number of bushels sold per day x Number of days)
= 220 - 15⁵/₈(7)
= 110 bushels of wheat
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A zoo has an agreement with the local farmers. They sell the daily waste from the elephants to the farmers for $5.00 per pound. If the amount of waste produced by the elephant on a given day is at the 10th percentile of the distribution of waste, how much money would the zoo make selling the waste that day?
The amount of money would be $1115.45 the zoo makes selling the waste that day.
What is Z - score?A Z-score is defined as the fractional representation of data point to the mean using standard deviations.
They charge farmers $5 per pound for the daily feces from the elephants. If an elephant's daily waste production is at or below the 10th percentile for the distribution of waste which is given in the question.
To determine the amount of money would the zoo make selling the waste that day.
P(z ≤ z₀) = 0.1
z₀ = -1.28
⇒z₀ =(x₀ -μ ) / σ
Substitute the values and solve for x₀,
⇒ -1.28 =(x₀ -250 ) / 21
⇒x₀ = (-1.28)×21 - 250
⇒x₀ = 223.09
So the amount of money would be as :
⇒ 223.09 × 5
⇒ 1115.45
Therefore, the amount of money would be $1115.45 the zoo makes selling the waste that day.
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