Answer:
x = 25
Explanation:
We can let an arbitrary rectangle has a length and width of 10, making the total area 10*10 or 100. We know that the length of the rectangle is reduced by 10%, meaning the new length is now 10 - (0.1*10), or 9. The actual width is unknown, but we do know that it will be an x% reduction of the original width: 10 - (0.01x*10), or 10 - 0.1x. We are also given that the area is reduced by 32.5%. This means the new area is 100 - (0.325*100), or 100 - 32.5, which is 67.5. Now, we can use the area formula (length*width) to find the value of x:
[tex]length*width=area\\9*(10-0.1x)=67.5\\90-0.9x=67.5\\-0.9x=-22.5\\x=25[/tex]
This means that the value of x is 25, or the width was reduced by 25%
If a train maintains a constant speed of 60 miles per
hour, it can travel 4 miles per gallon of diesel fuel. If
this train begins a trip with a full 200 gallon tank of
diesel fuel, and maintains a speed of 60 miles per
hour, which of the following equations represents the
number of gallons, g, left in the tank t hours into the
trip?
Answer: g=200-15t
Explanation: The speed is constant at 60 mph. That means every hour, the train is going 60 miles. Since a gallon allows it to travel 4 miles, to travel 60 we need 15 gallons. And since we are going 60 miles every hour, we are using 15 gallons an hour. So we start with 200 gallons, and every hour, t, we use 15 gallons to get gallons (g)=200-15t
An academic quiz show features local high
school students. Each correctly answered
question nets the team one point and an
incorrectly answered question results in a
two-point deduction. If a team scored 38
points on a fifty-question quiz, how many
questions did it answer incorrectly?
Answer:
4 questions
Explanation:
We can either reason this out with logic or solve it out using a system of equations. I will use a system of linear equations to make it easier to understand. We can use two variables in this case: let x equal the number of questions the team answered correctly, and let y equal the number of questions the team answered incorrectly. Since there are two unknown quantities, we will need two equations. Let's use the fact that there are 50 questions total to create our first equation. The total number of questions is just the sum of the correctly and incorrectly answered questions (assuming the team did not leave any answers blank). This means that our first equation is just the following: x + y = 50. For the purpose of the solution, I am going to isolate y and say that y = 50 - x
We can use the point values were know about to create our second equation. We know that the team got 38 points. We also know that correct answers add one point and incorrect answers subtract two points (meaning incorrect answers are worth twice as much as correct answers). Knowing this, we can set up the following equation: x - 2y = 38 (x number of 1-point questions answered correctly, minus 2 times the number of questions answered incorrectly, equals 38 total points).
The system is the following:
[tex]y=50-x\\x-2y=38[/tex]
Now, we can use substitution to solve this system of linear equations. We already know that y = 50-x, so let's substitute that into the second equation to solve for x:
[tex]x-2(50-x)=38\\x-100+2x=38\\3x=138\\x=46[/tex]
y represents the number of questions answered incorrectly, and if we solve for y we get that y = 50 - 46 = 4
Therefore, the team answered 4 questions incorrectly
The number of questions that the students answered incorrectly to get the 38 points was 6 questions.
How to find the number of questions?If we assume the team answered all questions correctly, it would have 50 points. However, the team scored 38 points, which is 12 points less than the maximum.
Because each incorrect answer results in a two-point deduction, we can find out how many questions they answered incorrectly by dividing the missing points by 2:
= 12 points / 2
= 6 incorrect answers
Therefore, the team answered 6 questions incorrectly.
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List two recommended strategies you can use to save money
Answer:
-save by the $100's and spend whatever you have left until you get payed again
A pair of hiking boots sells for $80.00. After
one week, the vendor reduced the cost of
the boots by 20%. After two weeks, he
raised the current price by 20%. What is the
cost of the hiking boots after two weeks?
Function f is defined by the equation
f(x)=ax² + [tex]\frac{2}{a} x[/tex]. If f(3) – f(2) = 11, what is the
smallest possible value of a?
The smallest possible value of a in the given function is 1/5.
Value of f(3)
From the given function, the value of f(3) is calculated as follows;
f(x)=ax² + [tex]\frac{2}{a} x[/tex]
f(3) = a(3)² + [tex]\frac{2}{a}(3)[/tex]
f(3) = 9a + 6/a
Value of f(2)f(x)=ax² + [tex]\frac{2}{a} x[/tex]
f(2) = a(2²) + [tex]\frac{2}{a} (2)[/tex]
f(2) = 4a + 4/a
f(3) – f(2) = 11
(9a + 6/a) - ( 4a + 4/a) = 11
9a + 6/a - 4a - 4/a = 11
5a + 2/a = 11
multiply through with "a"
5a² + 2 = 11a
5a² - 11a + 2 = 0
5a² - 10a - a + 2 = 0
5a(a - 2) - 1(a - 2) = 0
(5a - 1)(a - 2) = 0
a = 2, or
5a = 1
a = 1/5
Thus, the smallest possible value of a in the given function is 1/5.
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How 401k loans are different from other loans
Answer:
Technically, 401(k) loans are not true loans, because they do not involve either a lender or an evaluation of your credit history. They are more accurately described as the ability to access a portion of your own retirement plan money—usually up to $50,000 or 50% of the assets, whichever is less—on a tax-free basis.
A technology store sells tablets and
computers. In January they sell over 300
items, and more of those sales are tablets
than computers. In February they sell
exactly 100 tablets and 20 computers. The
graph at left shows two equations related
to this problem, where t is the total tablet
sales (in January and February combined),
and c is the total computer sales. Which of
the following combinations could be the
technology store's total sales?
A. 240 tablets and 100 computers
B. 360 tablets and 180 computers
C. 240 tablets and 260 computers
D. 120 tablets and 180 computers
The combination that could be the total sales would be 360 tablets and 180 computers.
Total sales
Over 300 total sales were made in January
100 tablets and 20 computers were sold in February.
This means that total sales would be: (300+) 100 + 20 = 420+
Only options B and C have 420+ total sales.
But, there are more tablet sales than computers.
Thus, we are left with only option B
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The statement of account brings out numerous information beneficially, to Two (2) important state who are these parties and list FIVE(5) information that would appear on this document.
Pls help!!!
The two parties that benefit from the information in a statement of account are:
BuyerSellerWhat is a Statement of Account?This refers to the financial record that states the exchange of goods and income between a buyer and seller during a certain period.
Hence, we can see that some information that would appear in a statement of account are:
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Which of the following expressions is equivalent to 2a(3a-4a^2)?
A. 5a-2a^2
B. 5a^2-2a^3
C. 6a-8a^2
D. 6a^2-8a^3
Answer:
D. 6a^2-8a^3
Explanation:
Using distributive property
Write one to two paragraphs describing your plan. In your answer, include all of the following: (a) what you would do about your grades; (b) activities in which you can get involved; (c) possible part-time jobs you can do; and (d) standardized tests you can take. (10 points)
My plan in terms of school work is to do a small research on how one can have a good grade without stress.
In terms of my grades, I will study hard and improve on it that previous semester. The activities that i will be involved is the science club
What is the possible part-time jobs you can do?The possible jobs are:
To work in the state libraryTo work as a janitor.In terms of the above, a standardized tests that i can take is random sampling to know what and what not to do.
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Answer:
my plan start with school so when i start
I am grade 9 student.
I hope to score average above 90
I am a student so my work, job is learning
I take a test tomorrow and I am studying now
whats the diference between 1/2 e to the x minus 4 and e to the x minus 4
The difference between [tex]\frac{1}{2}e^{x-4}[/tex] and [tex]e^{x-4}[/tex] is that the first equation is only half of the second equation. When we multiplied [tex]e^{x-4}[/tex] by [tex]\frac{1}{2}[/tex], the remaining result became half of [tex]e^{x-4}[/tex]. Hope this helps!
23. A lawn covers 108.6 square feet. Russ
mowed all of the lawn in three evenings. He
mowed 2/9 of the lawn during the first
evening. He mowed twice that amount on
the second evening. On the third and final
evening he mowed the remaining lawn.
How many square feet were mowed the
third evening?
The number of square feet that were mowed in the third evening is 36.201 ft².
Amount of lawn moved in the first dayAmount (day 1) = ²/₉ x 108.6 ft²
Amount (day 1) = 24.133 ft²
Amount of lawn moved in the second dayAmount (day 2) = 2(24.133 ft²) = 48.266 ft²
Amount of lawn moved in the third dayAmount (day 3) = 108.6 ft² - (24.133 ft² + 48.266 ft²)
Amount (day 3) = 36.201 ft²
Thus, the number of square feet that were mowed in the third evening is 36.201 ft².
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Johnny deposited $50 in a savings bank at
the beginning of the year. Johnny’s money
earns him interest at the rate of 8 percent
of the amount deposited, for each year that
Johnny leaves his money in the bank. If
Johnny leaves his $50 in the bank for
exactly one year and then decided to
withdraw all of his money, how much
money (including interest) can he withdraw?
(The interest is not compounded.)
Answer:
54 dollars
Explanation:
Because this problem involves simple interest, and the money is only deposited for one year, you can calculate the amount of money in the bank after one year by thinking about a percent increase. Johnny starts with 50 dollars in his bank account, and we are given that he will experience an 8% increase over the year. This means that the amount of money in his bank account after one year is just 50 + 0.08*50 (the principal amount plus the simple interest, or amount of money that increases during the year). This is equal to 50 + 4, or 54 dollars.
Note that, whenever we are dealing with simple interest, the amount of money in the bank after a certain number of years is just P(1 + PRT), where P is the principal amount, R is the interest rate, and T is the number of years the money is in the bank.
A customer service call center for a credit
card company asks 1 in 8 of the callers to
take a survey at the conclusion of the call.
Approximately 20% of those solicited
consent to the survey. If 400 callers were
serviced between 2:00 and 3:00 one
afternoon and 20% of the callers consented
to the survey, how many callers did not
consent to the survey?
The number of callers that did not consent to the survey is 40 callers.
Number of callers that did not consent to the surveyUsing this formula
Number of caller=Callers×(1-Percentage of those that solicited)÷Callers at conclusion survey
Let plug in the formula
Number of caller=400 ×(1-20%)÷8
Number of caller=400 ×80%÷8
Number of caller=320÷8
Number of caller=40 callers
Therefore the The number of callers that did not consent to the survey is 40 callers.
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3 reasons why a introductory rate or balance transfer APR of 0% might not be a good offer after all
Answer:
The APR doesn't last forever. Enjoy it while you can, because once your 0% introductory period is over, it's over. The 0% interest only lasts for the duration of the introductory period, and once it ends, the card will revert to its regular APR (the exact rate is determined based on your creditworthiness).
Answer:
Explanation:no
Explain how it is that many Americans find themselves swimming in credit card debt, unable to pay down their
debt quickly.
Answer:
People use their card for a purchase they can’t afford or want to defer payment, and then they make only the minimum payment that month. Soon, they are in the habit of using their card to purchase things beyond their budget. Since they are making only the minimum monthly payment, it won’t seem to matter much if their credit card balance gets a bit larger. This is a quick illustration to show how their “small balance” of just a few thousand dollars can really mean paying more than double that amount over the years because of interest. Also, when they are trapped in this mindset, their balance barely budges. With a debt of $5,000 and a minimum monthly payment of $150 (at 3% of the total balance), they will only be paying $47.30 each month toward their principal. The rest goes toward their interest accrued.
If 4^3a/8^b=1, what is a/b?
A. 1/3
B. 1/2
C. 3/4
D. 4/3
Answer:
B. 1/2
Explanation:
Here, 4^3a/8^b=1
or, 4^3a=8^b
or, (2²)^3a=(2³)^b
Equating powers of like bases,
6a/3b=1
or, a/b=3/6=1/2.
17. A supermarket buys cartons of orange juice
for k dollars each and then sells them for [tex]\frac{4k}{3}[/tex]
dollars each. How many cartons do
they need to sell to make a profit of $2,000?
A total of 6,000 cartons would be needed.
Miscellaneous calculationCost price = k dollars
Selling price = 4k/3 dollars
Assuming k = 1 dollar
Profit per carton = 4/3 - 1 = 1/3 dollars
2000/1/3 = 6,000 cartons.
Thus, irrespective of the cost price, 6,000 cartons would be needed to generate a profit of $2,000
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As you read the essay, “Congress and the Quest for Power” by Lawrence Dodd, answer the following questions.
1.) According to the author, people enter politics for what reason?
2.) Dodd asserts that “reelection” is necessary for three reasons. What are these three reasons?
3.) The “electoral connection” will lead members of Congress to emphasize what traits? What traits or actions will they begin to care about less?
4.) What motive causes each member of Congress to be in conflict with each other?
5.) Where do Congress members spend the most time? Why?
According to “Congress and the Quest for Power” by Lawrence Dodd, people enter politics because of their quest for power.
Dodd asserts that “reelection” is necessary for three reasons. What are these three reasons?The three reasons why reelections are required are:
Personal PowerAura of Personal LegitimacyOpportunity go gain expertise and experience.The “electoral connection” will lead members of Congress to emphasize what traits?The “electoral connection” will lead members of Congress to emphasize :
Form over substancePosition TakingAdvertisement Credit claiming.What traits or actions will they begin to care about less?The traits or actions they begin to care about less are:
Failure to take clear and controversial positions;Failure to make hard choicesFailure to exercise power.What motive causes each member of Congress to be in conflict with each other?The need to exercise power for making key policy decisions.
Where do Congress members spend the most time? Why?They spend most of their time in:
the committee or sub committee roomsin caucus meetings; orOffice work related to legislation.Learn more about congress at;
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15. Container A holds twice as much as
container B, and container C holds as much
as A and B put together. If we start with A
and B full, and C empty, and pour half the
contents of A and a third of the contents of
B into container C, what fraction of C’s
capacity will be filled?
The fraction of C’s capacity that will be filled is determined as 4/9.
Fraction of C's capacity filled
A = 2B
C = A + B
C = 2B + B
C = 3B
When half the contents of A and a third of the contents of B into container C.
C = (1/2)A + (1/3)B
C = (1/2)(2B) + (1/3)B
C = B + (1/3)B
C = (4/3)B
Fraction of C filled;
3B(x) = (4/3)B
3x = 4/3
9x = 4
x = 4/9
Thus, the fraction of C’s capacity that will be filled is determined as 4/9.
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The sum of three numbers is 780. One of
the numbers, n, is 50% more than the sum
of the other two numbers. What is the
value of n?
The value of n in the unknown three numbers is 468.
Value of the missing numberlet the first number = nlet the sum of the second and third number = y
n + y = 780
if n is 50% more than y;
n = 1.5y
1.5y + y = 780
2.5y = 780
y = 780/2.5
y = 312
n = 1.5y = 1.5 x 312 = 468
Thus, the value of n in the unknown three numbers is 468.
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Belts costs $11 and blouses cost $18. If Kara
spends at least $51 but no more than $62
for x belts and one blouse, what is one
possible value of x?
Answer:
Two possiable answers for X are 3 and 4
Explanation:
18+11(3)=51
18+11(4)=62
One possible value of x is 4. Kara buys 4 belts and one blouse, spending $62 (4 belts * $11 per belt + $18 for the blouse).
What is the cost?
Total cost = (Cost of x belts) + (Cost of one blouse)
Total cost = (11x) + 18
According to the given condition, Kara spends at least $51 but no more than $62:
51 ≤ (11x + 18) ≤ 62
Lower bound:
51 ≤ 11x + 18
Subtract 18 from both sides:
51 - 18 ≤ 11x
33 ≤ 11x
3 ≤ x
Upper bound:
11x + 18 ≤ 62
Subtract 18 from both sides:
11x ≤ 44
Divide both sides by 11:
x ≤ 4
Thus;
3 ≤ x ≤ 4
The only integer value of x that satisfies both inequalities is x = 4.
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y=x^3+kx^2-9x-18
One solution to the equation shown above is -2. What is the positive solution to the equation?
Answer:
3
Explanation:
A solution to a function is when the graph of the function crosses the x-axis. In other words, it's a point where y = 0. So, we can set x^3 + kx^2 - 9x -18 equal to 0. Note that there is an unknown coefficient in this equation (k) that we have to solve for. We are given that one solution to this equation is -2. This means that we can plus x = -2 into the equation and solve for the unknown k:
[tex](-2)^3+k(-2)^2-9(-2)-18=0\\-8+4k+18-18=0\\4k=8\\k=2[/tex]
Therefore, the complete equation is the following:
[tex]y=x^3+2x^2-9x-18[/tex]
As it turns out, we can use grouping to factor this polynomial. Let's start by re-ordering the terms to visualize it better:
[tex]x^3-9x+2x^2-18=0[/tex]
The first two terms have a GCF of x, and the last two terms have a GCF of 2:
[tex]x(x^2-9)+2(x^2-9)[/tex]
Now, there is a common term that we can bring to the front to complete our factoring process:
[tex](x^2-9)(x+2)[/tex]
First of all, note that x+2 is one of the factors, and if this was set to 0, we would get -2, which is consistent with the problem. Also, note that our other term can be factored more because it is a difference of two squares:
[tex](x-3)(x+3)(x+2)=0[/tex]
If we set each term to 0, we get x = 3, x = -3, and x = -2. We are only looking for the positive solution to this equation, which is 3
Amanda travels to work from home in 60
minutes. If, on her way home, she increases
her average speed by 20% and she travels
by the exact same route, how many
minutes will it take her to get home?
Answer:
50 minutes
Explanation:
We can set this up as a rate * time = distance problem. We can set the rate at which Amanda travels to work to be x, since that quantity is unknown. The time it takes is given to be 60 minutes. This means that the total distance she travels to get to work is 60x. On the other hand, the way back home has more unknown quantities. The exact rate is unknown, but we do know that it is 20% more than the rate at which Amanda travels to work. This means that the rate is x + .20x, or 1.2x. We can set the time to be y, which means the total distance she travels to get back home is 1.2xy. We are told that Amanda uses the same route to get to and from work, which means 60x = 1.2xy. All we have to do now is solve this equation:
[tex]60x=1.2xy\\60=1.2y\\y=50[/tex]
If we divide through by x and then isolate y, we get that it takes Amanda 50 minutes to get home
Karla tanner opened a web consulting business called link works and completed the following transaction in thr first month of operations
(x^5*y^6)^1/5(x^3*y^4)^1/4=x^m/4*y^n/5
If the equation above, where m and n are constants, is true for all positive values of x and y, what is the value of m+n?
If m and n are constants and it is true for all positive values of x and y, the value of m+n is 7+11 = 18
What is the simplification of the given algebra?The simplification of the given algebra can be evaluated by using the law of indices.
Given that:
[tex]\mathbf{=(x^5y^6)^{1/5}(x^3y^4)^{1/4}}[/tex]
[tex]\mathbf{=xy^{6/5}(x^3y^4)^{1/4} }[/tex]
Simplifying using the multiplication power rule.
[tex]\mathbf{=xy^{6/5}(x^{3/4}y)}[/tex]
[tex]\mathbf{=xy^{6/5} \times (x^{3/4}y)}[/tex]
Multiplying like terms.
[tex]\mathbf{=x^{\frac{4+3}{4}} y^{\frac{6+5}{5}}}[/tex]
[tex]\mathbf{=x^{\frac{7}{4}} y^{\frac{11}{5}}}[/tex]
where;
m = 7 and n = 11The value of m+n = 7+11 = 18.
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What are some strategies consumers can use to reduce the amount of interest they'll pay on credit card debt?
Answer:
Some strategies that consumers can use to reduce the amount of interest they'll pay on credit card debt are:
1. Pay off the debt with the highest interest rate first.
2. Make more than the minimum payment each month.
3. Try to negotiate a lower interest rate with your credit card company.
4. Use a balance transfer credit card to pay off your debt.
5. Get a personal loan to pay off your credit card debt.
Explanation:
Continue to pay your bills on time, get rid of any remaining debt, and establish a plan to give it another go in three to six months. The next time, you can make a stronger argument by repairing your credit.
What strategies consumers can use to reduce interest?Lower interest rates make borrowing less expensive, enabling people to spend and invest more freely. Interest rates have a long-term impact on the cost of borrowing money.
Interest rates are influenced by the supply and demand of money, government borrowing, inflation, and the Central Bank's monetary policy goals.
You may frequently be given a cheaper interest rate if you keep up good credit and a spotless payment history.
Therefore, On the other hand, higher rates increase the cost of borrowing and can cause consumers to spend less and save more.
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ax=5
In the equation above, a is a constant. For which of
the following values of a will the equation have no
solutions?
A) 0
B) 1
C) 5
D) 10
1, 5, and 10 would all result in a valid solution for x. Therefore options B, C, and D are correct.
To determine the values of "a" for which the equation Ax = 5 has no solutions, we can solve the equation for x. Since "a" is a constant, we can rearrange the equation to x = 5/a.
For the equation to have no solutions, the value of "a" must be such that the expression 5/a results in division by zero. Therefore, the value of "a" that would lead to no solutions is A) 0. If "a" is zero, then 5/0 is undefined, and the equation Ax = 5 would not have a valid solution for x.
The other options (B) 1, (C) 5, and (D) 10 would all result in a valid solution for x.
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If one pound of grain can feed five chickens
or two pigs, then ten pounds of grain can
feed 20 chickens and how many pigs?
Answer: 12 pigs
Explanation:
1 pig= 1/2 lb
1 chicken= 1/5 lb
20 divided by 5 = 4 lbs of grain used on chickens
10 - 4 = 6
6 x 2 (how many pigs could be fed with a pound) = 12 pigs
Which goal would people be most likely to set after reading this passage?
Recycle plastic and glass bottles.
Walk or ride a bike instead of driving.
Reduce the amount of water they use.
Turn off their electrical appliances.
Answer:
save environment
Explanation:
hope this helps
Answer:
Reuseing
Explanation:
Reducing and recling