Answer:
2K + 12L ≥ 87 and 1.5K + 8L > 63
Step-by-step explanation:
It takes 2 wooden sticks and 1.5 square feet of paper to make a kite, and it takes 12 wooden sticks and 8 square feet of paper to make a lamp.
If K denotes the number of kites that Min-Young made and L denotes the number of lamps she made then
2K + 12L is the number of wooden sticks that she used which is greater than equal to 87
i.e. 2K + 12L ≥ 87 ........ (1)
Again, 1.5K + 8L is the number of square feet of paper that she used which is greater than 63 sq. feet
i.e. 1.5K + 8L > 63 ........... (2)
Hence, inequalities (1) and (2) are the required answer. (Answer)
Answer:
1) 2K + 12L ≥ 87
2) 1.5K + 8L > 63
Step-by-step explanation:
what is the process of changing a mixed fraction into an improper fraction, like 4 1/3 into 13/3 ?
Answer:
multiply the whole number by the denominator, then add the number you get to the numerator. :) hope this was helpful!!!
Step-by-step explanation:
Answer: You have to multiply the Main number by the denominator, then add the numerator to that number, and put it above the original denominator.
Step-by-step explanation:
What is the equation of the line in slope-intercept form?
y = x –
y = x +
y = x –
y = x +
Answer:
Step-by-step explanation:
All of the answer choices are in slope-intercept form.
The slope-intercept form is y=mx+b where m=slope and b=y-intercept.
Answer:
B
Step-by-step explanation:
y-x=15 y-x=5 using elimination
Answer:
No solution
Step-by-step explanation:
To eliminate is to get rid of one of the variables.
You can choose to either add each term in the equations or subtract each term in the equation.
For a variable to be eliminated, there must one pair that have the same constant with it. Each equation already has the same constant with a variable.
Try adding them.
. y - x = 15
+ y - x = 5
2y - 2x = 20 No variables were eliminated.
Try subtracting.
. y - x = 15
- y - x = 5
0y - 0x = 10 All variables were eliminated.
. 0 = 10 This is false.
This system of equations cannot be solved.
Graphically, these two lines would have the same slope and are parallel. The solution to a system is same as the point of intersection. Parallel lines never meet, never intersect, therefore there is no solution.
Mike invested a total of $25,000, some money in stocks and some money in bonds. The stocks earned 7% simple interest while the bonds earned 11% simple interest. Mike earned $2010 interest on his investments. How much money did he invest in bonds?
He invested $6500 in bonds
Step-by-step explanation:
The formula of the simple interest is I = Prt, where
P is the invested amountr is the rate of interest in decimalt is the time of investmentAssume that Mike invested $x in stocks and $y in bonds
∵ Mike invested $x in stocks
∵ Mike invested $y in bonds
∵ Mike invested a total of $25,000
∴ x + y = 25000 ⇒ (1)
∵ The interest rate of the stocks is 7%
∴ r of the stocks = 7 ÷ 100 = 0.07
∴ I (stocks) = x(0.07)(1)
∴ I (stocks) = 0.07x
∵ The interest rate of the bonds is 11%
∴ r of the bonds = 11 ÷ 100 = 0.11
∴ I (bonds) = y(0.11)(1)
∴ I (bonds) = 0.11y
∵ Mike earned $2010 interest on his investments
- Equate the sum of I (stocks) and I (bonds) by 2010
∴ 0.07x + 0.11y = 2010 ⇒ (2)
Now we have a system of equations to solve it
Multiply equation (1) by -0.11 to eliminate y
∵ -0.11x - 0.11y = -2750 ⇒ (3)
- Add equations (2) and (3)
∴ -0.04x = -740
- Divide both sides by -0.04
∴ x = 18500
- Substitute the value of x in equation (1) to find y
∵ 18500 + y = 25000
- Subtract 18500 from both sides
∴ y = 6500
∵ y represents the amount of money he invested in bonds
∴ He invested $6500 in bonds
He invested $6500 in bonds
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Fred earned $5,000 during the month of June.
Use the paycheck statement to find the missing amounts and percent rates of the taxes Fred paid.
Answer:
Fred paid US$ 310 to Social Security as a payroll tax
Fred paid US$ 72.50 to Medicare as a payroll tax
Fred paid 18% of his income to the Federal government as an income tax
Fred paid 5% of his income to the state government as an income tax
Step-by-step explanation:
Fred's earnings in June were $ 5,000
A. Payment to Social Security
5,000 * 6.2% = 5,000 * 0.062 = 310
B. Payment to Medicare
5,000 * 1.45% = 5,000 * 0.0145 = 72.50
C. Federal Income Tax
900/5,000 = 0.18 = 18%
D. State Income Tax
250/5,000 = 0.05 = 5%
Final answer:
Calculating net income, monthly income, and tax rates based on Fred's earnings in June.
Explanation:
Mathematics
Calculate the Net Annual Income for Fred:
Calculate Social Security deduction: $5,000 * 6.2% = $310Calculate Medicare deduction: $5,000 * 1.45% = $72.50Calculate Federal and State taxes: $5,000 * 15% = $750Net Annual Income for Fred: $5,000 - $310 - $72.50 - $750 = $3,867.50Calculate Monthly Income for Fred: $3,867.50 / 12 = $322.29
Percent Rates of Taxes Paid by Fred:
Percent of Social Security Tax: ($310 / $5,000) * 100 = 6.2%Percent of Medicare Tax: ($72.50 / $5,000) * 100 = 1.45%Percent of Federal and State Taxes: ($750 / $5,000) * 100 = 15%(5x)+ (9y)+90 what is x and y
Answer:
Step-by-step explanation:
5x+9y+90
This is just an algebraic expression.
What is 10 to the power of 10
Marcella bought 12/14 yards of ribbon. She uses 2 1/2 yards of ribbon for gift packages and 3 2/3 yards to tie balloons.
How many yards of ribbon does Marcella have left?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
[tex]6\frac{1}{12}\ yd[/tex]
Step-by-step explanation:
The correct question is
Marcella bought 12 1/4 yards of ribbon. She uses 2 1/2 yards of ribbon for gift packages and 3 2/3 yards to tie balloons.
How many yards of ribbon does Marcella have left?
we know that
To find out how many yards of ribbon Marcella has left, add up the yards of ribbon used for the gift packages plus the yards of ribbon used to tie the balloons. and subtract this result from the total yards of ribbon bought by Marcella
so
[tex]12\frac{1}{4}-(2\frac{1}{2}+3\frac{2}{3})[/tex]
but first convert mixed number to an improper fractions
[tex]12\frac{1}{4}=\frac{12*4+1}{4}=\frac{49}{4}[/tex]
[tex]2\frac{1}{2}=\frac{2*2+1}{2}=\frac{5}{2}[/tex]
[tex]3\frac{2}{3}=\frac{3*3+2}{3}=\frac{11}{3}[/tex]
substitute in the expression above
[tex]\frac{49}{4}-(\frac{5}{2}+\frac{11}{3})[/tex]
[tex]\frac{49}{4}-(\frac{5*3+2*11}{6})[/tex]
[tex]\frac{49}{4}-(\frac{37}{6})[/tex]
[tex]\frac{3*49-37*2}{12}[/tex]
[tex]\frac{73}{12}\ yd[/tex]
Convert to mixed number
[tex]\frac{73}{12}\ yd=\frac{72}{12}+\frac{1}{12}=6\frac{1}{12}\ yd[/tex]
Final answer:
After calculating the total ribbon used in yards and subtracting it from the amount Marcella bought, we find that she has 5 13/42 yards of ribbon left.
Explanation:
To determine how many yards of ribbon Marcella has left, we need to subtract the total amount of ribbon she used from the initial amount she bought. Marcella originally bought 12/14 yards of ribbon. She used 2 1/2 yards for gift packages and 3 2/3 yards for tying balloons.
To make the subtraction easier, we'll first convert the mixed numbers to improper fractions. The mixed number 2 1/2 becomes 5/2 when we multiply 2 (the whole number) by the denominator (2) and then add the numerator (1), resulting in 4 + 1 = 5 over the original denominator 2. Similarly, 3 2/3 becomes 11/3 when we multiply 3 (the whole number) by the denominator (3) and then add the numerator (2), resulting in 9 + 2 = 11 over the original denominator 3.
Now, let's perform the subtraction:
First, simplify 12/14 to 6/7 by dividing both the numerator and denominator by 2.
Next, find a common denominator for all three fractions. The least common denominator for 2, 3, and 7 is 42.
Convert each fraction to have the denominator of 42.
12/14 yards (or 6/7 yards when simplified) is (6/7) * (42/42) which equals 36/42 yards.
2 1/2 yards as an improper fraction is 5/2, and when converted to have a denominator of 42, it becomes (5/2) * (21/21) which equals 105/42 yards. Similarly, 3 2/3 yards is 11/3, and when converted to have a denominator of 42, it becomes (11/3) * (14/14) which equals 154/42 yards.
Now subtract both of these amounts from 36/42 to find out how much ribbon Marcella has left:
36/42 - 105/42 - 154/42 = (36 - 105 - 154)/42 = -223/42
Because we cannot have a negative amount of ribbon, we realize we made an error. We should add the fractions instead of subtracting:
36/42 - (105/42 + 154/42) = (36/42) - (259/42)
This simplifies to -223/42, which is an improper fraction. To convert this back to a mixed number, we divide 223 by 42.
223 divided by 42 is 5 with a remainder of 13, so Marcella has 5 13/42 yards of ribbon left. However, we need the positive value since ribbon length cannot be negative. Thus, we keep the positive difference:
Marcella has 5 13/42 yards of ribbon remaining.
In conclusion, after Marcella uses ribbon for gift packages and tying balloons, she is left with 5 13/42 yards of ribbon.
Each student wears a name tag while at the aquarium the name tags are rectangles that are three inches long and five inches wide what is the area of each name tag
Answer:
15 in2
Step-by-step explanation:
3*5= 15
length*width= area
Hope it helped!!!
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Answer: 16 square inch
Step-by-step explanation: 5+5+3+3=16
with the exception of the first house, all the houses on sequence lane have an address whose numerical portions are greater than that of the prior house. if ainsley and lane are next door neighbors and the sun of the numerical portions of their addresses is 49, what are their addresses ?
Answer:
The address of Ainsley is 24 and that of Lane is 25.
Step-by-step explanation:
All the houses on sequence lane have an address whose numerical portions are greater than that of the prior house.
Now, if Ainsley and Lane are next-door neighbors and the sum of the numerical portions of their addresses is 49.
Let the Ainsley has the address with numeric portion x, then Lane has the address with numeric portion x + 1.
Therefore, x + (x + 1) = 49
⇒ 2x = 48
⇒ x = 24
So, the address of Ainsley is 24 and that of Lane is 25. (Answer)
Bryce can afford a $350-per-month car payment. If he is being offered a 6-
year car loan with an APR of 4.2%, compounded monthly, what is the value of
the most expensive car he can afford?
O
A. $25,196.78
B. $22,241.32
O
c. $25,167.83
O D. $24,880.83
Answer: $22,241.32 APEX
Final answer:
By calculating the present value of an annuity using the monthly payment, interest rate, and number of payments, we find that Bryce can afford a car with a value of approximately $22,241.32.
Explanation:
To calculate the value of the most expensive car Bryce can afford based on a $350-per-month car payment with a 6-year loan at an APR of 4.2%, compounded monthly, we use the formula for the present value of an annuity:
PV = PMT × ¶ [(1 - (1 + r)^-nt) / r]
Where:
PV = Present Value (what we're solving for, the cost of the car)
PMT = Monthly Payment ($350)
r = monthly interest rate (APR divided by 12)
n = number of times the payment is made per year (12)
t = number of years (6)
Given:
APR = 4.2% per year or 0.042
Monthly interest rate, r = 0.042 / 12 = 0.0035
nt = 12 × 6 = 72 payments in total
Now we substitute the given values into the formula:
PV = $350 × [(1 - (1 + 0.0035)^-72) / 0.0035]
PV = $350 × [(1 - (1 + 0.0035)^-72) / 0.0035]
PV ≈ $350 × [(1 - (1.0035)^-72) / 0.0035]
Using a calculator to find (1.0035)^-72 and then the whole expression, we get:
PV ≈ $350 × 60.4774
PV ≈ $21,167.09
The value that's closest to our calculation and offered in the options is $22,241.32, so the most expensive car Bryce can afford is approximately $22,241.32.
Using the diagram, find the value of x.
14x+4
◀----▶-▶--------------▶
A. -8
B. -7
C. 9
D. 11
Answer:
c are the correct answer
Frederick buys a can of three tennis balls. The empty can weighs 20 grams, and each tennis ball weighs 60 grams. What is the total weight of the can with 3 tennis balls
The total weight of the can with tennis balls is 200 grams
Step-by-step explanation:
Let b be the weight of one ball
and
c be the weight of can
Then
c = 20 grams
b = 60 grams
The weight of three balls will be:
[tex]3b\\=3*60\\=180\ grams[/tex]
Hence,
The total weight will be:
[tex]c+ 3b\\= 20+180\\= 200\ grams[/tex]
So,
The total weight of the can with tennis balls is 200 grams
Keywords: Measurement, weights
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Answer:
200
Step-by-step explanation:
Ryan is installing new flooring in his house. Ryan can install 121 square feet of flooring in 3 hours. How much new flooring can Ryan install in 24 hours?
Answer:
968 square feet
Step-by-step explanation:
Let x be the new flooring install in 24 hours.
Given:
Ryan can install 121 square feet of flooring in 3 hours.
So, Ryan can install flooring in one hour = [tex]\frac{121}{3} feet^{2}[/tex]
Ryan can install flooring in 24 hours.
[tex]x= 24\times flooring\ in\ one\ hour[/tex]
[tex]x=24\times \frac{121}{3}[/tex]
[tex]x=8\times 121[/tex]
[tex]x=968\ feet^{2}[/tex]
Therefore, Ryan can install 968 square feet of flooring in 24 hours.
If the volume of a cube is 729 cm3, what is the surface area of the cube?
A) 462 cm2
B) 474 cm2
C) 486 cm2
D) 494cm2
Answer:
Step-by-step explanation:
The answer is C because V = s3 → 729 = s3 → 9 = s
Therefore, SA = 6s2 = 6(9)2 = 486 cm2
What is the value of 5(x+2)−4(x+1) when x=1.5
Answer:
7.5
Step-by-step explanation:
5(x+2)-4(x+1)
5x+10-4x-4
5x-4x+10-4
x+6
1.5+6=7.5
Answer:
7.5
Step-by-step explanation:
Substitute 1.5 into the equation
5(1.5+2) − 4(1.5+1)
5(3.5) − 4(2.5)
17.5 - 10 = 7.5
If you arrange the like terms in the same columns, you can perform addition of polynomials in ”column” form. Find the following sums:
Answer: im going to solve it in one second
Step-by-step explanation:
Which of these is a complex number?
A. 9 + 375
OB. 5/1 3 - 2
oc. 2 - 1 / 1
OD. + A
Explanation:
Note: As you haven't clearly specified the answer choices. But, I am assuming one of the answer choices may have included some negative number under a square root, as a real number cannot have a negative number under a square root. So, whatever the choice may have contained the negative number under a square root would represent the complex number. Anyhow, I would try to clear your concept.
So, lets move forward.
A complex number is basically the combination of a real number and imaginary number which can be expressed in the form of [tex]a+ib[/tex]. where a and b are termed as real numbers and i is a solution of the equation x² = -1.
So,
In [tex]a+ib[/tex],
"i" is called iota.[tex]i=\sqrt{-1}[/tex]For example, let us consider
[tex]2 + \sqrt{-1}[/tex]
Here, 2 is a real part, And [tex]\sqrt{-1}[/tex] is imaginary part, meaning [tex]i=\sqrt{-1}[/tex], which is imaginary part.Therefore, [tex]2 + \sqrt{-1}[/tex] is a complex number.
Keywords: complex number, iota
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Marcus has a part-time job at the water park. He makes between $77.26 and $83.67 a day. Which is a reasonable amount of money that Marcus makes for working 5 days a week for 10 weeks? A. $4,202 B. $4,213 C. $4,001 D. $3,843
Answer:
c
Step-by-step explanation:
How is the graph of y = log (x) transformed to produce the graph of y = log (2 x) + 3?
Answer:
Step-by-step explanation:
The graph of log 2x has the same shape as that of log x, except that it is compressed horizontally by a factor of 2.
Additionally, that +3 indicates that we must translate the above graph upwards by 3 units.
we must replace [tex]x[/tex] by [tex]2\cdot x[/tex] and then translate the function 3 units in the +y direction.
We can transform [tex]y = \log x[/tex] into [tex]y = \log 2\cdot x +3[/tex] by means of the following operations:
Replace [tex]x[/tex] by [tex]2\cdot x[/tex]. (Dilation factor: 2)Translate the resulting expression 3 units in the +y direction. (Vertical translation)That is, we represent the operations defined above mathematically:
1) [tex]y = \log x[/tex]
2) [tex]y = \log 2\cdot x[/tex]
3) [tex]y = \log 2\cdot x + 3[/tex]
In a nutshell, we must replace [tex]x[/tex] by [tex]2\cdot x[/tex] and then translate the function 3 units in the +y direction.
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Solve 2 1/4 - 1 2/5=?
Answer:
17/20
Step-by-step explanation:
2 1/4=9/4
1 2/5=7/5
--------------
9/4-7/5
45/20-28/20
17/20
Find the measure of (Full question above)
Answer:
∠RUS = 90°
Step-by-step explanation:
PT is a line. This means that it has a measure of 180°
This means that all of the angles that it is broken up into must add together to equal 180°.
In this case, ∠PUQ +∠QUR +∠RUS +∠SUT = 180°
As we have the measures for all of the angles aside from ∠RUS, we can solve for that
First, let us input each of the measures of the angles
39+23+∠RUS+28=180
Now all we need to do is isolate ∠RUS by subtracting everything to the other side
Once that is done, we get
∠RUS = 90°
Answer:
[tex]\large\boxed{m\angle RUS=90^o}[/tex]
Step-by-step explanation:
[tex]m\angle PUT=m\angle PUQ+m\angle QUR+m\angle RUS+m\angle SUT\\\\\text{We have:}\\\\m\angle PUT=180^o,\ m\angle PUQ=39^o,\ m\angle QUR=23^o,\ m\angle SUT=28^o\\\\\text{Substitute:}\\\\180^o=39^o+23^o+m\angle RUS+28^o\\\\180^o=90^o+m\angle RUS\qquad\text{subtract}\ 90^o\ \text{from both sides}\\\\90^o=m\angle RUS[/tex]
For each trip they charge on intail fee of 100 in additoin to a constant fee for each vertical letter climbed for instance the price for climbing to the shura volcianc cone which in 3000 meters above the base of the mountain in 400. Let f represent the fee in dollors of a trip they climbed d vertical meters
Answer:
f = 100 + 0.133d
Step-by-step explanation:
For each trip, they charge an initial fee of 100 in addition to a constant fee for each vertical meter climbed.
For example, for 3000 meters of climbing, they charged the additional constant fee of 400.
Therefore, per meter climbing they charges [tex]\frac{400}{3000} = 0.133[/tex].
Therefore, if f represents the fee in dollars of a trip they climbed d vertical meters then we can model the situation as
f = 100 + 0.133d (Answer)
20.
When starting your credit history, a low-credit-limit, high-interest-rate credit card should be paid
as much as you can when due
in even payments each time
at least the minimum due
in full, on time, every time
Answer:
in full, on time, every time
Step-by-step explanation:
in full, on time, every time because even if little is left out it would again a large amount together with the interest. Also as the limit is low it can easily be reimbursed
15 POINTS!!!!!! HELPPPPP ASAP A music store has 500 guitar picks. They order 15 boxes with 9 picks each. They sell 19 boxes that have 10 picks each. The store manager says they now have about 450 guitar picks.
Is the manager's estimate reasonable?
500 guitar picks
order 15 boxes with 9 picks each
sell 19 boxes with 10 picks each
-> the store ordered about 150 picks (15 x 9 -> 15 x 10)
-> the store sold about 200 picks (19 x 10 -> 20 x 10)
it is reasonable, since they have 50 fewer picks which is about 450.
(second option)
Solve for m.
3.6m=14.4
Enter your answer in the box.
Answer:
10.8
Step-by-step explanation:
we move the 3.6 to tge other side so the sighn of it will be negative the we subtract them so m=10.8
Answer:
m=4
Step-by-step explanation:
The formula to determine continuously compounded interest is A = Pe^rt, where A is the amount of
money in the account, P is the initial investment, r is the interest rate, and t is the time, in years.
What equation could be used to determine the value of an account with an $18,000 initial
investment at an interest rate of 1.25% for 24 months?
Answer:
[tex]A=18000 \cdot e^{0.0125 \cdot 2}[/tex]
[tex]A=18455.67[/tex] (Approximated)
Step-by-step explanation:
[tex]A=Pe^{rt}[/tex]
We are given the following along with the equation we are to use:
[tex]P=18000[/tex]
[tex]r=1.25\%=\frac{1.25}{100}=0.0125[/tex]
Be careful it says [tex]t[/tex] is in years and it gives us a time that is in months.
[tex]12 \text{months}=1 \text{ year}[/tex]:
[tex]t=\frac{24}{12}=2[/tex]
Let's plug in our information:
[tex]A=18000 \cdot e^{0.0125 \cdot 2}[/tex]
Plugging in the right hand side into my calculator gives:
[tex]A=18455.67[/tex] (Approximated)
Can yall help me pls i really need help Pls
Answer:
Step-by-step explanation:
Money spent on jersey and pant = 65 * 17.50 + 65*11 = 65 * (17.50+11)
= 65 * 28.50 = $1852.50
Use the Distributive Property to rewrite the the expression -6 (r-8)
-6r+48
Step-by-step explanation:
What is 5/2 - blank = 1/3
Step-by-step explanation:
taking that blank as x
5/2 -x = 1/3
the x will go to the right hand side of the equation which then would make it positive ( making x the subject) and 1/3 will come to the left hand side of the equation becoming -1/3
so the equation will become 5/2-1/3=x
solving the fraction then gives 13/6 or 2.17 as the value of x
The value of the equation is x = 13 / 6
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the unknown number be represented as x
Substituting the values in the equation , we get
( 5/2 ) - x = 1/3 be equation (1)
Adding x on both sides of the equation , we get
( 5/2 ) = ( 1/3 ) + x
Subtracting ( 1/3 ) on both sides of the equation , we get
x = ( 5/2 ) - ( 1/3 )
On simplifying the equation , we get
x = ( 15 - 2 ) / 6
x = 13 / 6
Therefore , the value of x is 13/6
Hence , the equation is x = 13/6
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