Answer:
Price per mechanical pencil: [tex]\$ 0.5[/tex].
Price per ruler: [tex]\$ 1[/tex].
Step-by-step explanation:
Let the cost per mechanical pencil be [tex]\$ p[/tex], and let the cost per ruler be [tex]\$ r[/tex].
Set up two equations based on the amount of money that each teacher paid.
The cost of [tex]50[/tex] mechanical pencils ([tex]\$ p[/tex] each) and [tex]30[/tex] rulers ([tex]\$ r[/tex] each) would be [tex](50 \, p + 30\, r)[/tex]. That should be equal to the amount of money that Mrs. Ortiz paid. In other words, [tex]50 \, p + 30\, r = 55[/tex].
Similarly, the cost of [tex]30[/tex] mechanical pencils ([tex]\$ p[/tex] each) and [tex]30 \![/tex] rulers ([tex]\$ r[/tex] each) would be [tex](50 \, p + 30\, r)[/tex]. That should be equal to the amount of money that Mr. Donahue paid. In other words, [tex]30 \, p + 30\, r = 45[/tex].
That gives a system of two equations:
[tex]\left\lbrace \begin{aligned}& 50 \, p + 30\, r = 55 \\ & 30 \, p + 30\, r = 45 \end{aligned}\right.[/tex].
Subtract the second equation for the first:
[tex]20\, p = 10[/tex].
[tex]\displaystyle p = \frac{1}{2} = 0.5[/tex].
In other words, the cost of one mechanical pencil would be [tex]\$0.5[/tex].
Substitute [tex]p = 0.5[/tex] back to either equation and solve for [tex]r[/tex], the cost of one ruler.
[tex]50 \times 0.5 + 30\, r = 55[/tex].
[tex]30\, r = 55 - 25 = 30[/tex].
[tex]r = 1[/tex].
In other words, the cost of one ruler would be [tex]\$ 1[/tex].
Can somebody plz help ASAP!!
Answer: 6 sq cm
Step-by-step explanation:
Tony’s deposit earned $40.80 in simple interest over 3 years in an account with an interest rate of 1.7%. How much did Tony deposit?
Write your equation AND solve.
Answer:
3. Tony's deposit earned $40.80 in simple interest over 3 years in an account with an interest rate of 1.7%. How much did Tony deposit?
Home Prices The median selling price of an existing home in the United States increased continuously over the period 2011–2013 at the rate of 8.5% per year from approximately $166,000 in 2011.27 Write down a formula that predicts the median selling price of an existing home t years after 2011. Use your model to estimate, to the nearest $1,000, the median selling price of an existing home in 2013 and 2015
Answer:
166,000(1 + 0.085)^t ; $195,000 ; $230,000
Step-by-step explanation:
Given that :
Rate of increase = 8.5% = 0.085 per year
Initial value ; price in 2011 (A) = $166,000
Formula to predict the median price t years after 2011 ;
At a continous rate :
Median price, P:
P = initial price (1 + rate)^t
P = 166,000(1 + 0.085)^t
t = time since 2011 ;
Median price of home in 2013:
t = 2013 - 2011 = 2
P = 166,000(1 + 0.085)^2
P = 166000(1.085)^2
P = 166000(1.177225)
P = 195419.35
P = $195,000 ( nearest $1000)
Median price of home in 2013:
t = 2015 - 2011 = 4
P = 166,000(1 + 0.085)^4
P = 166000(1.085)^4
P = 166000(1.385858700625)
P = 230052.54430375
P = $230,000 ( nearest $1000)
IT'S FOR MIDDLE SCHOOOLLL PLZZZ HELPPPP
Tyler’s brother works in a shoe store. Tyler’s brother earns a commission. He makes 2.5% of the amount he sells. Last week, he sold $900 worth of shoes. How much was his commission?
Answer:
22.5 i think
Step-by-step explanation:
Answer: it is 22.5
Step-by-step explanation:
55 points and brainliest
What is the equation of the function that is graphed as line a?
y = 2 x - 1
y = - x - 1
y = - x
y = 3 x
Answer:
B. y = - x - 1Step-by-step explanation:
Line a is declining and has the y-intercept of -1
The equation with negative slope and - 1 y-intercept is:
y = - x - 1Correct option is B
55 points and brainliest
What is the equation of the function that is graphed as line a?
y = 2 x - 1y = - x - 1y = - xy = 3 xOption:-[tex]y = - x - 1[/tex]
EASY QUESTION DO NOT GUESS WILL LIST BRAINLIST PLS HELP MUCH APPRECIATED!
What is the slope of the line shown in the graph?
Answer:
-1/3
Step-by-step explanation:
slope = rise/run = -1/3
Grapes are priced at $2.25 per pound. Which of the following equations best represents the cost, c, of buying g, pounds of grapes?
a. c = 2.25g
b. c = g + 2.25
c. g = c + 2.25
d. g = 2.25c
Answer:
A- c=2.25g
Step-by-step explanation:
If you look at this problem, you will see that the only one that makes since is A. B is incorrect because its pounds and you are trying to find the total. C is incorrect because C stands for cost in the problem and we are trying to find the cost. D is the same explanation as C.
PLEASE ANSWER ASASP FOR BRAINLEST!!!!!!!!!!!!!!
Answer:
252 cm²
Step-by-step explanation:
Basically I just split up the figure into three smaller rectangles and then found the lengths and widths of all of them. Then I found the area of all of them by multiplying the sides and then added up all the three areas together.
Plz let me know if you want a more in depth explanation and I can help more in the comments!
Martin has 5 cups of flour if he needs 1/4 cups of flour for one jumbo cookie how many jumbo cookies can he make?
A. 20
B. 5
C. 4
D. 24
Answer:
martin can make 20 jumbo cookies
4m = -32 solve for M
will give brainliest.
Answer:
m = -8
Step-by-step explanation:
have a nice day! :)
Answer:
From this quation:
4m = -32
We need to get m, so we can divide both sides by 4:
4m / 4 = -32 /4
m = -8
You can try to replace it to see if it's correct:
4 * 8 = -32
PLEASE HELP?!?!?!
This graph shows how fast a commuter train travels on its route in an urban area. What is the meaning of the point with and x-coordinate of 2?
a. In 1 second, the commuter train travels 2 feet.
b. it takes the commuter train 60 seconds to go ten feet.
c. In 2 seconds, the commuter train train travels 120 feet.
d. the commuter train travels 2 feet in 120 seconds
Answer:
c. In 2 seconds, the commuter train travels 120 feet.
Step-by-step explanation:
Given
The attached graph
Required
What does x-coordinate of 2 represents
Represent this coordinate with (x,y)
From the graph:
[tex]x = 2[/tex] when [tex]y = 120[/tex]
Note that:
x = time and y = distance
So:
[tex](x,y) = (2,120)[/tex]
Which means:
At 2 seconds, the train has travelled a distance of 120ft
From the list of options, (c) is correct
C) C is correct
Step-by-step explanation:
Find the quotient.
0.15)6.435
Answer:
42.9
Step-by-step explanation:
Remember your decimal rules when doing long division
Jordan spent 5 hours over the weekend studying for 3 tests. He spent an equal amount of time studying for each test
Answer:
Option (4)
Step-by-step explanation:
Jordan spent 5 hours studying for 3 test with equal amount of time studying for each test.
On the number line, there are 3 small segments between each number.
Every small segment will represent time = [tex]\frac{1}{3}[/tex] hours
Total number of small segments = 15
If Jordan takes 3 equal durations for the study of each test,
Total number of small segments for each test = [tex]\frac{15}{3}=5[/tex]
Now we can plot these points on the number line.
Further count the segments for the answer ( 1 hour plus 2 small segments)
= 1 + [tex]2\times \frac{1}{3}[/tex]
= [tex]1\frac{2}{3}[/tex]
Therefore, time given for studying each test = [tex]1\frac{2}{3}[/tex] hours
Option (4) will be the answer.
solve for the roots in simplest form by completing the square
x^2-12x+20=0
Answer:
x = 10 or x = 2
Step-by-step explanation:
Solve for x:
x^2 - 12 x + 20 = 0
Hint: | Solve the quadratic equation by completing the square.
Subtract 20 from both sides:
x^2 - 12 x = -20
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 36 to both sides:
x^2 - 12 x + 36 = 16
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x - 6)^2 = 16
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x - 6 = 4 or x - 6 = -4
Hint: | Look at the first equation: Solve for x.
Add 6 to both sides:
x = 10 or x - 6 = -4
Hint: | Look at the second equation: Solve for x.
Add 6 to both sides:
Answer: x = 10 or x = 2
PLEASE HELP ME!!!!!
Amelia is going to invest $90,000 and leave it in an account for 12 years. Assuming the interest is compounded monthly, what interest rate, , would be required in order for Amelia to end up with $144,000?
Answer:
3.92%
Step-by-step explanation:
Determine a set of 3 numbers that are divisible by
6 and 5
Answer:
30
60
90
120
180
210
240
hope it helped have a good day mate
In ΔEFG, e = 690 cm, f = 650 cm and ∠G=58°. Find the length of g, to the nearest centimeter.
Answer:
651
Step-by-step explanation:
deltamath
Suppose that a football coach gets a salary of one million dollars now, and a raise of 10% every year (so exponential growth model). Let s be the salary in millions of dollars, and t is time in years. (a) Write an initial value problem to represent the salary s. Label 0.2.14 (modified) (b) What is s(0) and s(1)
Answer:
a)
initial value problem representing the salary is; S(t) = 1.[tex]e^{0.10t}[/tex]
b)
S(0) = 1
Therefore; S(0) is 1 million dollar
S(1) = 1.105170918075647
Therefore; S(1) is 1.105170918075647 million dollar
Step-by-step explanation:
Given that;
Initial salary of football coach = 1 million dollar
raise of 10% every year (so exponential growth model) r = 10% = 0.10
a) initial value problem to represent the salary
lets S represent salary in millions dollars and t represent time in years.
S(t) = S₀[tex]e^{rt}[/tex]
so,
at S₀ = 1 million dollars } { r = 0.10 }
S(t) = 1.[tex]e^{0.10t}[/tex]
Therefore, initial value problem representing the salary is; S(t) = 1.[tex]e^{0.10t}[/tex]
b) What is s(0) and s(1)
at s(0)
S(t) = 1.[tex]e^{0.10t}[/tex]
we substitute
S(0) = 1.[tex]e^{0.10*0}[/tex]
S(0) = 1.[tex]e^{0}[/tex]
S(0) = 1
Therefore; S(0) is 1 million dollar
at s(1)
S(t) = 1.[tex]e^{0.10t}[/tex]
we substitute
S(1) = 1.[tex]e^{0.10*1}[/tex]
S(1) = 1.[tex]e^{0.10}[/tex]
S(1) = [tex]e^{0.10}[/tex]
S(1) = 1.105170918075647
Therefore; S(1) is 1.105170918075647 million dollar
Find the area of the triangle.
Area=
(Simplify your answer)
Answer:
38.9?? or 40??
Step-by-step explanation:
you put the base and the height together then multiply it by 2
What is the answer to this?
Answer:
0 = 73
add 90 and 17 which equals 107 take 180 - 107 = 73
write an expression for the phase the difference of twice a number (n) and 3
Answer:
2n - 3
Step-by-step explanation:
twice a number means to multiply it by 2
difference of a number and 3 is a number being reduced by 3 so the 3 comes after the subtraction sign
A plumber charges $40 to come to your house and $25 for each hour of labor. If the final bill came to $165, how many hours did the plumber work?
Answer:5 hours
is the amount he worked
Write an equivalent expression for x + x + x
Answer:
x+2x is an equalent expression
Answer:
An equavalent expression is 3x+0
Find the total surface and each pyramid. Round to the sea
SHOW YOUR WORK!
Answer:
328 square inches
PLZ MARK AS BRAINLIEST
Step-by-step explanation:
Lateral Area of Pyramid:
L = 1/2Pl
l = 15.9
P = 2(8.2) + 2(8.2) = 32.8
L = 1/2(32.8)(15.9) = 260.76
Surface Area:
SA = B + L
B = (8.2)(8.2) = 67.24
L = 1/2(32.8)(15.9) = 260.76
SA = 67.24 + 260.76 = 328
A fitness club charges a onetime $75 initiation fee plus $30 each month for a member to maintain her membership. Which equation below models the total cost, c, the club charges as a function of the number of months, m, that the individual has maintained her membership?
1) c = 75m + 30
2) c = 1/30m + 75
3) c = 30m + 75
4) c = 900 + 30m
Answer:
c = 30m + 75
Step-by-step explanation:
Because the 75 dollars is only one time you add that to the total. Because it is 30 dollars PER MONTH and m is the number of months you would multiply those two in order to know how much you would be paying!
Hope this helps!
PLS HELP! WILL GIVE BRAINLIEST!
A test is worth 60 points. Multiple choice questions are
worth 2 points, and
short-answer questions are worth 5 points. If the test has
15 questions, how
many multiple-choice questions are there?
A. m+ s = 60
B. m+ s = 15
C. m:s= 15
D. 2m + 5s = 15
Answer:
2m + 5s = 15
I hope it helps.
have a great day.
Click on the picture.
Find the missing length
Triangle in each pair are similar.
5÷480 I’m trying to figure this out but when I get my answer it has a remainder
Answer:
The answer is 96.
Step-by-step explanation:
5 goes into 48, 9 times. 48 minus 45 is 3, bring down the zero to get 30. 5 goes into 30 6 times. So 30 minus 30 equals zero.
What is the supplement of a 54° angle?
Answer:
126
Step-by-step explanation:
The supplement of 54° is the angle that when added to 54° forms a straight angle (180° ). So,
54 + x = 180
x = 126
PLEASE HELP I WILL MARK BRAINLIST IF YOU ANSWER CORRECTLY OR IF YOU JUST TRY BUT IF YOU ANSWER FOR THE POINTS IM REPORTING btw I CAN tell and help on both if you can
Answer:130 85/288 ok check my explaination if its reasonable
Step-by-step explanation:
ok youre figuring out the volume right? base times height. 5x25 1/12=125 5/12. 125 5/12x 25 inches=260 85/144 /2=130 85/288. you have to divide it by 2 because i figured it out as a rectangle.