Lorenzo can spend $30 on a new bicycle helmet. He is
comparing sale prices at different stores.
Determine whether each amount is within Lorenzo's budget.
Select Yes or No for each amount.
5% off $35 plus 10% sales tax
25% off $40
30% off $50
10% off $38 plus additional $5 off
25% off $45 plus additional 10% off
O
O
O
O
Yes
Yes
Yes
Yes
Yes
O
No
O No
O No
O No
O No
Answers
1. 5% off $35 plus 10% sales tax:
The discount on $35 is $35 x 5% = $1.75.
The price after discount is $35 - $1.75 = $33.25.
The sales tax on $33.25 is $33.25 x 10% = $3.32.
The final price is $33.25 + $3.32 = $36.57.
Answer: No, this amount is not within Lorenzo's budget.
2. 25% off $40:
The discount on $40 is $40 x 25% = $10.
The price after discount is $40 - $10 = $30.
Answer: Yes, this amount is within Lorenzo's budget.
3. 30% off $50:
The discount on $50 is $50 x 30% = $15.
The price after discount is $50 - $15 = $35.
Answer: Yes, this amount is within Lorenzo's budget.
4. 10% off $38 plus additional $5 off:
The discount on $38 is $38 x 10% = $3.80.
The price after the firstdiscount is $38 - $3.80 = $34.20.
After an additional $5 off, the final price is $34.20 - $5 = $29.20.
Answer: Yes, this amount is within Lorenzo's budget.
5. 25% off $45 plus additional 10% off:
The discount on $45 is $45 x 25% = $11.25.
The price after the first discount is $45 - $11.25 = $33.75.
The discount on $33.75 is $33.75 x 10% = $3.38.
The final price after both discounts is $33.75 - $3.38 = $30.37.
Answer: Yes, this amount is within Lorenzo's budget.
Therefore, the answers are:
1. No
2. Yes
3. Yes
4. Yes
5. Yes
Related Questions
help me find the scale factor please!!
Answers
Answer:1.5 i think
Step-by-step explanation:
Answer:
the scale factor is 2/3
Step-by-step explanation:
to find the scale factor plug in values to \(\frac{new}{old}\)
the new figure is the one in which the scale factor is applied to, and the old is the original figure
so for new take any side from the dilated figure, I will pick HI, the size is 4
for old use what is congruent to HI, so OL, which is 6
plug this into your fraction and you get 4/6
this simplifies to 2/3
GEOMETRY! I will give brainliest
Answers
Answer:
538.8 (4th option)
Step-by-step explanation:
Area of Circle= 3.14(pi) x r^2
Area=615.44
Sector Area = 315/360 x 615.44 = 538
Adrian purchases a book for $9.86 and a poster for $3.49. If she gives the cashier
$15.00, how much change should she receive? (Don't worry about taxes!)
Answers
Hiru Tare | (If A + B + C = π and sin A = sin B sin C prove that): cot B + cot C = 1
Answers
Answer:
\(\textsf{If\;\;$A + B + C = \pi$\;\;and\;\;$\sin A = \sin B\sin C$,\;\;then\;\;$\cot B + \cot C = 1$.}\)
Step-by-step explanation:
We are given that:
\(\textsf{Equation 1:} \quad A + B + C = \pi\)
\(\textsf{Equation 2:} \quad \sin A = \sin B \sin C\)
We need to prove that:
\(\cot B + \cot C = 1\)
Begin by rearranging the first equation to isolate (π - A):
\(\implies \pi-A=B+C\)
Use this and the identity sin(A) = sin(π - A) to rewrite sin(A) in terms of B and C:
\(\implies \sin A=\sin(\pi - A)\)
\(\implies \sin A=\sin(B+C)\)
Expand sin(B + C) using the identity sin(x + y) = sin(x)cos(y) + cos(x)sin(y):
\(\implies \sin A=\sin(B+C)\)
\(\implies \sin A=\sin B \cos C +\cos B \sin C\)
Given that sin(A) = sin(B)sin(C), substitute the two equations for sin(A) to create an equation in B and C only:
\(\implies \sin B \cos C + \cos B\sin C=\sin B \sin C\)
Divide both sides of the equation by sin(B)sin(C):
\(\implies \dfrac{\sin B \cos C + \cos B \sin C}{\sin B \sin C}=\dfrac{\sin B \sin C}{\sin B \sin C}\)
\(\implies \dfrac{\sin B \cos C}{\sin B \sin C} + \dfrac{\cos B \sin C}{\sin B \sin C}=1\)
Cancel the common factors:
\(\implies \dfrac{\cos C}{ \sin C} + \dfrac{ \cos B}{\sin B}=1\)
Use the identity cos(x)/sin(x) = cot(x):
\(\implies \cot C +\cot B=1\)
Rearrange the terms on the left side of the equation:
\(\implies \cot B+ \cot C=1\)
Therefore, we have proved that cot(B) + cot(C) = 1, given that A + B + C = π and sin(A) = sin(B)sin(C).
3(-4x - 8) = (Use distributive property to rewrite each expression)
Answers
What are the coordinates of images 2? For B P Q
Answers
Recall that a reflection over a line y=k transforms the point (x,y) into:
\((x,k-(y-k))=(x,2k-y)\text{.}\)Therefore the given sequence of transformations will change point (x,y) into:
\((x,y)\rightarrow(x+3,y-3)\rightarrow(x+3,2(-2)-(y-3))=(x+3,-1-y)\text{.}\)Answer:
Since the original coordinates are P(-4,3), Q(0,3), and B(-3,-1), the coordinates of image 2 are:
\(\begin{gathered} P^{\doubleprime}(-4+3,-1-3)=P^{\doubleprime}(-1,-4), \\ Q^{\doubleprime}(0+3,-1-3)=Q^{\doubleprime}(3,-4), \\ B^{\doubleprime}(-3+3,-1-(-1))=B^{\doubleprime}(0,0)\text{.} \end{gathered}\)If anyone can help that would be amazing :)
Answers
6x
Discussion:
7x = 7 times x
x = 1 times x
So both terms are "like" terms in x:
7x - x = (7-1)x = 6x :D
A rectangle is transformed according to the rule R0, 90º. The image of the rectangle has vertices located at R'(–4, 4), S'(–4, 1), P'(–3, 1), and Q'(–3, 4). What is the location of Q?
(–4, –3)
(–3, –4)
(3, 4)
(4, 3)
Answers
Answer:
A
Step-by-step explanation:
i think...
The transformation is (4, 3)
what is transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation
If the there is rotation of 90° around the origin (0,0), that can be expressed as
(x, y) => (-y, x)
Which means a 90° rotation that can done by changing coordinates positions and inverting the sign of y-coordinate.
However, the problem is giving the transformed coordinates where
Q'(–3, 4)
Hence, the transformation is (4, 3)
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WILL GOVE BRAINLIEST AND $5 VENMO IF YOU GET IT RIGHT
Answers
Answer:
∠IGH = 57º
Step-by-step explanation:
The supplement to 99º is 180 - 99 = 81º
The vertical angle to 42º is 42 º
together they are two angles of ∆ GHI
81 + 42 = 123
The remaining angle of the triangle is ∠IGH
∠IGH = 180 - 123
∠IGH = 57º
∠IGH = 57º is the remaining answer
What is 8.170 in word form
Answers
Answer:
eight and seventeen hundredths
Step-by-step explanation:
eight and seventeen hundredths
Write the phrase as a expression the sum of 7 and 11
Answers
Answer:
7 + 11
Step-by-step explanation:
Sum means addition, so the sum of 7 and 11 is 7 + 11. I think that is what you meant. Hope this helps!
The given phrase written in expression as 18.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given phrase is the sum of 7 and 11.
Expression for the given phrase is
Here, sum means addition of numbers
The sum of 7 and 11 = 7+11
= 18
Therefore, the given phrase written in expression as 18.
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What is a closed line of credit? a. a line of credit with a set maximum credit limit. b. a line of credit with no interest rate. c. a line of credit with a fixed total amount. d. a line of credit with a legally mandated repayment schedule. please select the best answer from the choices provided a b c d
Answers
Answer:
c
Step-by-step explanation:
a line of credit with a fixed total amount.
The closed line of the credit is the line of credit with the fixed total amount. Option c is the correct option.
What is a line of credit?On the bases of the requirement, a person or firm takes the open or closed line of credit.
Open Line of Credit-This is a type of short period of loan in which many credit and deposit can be make, for example credit cards.Closed Line of Credit-This type of credit has to be repaid with total amount. The period of such credit is longer than the open line of credit. The deposits is make single time with fixed total amount.Thus, the closed line of the credit is the line of credit with the fixed total amount. Option c is the correct option.
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In a region where there is a uniform electric field, the potential, v1, is 1. 3 v at position y1=26 cm. At position y2=28 cm , the potential, v2, is 3. 9 v. What is the change in electric potential energy of an alpha particle (charge = +2e) if it is moved from y1 to y3?.
Answers
The change in electric potential energy of an alpha particle is:
1.3V/cm
"Information available from the question"
In a region where there is a uniform electric field, the potential, v1, is 1. 3 v at position y1=26 cm.
At position y2=28 cm , the potential, v2, is 3. 9 v.
Now, According to the question:
Calculation of magnitude:
Since V1 is 1.3 V at position y1=26 cm. At position y2=28 cm, the potential, V2, is 3.9 V
So, We know that
\(E =\frac{V_2-V_1}{Y_2-Y_1}\)
\(E=\frac{3.9-1.3}{28-26}\)
\(E=\frac{2.6}{2}\)
E = 1.3V/cm
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What is the y-value of the solution to the system of equations {3x+4y=4 and 2x−4y=6?
Answers
Answer: y = -1/2
Step-by-step explanation:
Use the elimination method. When setting the equations up, you can see that the y values already cancel out. This makes it easy to find the x value.
3x+4y=4 3x+4y=4
2x-4y=6 -----> (-) 2x-4y=6
For the x value, you would get 2. 5x=10 therefore x=2.
Now that you have your x value, choose one of the original equations(either works). I chose 3x+4y=4. Now, substitute 2 into the x value then solve your equation for the y-value.
3x+4y=4 ---> 3(2)+4y=4
3(2)+4y=4 then becomes 4y=-2 and when you isolate the variable, you get -1/2.
drought can cause the level of the local water supply to drop by a few inches each
week. Suppose the level of the water supply drops 2 inches each week. How much will it
change in 4 weeks? ________
Answers
Answer:
8 inches
Step-by-step explanation:
2 times 4=8
Answer:
Step-by-step explanation:
4w(-2in)/w=-8in
How do I find the variables here? ;-;
Answers
Answer:
y = 116
w = 116
x = 4
Step-by-step explanation:
a // b and t is transversal.
y + 64 = 180 {co-interior angles are supplementary}
y = 180- 64
y = 116
w = y {Alternate interior angles are equal}
w = 116
4x² = 64 {Alternate interior angles are equal}
x² = 64/4
x² = 16
x² = 4²
x = √(4*4)
x = 4
no contestant received the same score on two different days. if a contestant is selected at random, what is the probability that the selected contestant received a score of 5 55 on day 2 22 or day 3 33, given that the contestant received a score of 5 55 on one of the three days?
Answers
The probability that the selected contestant received a score of 5 55 on day 2 22 or day 3 33, given that the contestant received a score of 5 55 on one of the three days is 2/3 or approximately 0.67.
To see why, note that there are three possible cases: the contestant received a score of 5 55 on day 1 11, day 2 22, or day 3 33. We know that the contestant received a score of 5 55 on one of the days, so we can ignore the first case.
Now, since no contestant received the same score on two different days, the contestant who received a score of 5 55 on day 2 22 cannot have received that same score on day 3 33. Similarly, the contestant who received a score of 5 55 on day 3 33 cannot have received that same score on day 2 22. Therefore, if a contestant received a score of 5 55 on one of the days, there are only two possible days on which that could have happened (day 2 or day 3), and both of these have an equal chance of being the correct day. So, the probability is 2/3.
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what is the slope of a line parallel to the line y=3x-4=8y+1
Answers
Answer: If the original equation is y = 3x -4, the slope is 3.
Any equation of a line parallel to the line y = 3x -4 will have a slope of 3.
Step-by-step explanation:
In slope-intercept form, y =mx + b the coefficient of x, m is the slope.
Here 3 is that value.
It is very unusual to have two equal signs in a question about slope.
I am not sure what to do with the =8y + 1
Is this supposed to be another equation in the system, missing a term?
A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If cars are made, then the unit cost is given by the function C(x)=0.9x^2 - 414x + 59,366. What is the minimum unit cost? Do not round your answer.
Answers
The minimum unit cost of the car is $12232.1
How to determine the minimum unit cost?Given: cost function C(x)=0.9x² - 414x + 59,366
In order to find the minimum point, take the derivative of the cost function:
dC/dx = 2x - 414 (equate to zero and solve for x)
2x - 414 = 0
2x = 414
x = 414/2 = 207
Thus, the minimum point is at x =207
The minimum unit cost can be obtained by substituting x = 207 into the cost equation:
C(x) = 0.9x² - 414x + 59,366
C(207) = 0.9(207)² - 414(207) + 59,366
= 38564.1 - 85698 + 59,366
= $12232.1
Therefore, the minimum unit cost is $12232.1
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Adrian bought a car worth $12000 on 36 easy installments of $375. Answer the following questions. (1) How much total amount did Adrian pay in 36 months? Answer: Total payment A = $ (2) Identify the letters used in the simple interest formula I = Prt. I= $ P= $ and t years. (3) Find the rate of interest in percentage. Answer: r %. ASK YOUR TEACHER
Answers
3) since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.
(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:
Total payment A = Monthly installment * Number of installments
= $375 * 36
= $13,500
Therefore, Adrian paid a total of $13,500 over the course of 36 months.
(2) In the simple interest formula I = Prt, the letters used represent the following variables:
I: Interest (the amount of interest paid)
P: Principal (the initial amount, or in this case, the car worth)
r: Rate of interest (expressed as a decimal)
t: Time (in years)
(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:
r = (I / Pt) * 100
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Mr. Brust can eat 3/4 of a bucket of wings in 3/4 hour. How many wings does Mr. Brust eat in one hour?
Answers
Answer:
1 bucket
Step-by-step explanation:
3/4 buckets = 3/4 hours
multiply both sides by 4/3 to get one hour
(4/3) * (3/4) buckets = (4/3) * (3/4) hours
1 bucket = 1 hour
if <1 and <2 are vertical angels and m<1 = 180, find <2
Answers
Answer: i would say 280.
Step-by-step explanation: because if you add 180 plus another set of it it would make 280
Answer:
180
Step-by-step explanation:
Since they are vertical angles, they are congruent to each other
m<1 = m<2
A bike is priced at $63.50. There is an 8% sales tax rate. What is the sales tax for the bike in
dollars and cents?
Answers
The sales tax is $5.08
Answer:
The answer is $68.58
Step-by-step explanation:
The total cost of the tax is $5.08 so if you add that to $63.50 you get $68.58.
PLEASE MARK BRAINLIEST
LeashTYPE 1TYPE 273DogLadder20 ft19.5 ftThe end of a dog's leash is attachedDon placed a ladder againstto the top of a 5-foot-tall fence post,the side of his house asas shown in the diagram below. Theshown in the diagramdog is 7 feet away from the base ofbelow. Write an equation tothe fence post. How long is thefind the distance, x, fromleash, to the nearest tenth of a foot.the foot of the ladder to thebase of the house.WHAT IS THE DIRERENCESolve the equation for x,BETWEEN TYPE 1 AND TYPE 2?round to the nearesthundredth of a foot.BREAKOUTROOMSх
Answers
Type 1
this is a right triangle, the we can apply pythagoras
\(a^2+b^2=h^2\)where a and b are sides and h the hypotenuse on this case L(leash)
replacing
\(5^2+7^2=L^2\)simplify
\(\begin{gathered} 25+49=L^2 \\ 74=L^2 \end{gathered}\)now solve for L
\(L=\sqrt[]{74}\approx8.6\)The leash is 8.6ft
Type 2
we have a right triangle too
on this case the missing number is a side, not hypotenuse
remember pythagoras
\(a^2+b^2=h^2\)and replace for this case
\(x^2+19.5^2=20^2\)simplify
\(\begin{gathered} x^2+380.25=400 \\ \end{gathered}\)and solve for x
\(\begin{gathered} x^2=19.75 \\ x=\sqrt[]{19.75}\approx4.44 \\ \end{gathered}\)then le length of the side x is 4.44ft
7m + 2 = 6n - 5
Write a formula for f(m) in terms of m.
Answers
Answer: m = 6/7n-1
Step-by-step explanation: to get 7m alone dirst we must subtract 2 from both sides so 2-2 = 0 and -5 - 2= -7 so 7m= 6n-7 and divide both sides by 7 to get m alone so 6n divided by 7 = 6/7n and -7 divided by 7 equals -1 so we're left with m= 6/7n-1
The formula for f(m) in terms of m is:
f(m) = (6m - 7) / 7
To write a formula for f(m) in terms of m, we need to isolate m on one side of the equation.
Given the equation 7m + 2 = 6n - 5, we can start by moving all terms involving m to one side and all terms involving n to the other side:
7m - 6n = -5 - 2
Simplifying:
7m - 6n = -7
Now, we can express m in terms of n:
7m = 6n - 7
Dividing both sides of the equation by 7:
m = (6n - 7) / 7
Thus, the formula for f(m) in terms of m is:
f(m) = (6m - 7) / 7
This formula allows us to calculate the value of f(m) based on the given relationship between m and n. By substituting different values of m into the formula, we can determine the corresponding values of f(m) for those inputs.
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- a gambler offers you to pay even odds if you get 9, 10 or 11 heads in 20 tosses. should you take the bet?
Answers
How do i graph it And this is for ixl i have to get a 80 or above to past help me guys please and there will be more questions like this one so if yall want me to get a 80 or above and past math class please help me bc rn i have a 13 in there and this is a major grade so please help me!
Answers
The required graph of the line y = 9x + 1 will be displayed in the as attached file.
What is a graph?A graph can be described as a visual representation or a diagram that represents data or values.
We have been given the equation as:
y = 9x + 1
Rewrite in slope-intercept form.
y = (9)x + 1
To find the slope and y-intercept, use the slope-intercept form.
Here the slope is 9 and y-intercept = (0, 1)
Using two points, any line may be graphed. Plug two x values into the equation to discover the associated y values.
When substitute the value of x = 0, then the value of y = 1, and When substitute the value of x = 1, then the value of y = 10,
Therefore, the graph represents the line y = 9x + 1
Hence, the required graph of the line y = 9x + 1 will be displayed in the as attached file.
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convert 336g to m³
\(336g \: to \: m3\)
Answers
The conversion 336g to m³ is impossible because they measure different units
How to convert 336g to m³From the question, we have the following parameters that can be used in our computation:
Convert 336g to m³
To convert a unit to another, the units must measure the same quantity
Take for instance:
Grams can be converted to kilograms because they both measure mass
Using the above as a guide, we have the following:
336g to m³ cannot be done because of the different quantities they represent
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How does the wax in a person's ear help keep that person healthy?
Answers
The solution to a linear programming problem is (x1,x2,x3)=(5,0,10) and the objective function value is 45,000. The constraints of this linear program are: i. 2x1 + x2 – 0.5x3 <= 5 ii. 0.9x1 - 0.1x2 - 0.1x3 <= 10 iii. X1 <= 14 iv. X2 <= 20 v. X3 <= 10 vi. 3x1 + x2 + 2x3 <= 50 The dual to this LP is: Min 5y1+10y2 + 14y3 + 20y4 +10y5 + 15,000y6 s.t. 2y1 + 0.9y2 + y3 + 3y6 >= 5000 y1 - 0.1y2 + y4 + y6 >= 2000 -0.5y1 - 0.1y2 + y5 + 2y6 >= 2000 Nonnegativity Use the strong duality and/or complementary slackness theorem to solve this problem [do not use solver to find the solution].
PLEASE SOLVE BY USING EXCEL. THANK YOU!
Answers
Life Insurance Corporation (LIC) issued a policy in his favor charging a lower premium than what it should have charged if the actual age had been given. the optimal solution of the primal problem is (x1,x2,x3)=(5,0,10) and the objective function value is 45,000.
The optimal value of the given LP problem is 45,000. In this problem, x1 = 5,
x2 = 0 and
x3 = 10.
Therefore, the objective function value = 7x1 + 5x2 + 9x3 will be 45,000, which is the optimal value.
problem is Minimize z = 7x1 + 5x2 + 9x3
subject to the constraints: i. 2x1 + x2 – 0.5x3 ≤ 5ii. 0.9x1 - 0.1x2 - 0.1x3 ≤ 10iii. x1 ≤ 14iv. x2 ≤ 20v. x3 ≤ 10vi. 3x1 + x2 + 2x3 ≤ 50
Duality: Maximize z = 5y1 + 10y2 + 14y3 + 20y4 + 10y5 + 15,000y6
subject to the constraints:2y1 + 0.9y2 + y3 + 3y6 ≥ 7y1 - 0.1y2 + y4 + y6 ≥ 0.5y1 - 0.1y2 + y5 + 2y6 ≥ 0y3, y4, y5, y6 ≥ 0 Now, we will solve the dual problem using the Simplex method. Using Excel Solver, As per complementary slackness theorem, the value of the objective function of the dual problem = 45,000, which is same as the optimal value of the primal problem. Therefore, the optimal solution of the primal problem is (x1,x2,x3)=(5,0,10) and the objective function value is 45,000.
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