gloria has a lunch account in the school cafeteria. the balance, f(x), in her account can be represented by the function f(x)
Answers
The given function is an equation describing the expenses of Gloria at her school cafeteria: She has 40 dollars in total and spends 2.75 dollars for each meal; 40 - 2.75x is the new function of linear equation.
What is a linear equation?Linear equations refer to the equations that involve two or more variables in the form of "ax + b".
Now,
Given: The expenses of Gloria at her school cafeteria is given by the linear equation: 40 - 1.5x, where x = number of meals purchased.
To find: The relation when 1.50 changes to 2.75.
Finding:
AS given in the question, 40 - 1.50(x) represents the money spent by Gloria in her school cafeteria, where:40 represents the total money she has.1.50 represents the money spent on each meal by her.x represents the number of meals.If 1.50 changes to 2.75, it means that the cost of her meal increased from 1.50 to 2.75, by 1.25 dollars. Further, it means that her expenses have increased now and that her total money will now be spent earlier than what would have been spent if she spent 1.50 dollars on each meal.The new relation will be given by the linear equation: 40 - 2.75x.Hence, The given function is an equation describing the expenses of Gloria at her school cafeteria: She has 40 dollars in total and spends 2.75 dollars for each meal; 40 - 2.75x is the new function of linear equation.
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(COMPLETE QUESTION:
Gloria has a lunch account in the school cafeteria. The balance, f(x), in her account can be represented by the function f(x) = –1.50x + 40, where x is the number of meals purchased. Suppose –1.50 changed to –2.75. What does this mean in the context of the problem?)
Related Questions
How many times will the following loop execute?
int x = 0;
do {
x++;
cout << x << endl;
}while(x < 5)
Answers:
a. - 5 times
b. - 4 times
c. - It doesn't
d. - Infinite times
e. - 6 times
Answers
Answer:
Step-by-step explanation:
The loop will run an infinite number of times
what is 1 and 2/5 as an improper fraction
Answers
Answer:
\(\displaystyle 1\frac{2}{5}=\frac{7}{5}\)
Step-by-step explanation:
\(\displaystyle a\frac{b}{c}=\frac{ac+b}{c}\\\\1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{5+2}{5}=\frac{7}{5}\)
Using the 100/50/20 Rule for daily fluid requirements (DFR). Calculate the following questions, do not round the patient's weight but round all final answers to a whole number. 1-10 kg = 100ml/kg/day 11-20 kg = 50ml/kg/day (+ 1000 mL/day for 1* 10kg) Over 20kg = 20mL/kg/day (1500 mL/day for 1s 20kg) 18. An infant weighs 11 pounds. What is the required amount of fluid per day in ml? I 19. A child weighs 31 lbs and 8 ozs. What is the required amount of fluid per day in ml? If no oral fluids are consumed, what is the hourly IV flow rate to maintain proper hydration?
Answers
18. An infant weighs 11 pounds which is equivalent to 4.98 kg. Using the 100/50/20 Rule, the required amount of fluid per day for an infant between 11-20 kg is 50 ml/kg/day. So, the required amount of fluid per day in ml is 4.98 kg x 50 ml/kg/day = 249 ml/day.
19. A child weighs 31lbs and 8 ozs which is equivalent to 14.21 kg. Using the 100/50/24 Rule, the required amount of fluid per day for a child over 20 kg is 20 ml/kg/day. So, the required amount of fluid per day in ml is 14.21 kg x 20 ml/kg/day = 284.2 ml/day.
If no oral fluids are consumed, the hourly IV flow rate to maintain proper hydration would be: 284.2 ml/day / 24 hours/day = 11.8 ml/hour.
Daily Fluid Requirements (DFR)The question is about fluid requirements for infants and children, and it is using the 100/50/20 Rule for Daily Fluid Requirements (DFR) to calculate the required amount of fluid per day for different weight ranges. The 100/50/20 Rule is a guideline used to determine the appropriate amount of fluid that infants and children should receive on a daily basis based on their weight. The rule states that for infants and children up to 10 kg, the recommended fluid intake is 100 ml/kg/day, for those between 11-20 kg it is 50 ml/kg/day, and for those over 20 kg it is 20 ml/kg/day.
The question also asking about the hourly IV flow rate to maintain proper hydration if no oral fluids are consumed.
This subject is part of pediatrics, more specifically in the field of fluid and electrolyte balance and management.
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(PLS HURRY!) On Melissa's 6th birthday, she gets a 2000$ CD that earns 6% interest, compounded. If the CD matures on her 14th birthday, how much money will be available?
Answers
Using compound interest formula when the CD matures on Melissa's 14th birthday, there will be $3187.69 available.
What is Compound Interest?The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
Use the formula for compound interest to calculate the amount of money that will be available when the CD matures -
\(A = P(1 + r/n)^(nt)\)
Where A is the amount of money available when the CD matures, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, the initial principal is $2000, the interest rate is 6%, and the CD will be held for 8 years (from Melissa's 6th to 14th birthday).
It is not given how many times per year the interest is compounded, so assume it is compounded annually.
Using these values in the formula -
\(A = $2000(1 + 0.06/1)^(1*8)A = $2000(1.06)^8A = $3187.69\)
Therefore, the value is obtained as $3187.69.
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In 2011, the population of Los Angeles, California was approximately
3.81
×
10
6
while the population of Oakland, California was approximately
390
,
000
for the same year. In the same year, the population in Moscow, Russia was approximately
1.2
×
10
7
while the population in Memphis, Tennessee was approximately
642
,
000
.
Determine whether this statement is true or false.
In 2011, the population of Los Angeles, California was approximately 10 times the population of Oakland, California. True or false?
Answers
False. The population of Los Angeles in 2011 was approximately 9.77 times the population of Oakland, not 10 times. However, it is worth noting that population numbers can fluctuate over time and these figures may have changed since 2011.
Additionally, comparing the population of cities in different states or countries can be difficult as they may have different population growth rates, economic factors, and cultural influences.
In 2011, the population of Los Angeles, California was approximately 3.81 x 10^6, and the population of Oakland, California was approximately 390,000. To determine whether the statement is true or false, we need to compare these two populations.
3.81 x 10^6 (Los Angeles population) divided by 390,000 (Oakland population) is approximately 9.77. This shows that the population of Los Angeles was about 9.77 times the population of Oakland in 2011.
Since the statement claims that the population of Los Angeles was approximately 10 times the population of Oakland, it can be considered true, given that 9.77 is close to 10. So, the answer is true.
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It's the total price for 2 cars at a dealership is a $102,000 where 1 car price is 15,000 less than twice the other. What's the price of the cheapest vehicle
Answers
The cost of the cheaper vehicle is $43,500.
Let the cost of the cheaper vehicle be x
the cost of the other vehicle = x+15000
According to the question,
Total price = 102,000
x+x+15,000 = 102,000
2x+15,000=102,000
2x=102,000-15,000
2x=87,000
x=43,500
Therefore, the cost of the cheaper vehicle is $43,500
And the cost of the expensive vehicle is $43,500+15,000= $58,500
A linear equation is an algebraic equation of the form y=mx+b.
where m is the slope and b is the y-intercept.
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(4 x superscript a baseline) superscript b baseline = startfraction 256 over x superscript 8 endfraction?
Answers
The equation (4^a)^b = 256 / x^8 is given. We need to solve for the values of a and b.
To solve the equation (4^a)^b = 256 / x^8, we can simplify the left side of the equation using the exponent rules.
Recall that when we raise an exponent to another exponent, we multiply the exponents. Applying this rule, we have (4^a)^b = 4^(a*b).
Now, the equation becomes 4^(a*b) = 256 / x^8.
To further simplify, we need to express both sides of the equation with the same base. Since 256 is a power of 4 (4^4 = 256), we can rewrite the right side as 4^(4 * (8/2)) = 4^(4 * 4) = 4^16.
Therefore, we have 4^(a*b) = 4^16. In order for the bases to be equal, the exponents must also be equal.
Hence, we have a*b = 16.
To solve for the values of a and b, we need additional information or constraints provided in the problem. Without such information, we cannot determine the specific values of a and b that satisfy the equation.
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Complete Question - What are the values of a and b in the equation (4 x Superscript a Baseline) Superscript b Baseline = StartFraction 256 Over x Superscript 8 EndFraction?
ameson has the following sources of income: Sole proprietorship income $40,000 General partnership operating income $5,000 Interest income from general partnership $1,200 What is the amount of self-employment tax Jameson owes
Answers
Jameson's self-employment tax amount depends on the income from his sole proprietorship and general partnership. Self-employment tax is calculated based on the net earnings from self-employment, which include both sole proprietorship income and a portion of general partnership income.
To determine the self-employment tax owed by Jameson, he first needs to calculate his net earnings from self-employment. This is done by combining the income from his sole proprietorship ($40,000) and a portion of the general partnership operating income ($5,000).
Since Jameson is a general partner, he is subject to self-employment tax on his distributive share of the partnership income.
Assuming his distributive share is 50% (for illustrative purposes), his net earnings from self-employment would be $40,000
(sole proprietorship income) + $2,500 (50% of general partnership operating income) = $42,500.
Jameson would then apply the self-employment tax rate, which is currently 15.3% for the year 2021, to his net earnings from self-employment ($42,500) to calculate the amount of self-employment tax he owes.
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Given the points
(
3
,
−
5
)
and
(
0
,
0
)
on a line, find its equation in the form
y
=
m
x
+
b
Answers
Answer:
y = -53x
Step-by-step explanation:
since 0,0 is a point, there is no b, and -5/3 times 3 is -5
The number of views on a cat video and a dog video after they're uploaded are represented by the following tables:
Answers
Answer:
Cat video: exponential function
Dog video: linear function
Step-by-step explanation: I did it until I got it right.
The cat video is a exponential function and dog video is a linear function .
What is linear function?Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
What is exponential function?An exponential function is a mathematical function of the following form:
f ( x ) = . where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.
According to the question
The tables for
Cat video
Time(month) Views
0 50
5 313
10 1950
15 12210
20 76300
So, as we can observe that values of views are increasing rapidly which can only be possible if function is exponential .
Dog video
Time(days) Views
0 10
6 452
12 889
18 1330
24 1770
So, as we can observe that values of views are increasing in constant pace which can be possible if function is linear .
We can plot graph of both the tables to check for the function nature .
Hence, the cat video is a exponential function and dog video is a linear function .
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2) The representative agent lives for infinite periods (0,1,2,…) and receives exogenous incomes of y0,y1,y2,…, respectively. The lifetime present discounted value of utility is given by: ∑t=0[infinity]βtln(ct) with β(<1) being the discount factor and ct is consumption at time t. The agent is allowed to save or borrow at the real interest rate r, but she cannot die with debt or wealth. Assume also that the initial wealth is zero. a. Solve the optimization problem of the agent using the period-by-period budget constraints. In particular, show the Euler equation. b. Using the given functional form, write the Euler equation between time 1 and time 3 . In other words, show how c1 and c3 are related. c. Write the present discounted value of optimal lifetime consumption as a function of c0 (and, potentially, other parameters or exogenous variables). d. Write the present discounted value of optimal lifetime utility as a function of c0 (and, potentially, other parameters or exogenous variables). e. Find the present discounted value of lifetime income as a function of y0 (and, potentially, other parameters or exogenous variables) when income is growing each period at the rate of γ, where 0<γ0 ? Explain!
Answers
a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.
b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.
c. C0 = ∑t=0[infinity](β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.
d. U0 = ∑t=0[infinity](β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.
Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.
a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:
At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.
b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.
Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin
d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.
c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity](β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.
d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity](β(1 + r))^tln(ct).
This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.
e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.
This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.
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If 5k = -25, then 5k - 1 = -25 - 1
Segment proof
Answers
Please can someone help me?
−12(7z+4)+15(5z−15)
Answers
Step-by-step explanation:
ghofuikgcjjivbiucbkhfkhcuvijnochm
NEED HELP ASAP algebra 2
Answers
Answer:
b = sqrt(39)
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2
5^2 + b^2 = 8^2
25+b^2 =64
b^2 =64-25
b^2 =39
Take the square root of each side
b = sqrt(39)
Answer:
\(\sqrt{39}\)
Step-by-step explanation:
Step 1: Find the unknown wide using Pythagorean Theorem
\(a^{2}+ b^{2} = c^{2}\)
\(a^{2}+ 5^{2} = 8^{2}\)
\(a^{2}+ 25 = 64\)
\(a^{2}= 64-25\)
\(a^{2=39\)
\(\sqrt{a^{2}} = \sqrt{39}\)
\(a=\sqrt{39}\)
\(\sqrt{39}\) cannot be simplified and more
Therefore the unknown side is \(\sqrt{39}\)
Question 5 (5 points)
What is the volume of the right prism?
35 in.
37 in.
12 in.
40 in.
Answers
The volume of the right prism include the following: 8,640 in³.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height or depth of a rectangular prism.Next, we would determine the area of the triangle at the base of the right prism as follows:
Base area = 1/2 × ( 36 × 12)
Base area = 1/2 × 432
Base area = 216 in².
Now, we can calculate the the volume of this right prism:
Volume = base area × height
Volume = 216 × 40
Volume = 8,640 in³.
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What is 8 x 1 + 9 x (1/10) + 6 x (1/100) + 2 x (1/1000)?
Answers
Answer:
8962
Step-by-step explanation:
8×1+9...etc..etc
= 8962
Answer:
8.962
Step-by-step explanation:
please help me on this question
Answers
Answer:
The answer is A
Step-by-step explanation:
\( \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \\ \\ \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \)
Two lines are perpendicular if their slopes are the same.TrueFalse
Answers
ANSWER :
False
EXPLANATION :
Two lines are perpendicular if their slopes, m1 and m2, are the negative reciprocal of each other.
\(m_2=-\frac{1}{m_1}\)Therefore, the given statement is False
biggg factssss♡♡♡♡lm.aoo
Answers
Answer:
this is soo deep lol. free point epic pogg
if the demand curve shifts to the left, what happens to price and quantity?
Answers
Answer:
A lower price and quantity would result.
An equilateral triangle ABC is rotated clockwise by 90° to form triangle A’B’C’
What is the measure of angle B’A’C’, in degrees?
Answers
To determine the measure of angle B’A’C’, we first need to understand the properties of equilateral triangles and their rotation. An equilateral triangle has three equal sides and angles measuring 60 degrees each. When rotated clockwise by 90 degrees, the new triangle A’B’C’ will have its vertices shifted to the right, with vertex A’ above vertex C’ and B’ in between them.
Since the triangle is equilateral, we know that the angle A’C’B’ is also 60 degrees. To determine angle B’A’C’, we need to subtract the angle A’C’B’ from 180 degrees (the total measure of the triangle). Therefore, angle B’A’C’ is equal to 120 degrees.
In summary, when an equilateral triangle is rotated clockwise by 90 degrees to form a new triangle A’B’C’, the measure of angle B’A’C’ is 120 degrees.
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6.4 ÷ 1.6 of 5 + 1.3 × 3.1 - 0.07
Answers
explanation s
Answer: 23.96
first you gotta put in the parenthese in. (6.4/1.6)x 5+( 1.3x3.1)-0.07.
second: do the Equation in the parentheses.
6.4/1.6=4
1.3x3.1=4.03
4x5=20
20+4.03=24.03
24.03-0.07=23.96 final answer
Hope this helps!!
The length of a rectangle is 4 inches more than its width and its perimeter is 34 inches find the length and width of the rectangle if w= the width of the rectangle then the length equals
Answers
Answer:
The length and width of the rectangle are 10.5 in and 6.5 in respectively.
Step-by-step explanation:
P = 2L + 2W
P (perimeter of the rectangle) = 34 in
L (length of the rectangle) = 4 in + W (width of the rectangle)
Therefore, L = 4 + W
P = 2L + 2W
34 = 2(4 + W) + 2W
34 = 8 + 2W + 2W
34 - 8 = 4W
26 = 4W
W = 26/4 = 6.5 in
L = 4 + W = 4 + 6.5 = 10.5 in
L = 10.5 in
W = 6.5 in
I need help with this ASAP
Answers
Solution : Straight line question : y= 2x-3
Straight Line:
A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.
Slope:
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
Use the slope and one of the points to solve for the y-intercept (b).
One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.
Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line
1)Point (3,3) (4,5)
slope: (5-3)/(4-3) = 2/1 = 2
Y= mx+c
y -3 = 2(x-3)
y-3= 2x-6
y= 2x-6+3
y= 2x-3
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f(x)=5sinx+cosx then f ′
(x)=−5cosx−sinx Select one: True False
Answers
False. The derivative of the function f(x) = 5sin(x) + cos(x) is not equal to -5cos(x) - sin(x). The correct derivative of f(x) can be obtained by applying the rules of differentiation.
To find the derivative, we differentiate each term separately. The derivative of 5sin(x) is obtained using the chain rule, which states that the derivative of sin(u) is cos(u) multiplied by the derivative of u. In this case, u = x, so the derivative of 5sin(x) is 5cos(x).
Similarly, the derivative of cos(x) is obtained as -sin(x) using the chain rule.
Therefore, the derivative of f(x) = 5sin(x) + cos(x) is:
f'(x) = 5cos(x) - sin(x).
This result shows that the derivative of f(x) is not equal to -5cos(x) - sin(x).
In summary, the statement that f'(x) = -5cos(x) - sin(x) is false. The correct derivative of f(x) = 5sin(x) + cos(x) is f'(x) = 5cos(x) - sin(x).
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A swimming pool is draining at a constant rate. The table shows the proportional relationship between the change in the water level and the number of hours the pool is draining. Find the constant of proportionality. Then find the change in the water level at 9 hours and at 23 hours of draining.
Draining Swimming Pool
Hours Draining
Change in Water Level (in.)
2
3.5
9
?
17
29.75
23
?
The swimming pool is draining at a rate of
nothing inches per hour.
(Type an integer or a decimal.)
Enter your answer in the answer box and then click Check Answer.
Answers
Answer:
first answer:-1.75
second:-15.75
third:-40.25
Step-by-step explanation:i am too lazy srry
pls i need HeLp
13 + 7 to the 2nd power ÷7
______________________
9 - 20 ÷ 4 +16
Answers
Answer:
1
Step-by-step explanation:
By using Order of Operations, or Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction, or (PEMDAS) for short.
PLEASE HELP THIS IS MY FINAL EXAM FOR ALGEBRA
The population of a town is decreasing at a rate of 1% per year. In 2000 there were 1300 people. Find the population of the town in 2008. *
Answers
Answer:
The answer is 1,300 people
pls help tysm will give brainliest!!
Answers
Answer:
% change in perimeter = 43. 44 %
% change in area = 16 %
Step-by-step explanation:
initial perimeter of the rectangle = 2(2p + p)
= 6p
initial area of the rectangle = 2p × p
= 2p²
25% is equal to 0.4therefore,
new length = 2p + (2p × 0.4)= 2p + 0.8p = 2.8 p
new breadth= p - 0.4p
= 0.6 p
new perimeter = 2 ( 2.8 p + 0.6p)= 3.4 p
new area = 2.8p × 0.6p= 1.68 p²
% change in perimeter
\( = \frac{6p - 3.4p}{6p} \times 100 \\ = \frac{2.6p}{6p} \times 100 \\ = 43.33\%\)
% change in area
\( \frac{2 {p}^{2} - 1.68 {p}^{2} }{2 {p}^{2} } \times 100 \\ = \frac{0.32}{2} \times 100 \\ = 16\%\)
You are at a restaurant and the check comes to a total of $16. If you want to leave a 16% tip, how much total money should you pay, to the nearest cent?
Answers
Answer:
Step-by-step explanation:
12