Answers
Answer:
This is a guess but I think it's 5 min per table.
Step-by-step explanation:
The reason being:
if we know that she has 9 tables to get to and each table can seat 4 people, we would have to multiply both numbers to find how many TOTAL people are in the restaurant during the first few hours.
9x4 = 36 people in total
then, we need to convert 3hrs into minutes to get a more accurate rep as to how much time she would spend at each table (she isn't going to spend the entire 3 hrs with only one table now, is she?)
so for this, we convert 3hrs into minutes
1 min = 60 secs
1 hr = 60 minutes
3hrs -> 60 x 3 = 180 minutes
now, to understand how many time she spends at each table, we need to figure out by dividing the # of people by the amount of minutes.
180 minutes/36 people = 5 mins per table.
Related Questions
Prudence solves the rational equation -7x-20/(x-2)(x+4)+2 *x/x+4
and obtains the solutions x = 1 and x = -4. What are some correct possible comments her math instructor would say about her solution?
Answers
A possible comment from Prudence math instructor would be Great job solving the rational equation! It's not an easy task, and you managed to find the solutions x = 1 and x = -4, which is correct.
What are the possible comments from Prudence instructor?Here are some other possible comments that Prudence's math instructor might make about her solution:
Make sure to check your solutions by plugging them back into the original equation. It's always a good practice to do so, as it helps you avoid mistakes and verify that your solutions are indeed valid.
When dealing with rational equations, you need to be careful about the restrictions on the domain. In this case, the denominator cannot be equal to zero, so x = -4 and x = 2 are not valid solutions. Make sure to mention this in your solution.
When simplifying the expression, make sure to distribute the negative sign (-) properly. In this case, you should have -7x - 20 instead of -7x + 20. Double-check your calculations to avoid such errors.
Make sure to show all the steps in your solution, including how you obtained the common denominator and how you simplified the expression. This helps the reader follow your thought process and understand your solution better.
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Solve 2x^2+8x-3 by completing the square
Answers
2x^2+8x-3
1 Move the coefficient of x to the front & write the rest normally
2(x^2+4x-3/2)
2 Divide coefficient of x by 2 squared
2[x^2+4x+(4/2)^2-(4/2^2)-3/2]
3 Put the first terms into ( )^2
2[(x+2)^2-4-3/2]
4 Add the last 2 terms
= 2(x+2)^2-11
Select the expression that is correctly evaluated.
a.) 6² = 36
b.) 12¹ = 0
c.) 34 = 12
d.) 10⁰ = 10
Answers
From the list of options, the expression that is correctly evaluated is: (a.) 6² = 36
Calculating the expression that is evaluated correctlyThe expression that is correctly evaluated is:
a.) 6² = 36
This is because 6² means 6 raised to the power of 2, which is the same as 6 multiplied by itself. So, 6² equals 6 times 6, which is 36.
For other expressions, we have
b.) 12¹ means 12 raised to the power of 1, which is simply 12. Therefore, 12¹ equals 12, not 0.
c.) 3^4 means 3 raised to the power of 4, which is 81, not 12.
d.) 10⁰ means 10 raised to the power of 0, which is always equal to 1, not 10.
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Which of the following sets of side lengths could produce a triangle. SELECT ALL THAT APPLY.
A. 4,4,4
B. 13, 5, 6
C. 5,5,10
D. 3,6, 9
E. 5, 7, 11
Answers
The set of side lengths that can produce a triangle as required in the task content is; Choice E; 5, 7, 11.
Which values could be side lengths of a triangle?It follows from the task content that the set of side lengths that could produce a triangle.
Recall from the triangle inequality theorem that the sum of any two side lengths is greater than the third side length. Also, the difference of any two side lengths is less than the third side length.
Hence, the correct answer choice is; Choice E; 5, 7, 11.
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Hi guys! I'm struggling to start and answer this question on the syllabus.
help would be much appreciated
thanks in advance.
Answers
Answer:
I₁ ≈ 0.1036∠68.75°I₂ ≈ 0.1637∠50.31°Step-by-step explanation:
You want the solution in polar form of the system of equations ...
(2+j6)I₁ -j4·I₂ = 0j·I₁ +(8-j10)I₂ = 2The usual solution methods for a system of equations apply. The attached calculator shows the currents to be ...
I₁ ≈ 0.1036∠68.75°I₂ ≈ 0.1637∠50.31°__
Additional comment
For systems of equations in which the coefficients don't lend themselves to elimination or substitution methods, we prefer matrix methods to find a solution. A suitable calculator makes this relatively easy.
Last year Thomson Inc's earnings per share were $3.50, and its growth rate during the prior 5
years was 5.6% per year. If that growth rate were maintained, how many years would it take for
Thomson's EPS to triple? (Note: EPS is calculated annually.)
a. 23 years
b. 25 years
c. 21 years
d. 15 years
e. 22 years
Answers
Answer:
e. 22 years
Step-by-step explanation:
Solving a System of Linear Equations - Applications - Item 35812
A sandwich shop only sells sandwiches and homemade soup.
The table shows the number of sandwiches and bowls of soup purchased in the past
2 hours.
The total earnings for hours 1 and 2 are given.
Each sandwich costs the same price, and each bowl of soup costs the same price.
The system of equations can be used to represent the situation.
Use the drop-down menus to complete each statement.
Answers
the answer is in the attachment below:
7x/2x^2 - 12x - 5/3x
Answers
Answer:
1/6 x (21x^2 -82)
Step-by-step explanation:
1.) Multiply the numbers.
2.) Combine Exponents.
3.) Combine like terms.
4.) Common factor.
5.) Find one factor.
this should be right
There was a plate of 2
mint brownies, 2 chocolate
brownies and 5 chocolate
brownies with nuts. What
is the probability that
Gavin will randomly take a
brownie with nuts,
put it back, and grab one
without nuts?
Answers
Answer:
20/81
Step-by-step explanation:
The total number of brownies is 2 + 2 + 5 = 9. The probability of Gavin taking a brownie with nuts on the first pick is 5/9. After putting it back, the total number of brownies is still 9, but the number of brownies with nuts is now 4. Therefore, the probability of Gavin taking a brownie without nuts on the second pick is 4/9. The probability of both events happening together is the product of the individual probabilities: (5/9) x (4/9) = 20/81. Therefore, the probability that Gavin will randomly take a brownie with nuts, put it back, and grab one without nuts is 20/81.
Answer:
if you add the whole amount, then 2+2+5 is 9. then divide by 4 (the number without nuts) 4/9 is 44 percent
Step-by-step explanation:
How do I make x the subject of y=ax^2 + b
Answers
Answer:
Step-by-step explanation:
To make x the subject of y = ax^2 + b, we can use the following steps:
1.Subtract b from both sides to isolate the term with x^2:
y - b = ax^2
2.Divide both sides by a to isolate x^2:
(y - b) / a = x^2
3.Take the square root of both sides to solve for x:
x = ± sqrt((y - b) / a))
Therefore, the expression for x as a subject of y = ax^2 + b is:
x = ± sqrt((y - b) / a))
Someone Help with this question pls
Brainliest+30 Points
Answers
Answer:1
Step-by-step explanation:
then, x should be smaller than 3
in this canse it is 1;
A rancher wants to fence an area of 1,500 square yards in a rectangular field that borders a straight river, and then divide it in half with a fence perpendicular to the river. He needs no fence along the river. The dividing fence costs half as much as the surrounding fence. How can he do this so that the cost of the fence is minimized?
Answers
The cost of the fence for a rectangular field of 1,500 square yards will be 150k√50 dollars.
Let the length of the rectangular field be L and the width be W. Since the area of the field is 1,500 square yards, we have:
L × W = 1,500
P = 2L + W
C = kP + (1/2)k(L/2)
C = (2k)L + (k/2)W
W = 1500/L
Substituting this into the expression for C, we get:
C = (2k)L + (k/2)(1500/L)
dC/dL = 2k - (k/2)(1500/[tex]L^2[/tex]) = 0
Solving for L, we get:
L = 30√50 yards
Substituting this back into the equation for W, we get:
W = 50/√50 yards
Therefore, the dimensions of the rectangular field that minimize the cost of the fence are L = 30√50 yards and W = 50/√50 yards.
P = 2L + W = 60√50 + 50/√50 yards
C = (2k)L + (k/2)(1500/L) = 90k√50 dollars
k/2 = k/2
Substituting this into the expression for C, we get:
C = 150k√50 dollars
Therefore, to minimize the cost of the fence, the rancher should build a rectangular field with dimensions of L = 30√50 yards and W = 50/√50 yards, and the total cost of the fence will be 150k√50 dollars.
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Jessica works in a cake shop . Each cake is cut into 6 slices.
On Saturday 20 slices of chocolate cake were sold 25 slices of lemon cake were sold and 17 slices of carrot cake were sold .
Answers
Answer:
What is the question?
Step-by-step explanation:
N/A
find the perimeter of the following figures. 21 cm- b. 35 cm 35 cm 35 cm C. 6.75 cm 2.25 cm
Answers
Answer:
a. To find the perimeter of the first figure, we need to add up the lengths of all four sides. If the sides are equal, we can simply multiply the length of one side by 4. Therefore, the perimeter of a square with sides of 21 cm is:
Perimeter = 4 x side
Perimeter = 4 x 21 cm
Perimeter = 84 cm
b. To find the perimeter of the second figure, we need to add up the lengths of all three sides. Since all three sides are equal, we can simply multiply the length of one side by 3. Therefore, the perimeter of an equilateral triangle with sides of 35 cm is:
Perimeter = 3 x side
Perimeter = 3 x 35 cm
Perimeter = 105 cm
c. To find the perimeter of the third figure, we need to add up the lengths of all four sides. Therefore, the perimeter of a rectangle with sides of 6.75 cm and 2.25 cm is:
Perimeter = 2 x (length + width)
Perimeter = 2 x (6.75 cm + 2.25 cm)
Perimeter = 2 x 9 cm
Perimeter = 18 cm
Step-by-step explanation:
a. To find the perimeter of the first figure (a square with sides of 21 cm), we need to add up the lengths of all four sides. Since all four sides are equal, we can simply multiply the length of one side by 4. Therefore:
Perimeter = 4 x side
Perimeter = 4 x 21 cm
Perimeter = 84 cm
So the perimeter of the square is 84 cm.
b. To find the perimeter of the second figure (an equilateral triangle with sides of 35 cm), we need to add up the lengths of all three sides. Since all three sides are equal, we can simply multiply the length of one side by 3. Therefore:
Perimeter = 3 x side
Perimeter = 3 x 35 cm
Perimeter = 105 cm
So the perimeter of the equilateral triangle is 105 cm.
c. To find the perimeter of the third figure (a rectangle with sides of 6.75 cm and 2.25 cm), we need to add up the lengths of all four sides. Therefore:
Perimeter = 2 x (length + width)
Perimeter = 2 x (6.75 cm + 2.25 cm)
Perimeter = 2 x 9 cm
Perimeter = 18 cm
So the perimeter of the rectangle is 18 cm.
Lyla goes out to dinner with her freinds where the subtotal is $23.89. A 7% tax and 18% tip is added to the subtotal. How much did she pay in total?
Answers
Lyla pays $ 24.14 in total.
What is the total amount?
To add two or more numbers and determine the final total, use the sum. A series of any form of numbers, known as addends or summands, is added; the outcome is their sum or total.
Here, we have
Given: Lyla goes out to dinner with her friends where the subtotal is $23.89. A 7% tax and 18% tip are added to the subtotal.
we have to find out how much did she pay in total.
= $23.89 + 7% + 18%
= $23.89 + 7/100 + 18/100
= $23.89 + 0.07 + 0.18
= $ 24.14
Hence, Lyla pays $ 24.14 in total.
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(24x3−2x2−8x+30)÷(x−2)
Answers
We can long divide (24x^3 - 2x^2 - 8x + 30) by (x - 2) as follows:
24x^2 + 46x + 86
_______________________
x - 2 | 24x^3 - 2x^2 - 8x + 30
-(24x^3 - 48x^2)
_______________
46x^2 - 8x
46x^2 - 92x
___________
84x + 30
84x - 168
________
198
Therefore, (24x^3 - 2x^2 - 8x + 30) ÷ (x - 2) = 24x^2 + 46x + 86 with a remainder of 198/(x - 2).
Answer:
the quotient is 24x² + 46x + 86 and the remainder is 198. Thus, we can write:
(24x³ - 2x² - 8x + 30) ÷ (x - 2) = 24x² + 46x + 86 + 198/(x - 2)
Step-by-step explanation:
We can perform polynomial long division to divide (24x³ - 2x² - 8x + 30) by (x - 2).
24x² + 46x + 86
----------------------
x - 2 | 24x³ - 2x² - 8x + 30
- (24x³ - 48x²)
------------------
46x² - 8x
- (46x² - 92x)
--------------
84x + 30
- (84x - 168)
--------------
198
Therefore, the quotient is 24x² + 46x + 86 and the remainder is 198. Thus, we can write:
(24x³ - 2x² - 8x + 30) ÷ (x - 2) = 24x² + 46x + 86 + 198/(x - 2)
Find all unknown measures in the triangle
Answers
The value of angle B is 68 degrees and the length of the segments b is 27.81 and c is 11.28.
What is Law of sines?A triangle's sides and angles are related by the Law of Sines, a trigonometric formula. It specifically specifies that for all three sides and angles of the triangle, the ratio of the length of one side to the sine of the angle opposite that side is the same. This may be expressed as the following equation:
sin A/a = sin B/b = sin C/c
where a, b, and c are the lengths of the sides that are on each side of the triangle's three angles, A, B, and C.
For the give triangle we can use the Law of sines to find the missing values.
The law of sine is given as:
sin A/a = sin B/b = sin C/c
Given A = 90 degrees and C = 22 degrees,
sin 90 / 30 = sin 22 / c
c = 30 sin 22 / sin 90
c = 30 (0.37) / 1
c = 11.28
Now, Using the sum of triangles:
90 + 22 + B = 180
112 + b = 180
B = 68
Now,
sin A/a = sin B/b
Sin 90 / 30 = sin (68) / b
b = 30 sin (68) sin 90
b = 27.81
Hence, the value of angle B is 68 degrees and the length of the segments b is 27.81 and c is 11.28.
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A scientist is conducting an experiment with the bacteria E-coli, in the begining of the experiment there are 15 E-coli. The E-coli grow at a rate of 26% per hour. At the end of the experiment there are 7693 E-coli bacteria. How long did the experiment last?
Group of answer choices
a.) 30 days
b.) 27 hours
c.) 30 hours
d.) 27 days
Answers
Answer: 27 hours
Step-by-step explanation:
The E-cοli grοwth rate οf 26% per hοur. At the end οf the experiment there are 7693 E-cοli bacteria. The experiment was dοne last tο 27 hοurs.
What is grοwth rate?Grοwth rates are the percentage changes in a given measure οver a given span οf time. Depending οn whether the size οf the variable is grοwing οr declining οver time, grοwth rates can be either pοsitive οr negative.
Grοwth rates have been used tο study ecοnοmic activity, business management, and financial yields since they were first used by biοlοgists tο study pοpulatiοn sizes.
Using the fοrmula mentiοned belοw-
[tex]A = P(1 + r) \wedge t[/tex]
Grοwth rate (r)= 26%= 26/100= 0.26
Initial vοlume (P)= 15
Final vοlume [tex](A)= 76937693= 15(1+0.26)^t[/tex]
Or, [tex](1.26)^t= 7693/15[/tex]
Or, t ln(1.26)= ln(7693/15)
Or, t≅27
Hence the experiment was dοne at 27 hοurs.
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Using a graphing tool to solve the equation below for x. -3(-^×)-6=-3^×+10
Answers
The solution of x using the graphing tool for the expression [tex]-3^{-x} -6 = -3^{x} + 10[/tex] is found as: x = 2.5.
How to find solution using graphing tool?A line represents the graph of a linear equation. The equation has a solution at each point along the line. We shall plot two lines for a set of two equations.
The points that are the answers to each equation are then all visible to us. We will also discover the system's answer by identifying the characteristics that the lines share.The majority of one-variable linear equations have just one solution; nevertheless, we observed that some equations, known as contradictions, really had no solutions and that for other equations, known as identities, all possible values are the solutions. Similar to this, there are three possible outcomes when we solve a set of two linear equations illustrated by a graph containing two lines in the same plane.The given expression is-
[tex]-3^{-x} -6 = -3^{x} + 10[/tex]
The graph of the equation for this expression if plotted using graphing tool.
From the graph, the solution of x is found as: x = 2.5.
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There are 5 passengers in a car. In how many ways can the passengers sit in the 5 passenger seats of the car?
Answers
Answer:
there are 120 different ways
Step-by-step explanation:
the factorial of 5
:)
Fill out the box please
Answers
The value of the functions are;
x = 1, f(x) = 1/2
x = 2, f(x) = -1
x = 3 , f(x) = -5/2
x = 3, f(x) = -4
How to determine the valueNote that functions are expressions or equations that shows the relationship between variables.
The variables are;
The independent variableThe dependent variableFrom the information given, we have the function as;
f(x) = -3/2x + 2
Now, substitute the value of x as 1
f(1) = -3/2(1) + 2
f(1) = -3/2 + 2 = -3 + 4 /2 = 1/2
f(2) = -3/2(2) + 2
expand the bracket
f(2) = -6/2 + 2 =-6 + 4 /2 = -2/2 = -1
For the value of x = 3
f(3) = -3/2(3) + 2
expand the bracket'
f(3) = -9/2 + 2
f(3) = -5/2
For the value of x = 4
f(4) = -3/2(4) + 2
f(4) = -8/2
f(4) = -4
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What are the answer for all of these 1-13
Answers
1. The length of the arc is 2π
2. The value of x is 22.95°
3. The measure of side m is (4√3)x
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
1. The length of an arc = tetha/360 × 2πr
= π/3 × 1/360 × 2 × π × 6
= 2π
the length of the arc is 2π
2. Sin60 = y/23
√3/2 = y/23
23√3 = 2y
y = 11.5√3
sin x = 11.5√3/51
sinx = 0.39
x = sin^-1(0.39)
x= 22.95°
3. the measure of mis calculated from
cos 30 = 6x/m
√3/2 = 6x/m
12x = √3m
m = 12x/√3
= 12x√3/3
= 4x√3.
= (4√3)x.
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Please help brainlesst and pints
Answers
The ball will reach its maximum height after 3.5 seconds.
What is projectile motion?
Projectile motion is the motion of an object that is launched into the air and then moves along a curved path under the influence of gravity.
In projectile motion, the object follows a parabolic trajectory, which is a curve described by a quadratic function. The path of the object depends on the initial velocity, angle of projection, and acceleration due to gravity.
The key characteristics of projectile motion are that the object moves in two dimensions, typically horizontally and vertically, and that the motion in each dimension is independent of the other. This means that the horizontal and vertical components of motion can be analyzed separately.
The height function of the ball thrown The key characteristics of projectile motion are that the object moves in two dimensions, typically horizontally and vertically, and that the motion in each dimension is independent of the other. This means that the horizontal and vertical components of motion can be analyzed separately. is given by h(t) = 112t - 16t^2, where t is the time in seconds and h(t) is the height of the ball at time t.
To find the maximum height, we need to find the vertex of the parabolic function h(t). The vertex of a parabola given by the equation y = ax^2 + bx + c is located at x = -b/2a.
In the case of our height function h(t) = -16t^2 + 112t, the coefficient of the squared term is -16, and the coefficient of the linear term is 112. Therefore, the time at which the ball reaches its maximum height is given by:
t = -b/2a = -112/(2*(-16)) = 3.5
So, the ball will reach its maximum height after 3.5 seconds.
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A computer algorithm is going to pick a day at random from the seven days of
the week.
The table below shows the probabilities of the algorithm choosing each of the
weekdays.
Weekdays
Probability
Monday
0.12
Tuesday Wednesday Thursday
0.07
0.05
0.28
Work out the probability that it will not choose one of the weekdays.
Friday
0.15
Answers
The sum of the probabilities of choosing each weekday is:
0.12 + 0.07 + 0.05 + 0.28 + 0.15 + p(Friday) + p(Weekend) = 1
where p(Friday) is the probability of choosing Friday and p(Weekend) is the probability of choosing one of the weekend days (Saturday or Sunday).
We know that the probability of choosing one of the weekdays is:
p(Weekdays) = 0.12 + 0.07 + 0.05 + 0.28 = 0.52
So, the probability of not choosing one of the weekdays is:
p(Not Weekdays) = 1 - p(Weekdays) = 1 - 0.52 = 0.48
Therefore, the probability that it will not choose one of the weekdays is 0.48.
if x is multiplied by 5 and then 3 is subtracted, then the function is f(x)=5x-3.
Answers
If x is multiplied by 5 and then 3 is subtracted, then the function is f(x)=5x-3. the inverse function of f(x) = 5x - 3 is f^(-1)(x) = (x + 3)/5.
How to find the inverse function?To find the inverse function of f(x) = 5x - 3, we need to follow these steps:
Step 1: Replace f(x) with y:
y = 5x - 3
Step 2: Solve for x in terms of y:
y = 5x - 3
y + 3 = 5x
x = (y + 3)/5
Step 3: Replace x with f^(-1)(x) and y with x:
f^(-1)(x) = (x + 3)/5
Step 4: Check if the inverse function is valid by verifying if f(f^(-1)(x)) = x and f^(-1)(f(x)) = x:
f(f^(-1)(x)) = f((x+3)/5) = 5((x+3)/5) - 3 = x + 2
f^(-1)(f(x)) = f^(-1)(5x - 3) = (5x - 3 + 3)/5 = x/5
Since f(f^(-1)(x)) = x + 2 and f^(-1)(f(x)) = x/5, the inverse function is valid.
Therefore, the inverse function of f(x) = 5x - 3 is f^(-1)(x) = (x + 3)/5.
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The complete question is:
if x is multiplied by 5 and then 3 is subtracted, then the function is f(x)=5x-3.
What are the step to find the inverse to this function?
Prudence solves the rational equation frac(-7x-20,bracket(x+2)bracket(x+4))+2=frac(x,x+4) and obtains the solutions x = 1 and x = -4. What are some correct possible comments her math instructor would say about her solution?
Answers
Math instructor may provide feedback on Prudence's solution by advising her to check her solutions for extraneous solutions, showing more detailed work, and continuing to practice solving challenging problems to improve her skills for equation.
One possible comment the math instructor could make about Prudence's solution is that it is important to check the solutions she obtained to make sure they are valid. When solving rational equations, it is possible to obtain extraneous solutions, which are solutions that do not work in the original equation. Therefore, the instructor may advise Prudence to substitute her solutions back into the original equation and verify that they satisfy the equation.
Another comment the instructor could make is that Prudence should show her work and steps in more detail, especially if she is turning in her solution for a graded assignment. By showing more detailed work, Prudence can demonstrate a deeper understanding of the problem and how she arrived at her solution.
The instructor may also commend Prudence on her ability to solve a complex rational equation with multiple variables and parentheses. This shows that she has a strong grasp of algebraic concepts and can apply them effectively. However, the instructor may also suggest that Prudence continue to practice solving more challenging problems to further improve her skills.
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need help
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
Answers
Rounding to the nearest 50 dollars, we get:
value = $12,550.
What is annual rate of change?The annual rate of change refers to the percentage change in a quantity over a period of one year. It is commonly used to express the growth or decline of economic indicators, such as GDP, inflation, or employment, as well as the performance of financial assets, such as stocks or bonds. To calculate the annual rate of change, you need to take the difference between the initial and final values of the quantity, divide it by the initial value, and multiply the result by 100 to express it as a percentage. For example, if a company's revenue was $1 million in 2021 and $1.2 million in 2022, the annual rate of change in revenue would be (1.2-1)/1 * 100 = 20%.
A) The car depreciated from $44,000 in 1992 to $15,000 in 2006, a period of 14 years.
The annual rate of change can be found using the formula:
[tex]r = (V2/V1)^{(1/n)} - 1[/tex]
where V1 is the initial value, V2 is the final value, and n is the number of years.
Substituting the given values, we get:
[tex]r = ($15,000/$44,000)^{(1/14)} - 1[/tex]
[tex]r = 0.0576[/tex]
So, the annual rate of change (or depreciation) is 0.0576.
B) To express this rate as a percentage, we can multiply it by 100 and add a percent sign:
[tex]r = 0.0576 x 100%[/tex]
[tex]r = 5.76%[/tex]
So, the car depreciated at an annual rate of 5.76%.
C) If we assume that the car value continues to drop by the same percentage, we can use the formula for exponential decay:
[tex]V = V0*(1-r)^t[/tex]
where V0 is the initial value, r is the rate of change, and t is the time elapsed.
Substituting the given values, we get:
[tex]V = $15,000*(1-0.0576)^3[/tex]
[tex]V = $12,527.31[/tex]
Rounding to the nearest 50 dollars, we get:
[tex]value=12,550[/tex]
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Use the ALEKS graphing calculator to solve the system of equations.
5-0.7x=0.2y
-y+0.4x = 4.3
Round to the nearest hundredth.
(x, y) = (.D
X
Ś
Answers
Answer:
(7.51,-1.3)
Step-by-step explanation:
rewrite 5-0.7x=0.2y in terms of x,
divide both sides by 0.2 to get: 25-3.5x = y
substitute the y part in -y+0.4x=4.3 with the new equation that we made
(in bold)
so,
-(25-3.5x) +0.4x = 4.3
expand and simplify
so,
-25 +3.5x +0.4x = 4.3 -> -25 +3.9x = 4.3 -> 3.9x = 29.3 -> x ≈ 7.51
now, substitute the new x (underlined) to the equation in bold
so,
25-3.5(7.51) = y -> y ≈ -1.3
graphing both equations on desmos can verify the answers (only if you rearrange the two equations to get y by itself)
Skills cimals Jiz 03/07 The material for the different dresses cost £7.99 per metre, £9.77 per metre and £9.07 per metre. What was the difference in price between the most expensive and the cheapest material? O о O £1.08 £1.23 £0.70 £1.78
Answers
The difference between the most expensive and the cheapest material is £1.78
What is meant by "difference" in mathematics?The term "difference" can also be used more generally to refer to the amount by which two quantities differ.
The concept of difference is closely related to the concept of distance, which refers to the numerical value of the separation between two points, or to prices as in the case we have here.
The difference between the most expensive and the cheapest material is; £9.77 - £7.99 = £1.78
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Nikki invested $1000 at 2% interested compound daily how long will it be until the balance reaches $5000 round to the nearest whole number
Answers
now, we could use the compound interest equation using a compounding period of 365 for a year with 365 days, so a daily compounding, OR we can just use the continuously compounding equation, which is equivalent.
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 5000\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=years \end{cases} \\\\\\ 5000 = 1000e^{0.02\cdot t} \implies \cfrac{5000}{1000}=e^{0.02t}\implies 5=e^{0.02t} \\\\\\ \log_e(5)=\log_e(e^{0.02t})\implies \log_e(5)=0.02t\implies \ln(5)=0.02t \\\\\\ \cfrac{\ln(5)}{0.02}=t\implies \boxed{80\approx t}[/tex]