Answer:
Step-by-step explanation:
a. The number of red roses left t hours before the store opens can be represented by the formula:
N(t) = 400 * (1/2)^(t/2)
Here, we're dividing the number of available roses by 2 every 2 hours, so the exponent t/2 represents the number of 2-hour intervals that have passed since the store opened.
b. The number of box chocolates left t hours after the store opens can be represented by the formula:
M(t) = 200 * (0.85)^t
Here, we're multiplying the number of available boxes by 0.85 every hour, so the exponent t represents the number of hours that have passed since the store opened.
c. We need to find the time t when the number of roses is equal to the number of boxes of chocolates:
400 * (1/2)^(t/2) = 200 * (0.85)^t
Dividing both sides by 200:
2 * (1/2)^(t/2) = 0.85^t
Taking the logarithm of both sides:
log(2) - (t/2) * log(2) = t * log(0.85)
Simplifying:
t * (log(0.85) + (log(2)/2)) = log(2)
t = log(2) / (log(0.85) + (log(2)/2))
Using a calculator, we get:
t ≈ 11.9 hours
Therefore, the number of roses will be equal to the number of boxes of chocolates approximately 11.9 hours before the store opens, or around 9 p.m. on the day before Valentine's Day.
d. To find the number of boxes of chocolate left at 12:30 p.m. (3.5 hours after the store opens), we can use the formula:
M(3.5) = 200 * (0.85)^3.5
M(3.5) ≈ 97.4
Therefore, there are approximately 97 boxes of chocolate left at 12:30 p.m.
e. To buy 36 red roses, we need to find the latest time we can arrive before the store runs out of roses. We can set N(t) equal to 36 and solve for t:
400 * (1/2)^(t/2) = 36
Dividing both sides by 400:
(1/2)^(t/2) = 0.09
Taking the logarithm of both sides:
t/2 * log(1/2) = log(0.09)
Simplifying:
t ≈ 5.2 hours
Therefore, the latest time we can arrive to successfully buy 36 red roses is approximately 5.2 hours before the store opens, or around 3:50 a.m. on the day before Valentine's Day.
George plans to order flowers for his daughter's graduation. A bouquet of 12 roses will cost $61, while a bouquet of 18 roses will cost $79. What is the equation that represents the linear relationship between price and number of roses? Let P represent the price, and r the number of roses.
Answer:
Step-by-step explanation:
Start by finding the slope of the line that passes through both the 12 roses bouquet and the 18 roses bouquet.
point 1: (12,61)
point 2: (18,79)
m=y^2-y^1/x^2-x^1
m=79-61/18-12
m=18/6
m=3
then, using one of the points find the fixed costs
P=m*r+b
using 12,61
61=3*12+b
61-36=b
b=25
Answer:
The general equation that represents the linear relationship is:
P=25+3r
A BOAT NEEDS TO TRAVEL NORTH AT 30KM PER HOUR AND A CONSTANT CURRENT OF 4KM PER HOUR IS FLOWING IN NORTH-WEST DIRECTION WHAT IS THE EQUIVALENT SPEED IN STILL WATER TO ACHIEVE ACTUAL SPEED OF 30KM PER HOUR?
If the boat travel north at 30 km per hour . the equivalent speed in still water required to achieve an actual speed of 30 km/h is 30.1 km/h.
What is the speed?Finding the boat's true speed using Pythagoras' theorem using this formula
Speed = √((30 km/h)^2 + (4/√(2) km/h)^2)
Let plug in the formula
Speed = √(900 + 8) km/h
Speed = √(908) km/h
Speed = 30.1 km/h
Speed = 30 km/h ( Approximately)
Therefore the speed is 30km/h.
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find the average rate of change of f(x)=2x^2-2 from 2 to 4
Answer:
average rate of change = 12
Step-by-step explanation:
the average rate of change of f(x) in the interval a ≤ x ≤ b is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here the interval is 2 ≤ x ≤ 4 , then
f(b) = f(4) = 2(4)² - 2 = 2(16) - 2 = 32 - 2 = 30
f(a) = 2(2)² - 2 = 2(4) - 2 = 8 - 2 = 6
then
average rate of change = [tex]\frac{30-6}{4-2}[/tex] = [tex]\frac{24}{2}[/tex] = 12
f(x)=2(x−7)(x−3) y intercept
The y-intercept of the function F(x) = 2(x - 7)(x - 3) is 42, which means that the graph of the function intersects the y-axis at the point (0, 42).
What is y-intercept?The y-intercept is the point where a function or a curve intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is equal to zero.
According to question:The y-intercept of a function is the point where the graph of the function intersects the y-axis. To find the y-intercept of the function F(x) = 2(x - 7)(x - 3), we need to substitute 0 for x in the equation:
F(x) = 2(x - 7)(x - 3)
So, we have:
F(0) = 2(0 - 7)(0 - 3)
Simplifying this expression, we get:
F(0) = 2(-7)(-3)
F(0) = 42
Therefore, the y-intercept of the function F(x) = 2(x - 7)(x - 3) is 42, which means that the graph of the function intersects the y-axis at the point (0, 42).
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Me podrían ayudar a resolver esto? Tengo la respuesta lo que necesito es el procedimiento. Muchas gracias
2√8p²q³r
The algebraic expression can be simplified to 4p√2q³r
How to simplify an algebraic expression?An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.
The expression can be simplified as follow:
2√(8p²q³r) = 2 * √8 * √p² √(q³r)
= 2 * √(4 * 2) * p √(q³r)
= 2 * √4 * √2 * p √(q³r)
= 2 * 2 * √2 * p √(q³r)
= 4p√2q³r
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Question in English
Could you help me solve this? I have the answer what I need is the procedure. Thank you so much
2√8p²q³r
If the sides of a square are increased by 11, the area becomes 400. What is the length of the original side?
Answer: x = 9 units
Step-by-step explanation:
You’re flying your dragon kite. it’s connected to 37 yards of string. The kite is directly above the edge of a pond. The edge of the pond is 32 yards from where the kite is tied to the ground. how high Is the kite above the edge of the pond? Round to one decimal place as needed
The kite is approximately 18.57 yards high above the edge of the pond.
How to solve for the height of the kiteThe Pythagorean theorem would be used to solve the prob;lem that we have here
The theorye tell us that the squatre of the hypotenuse is the same as the sum of the square of the other two sides
The formula is written as
c^2 = a^2 + b^2
In this case:
c = 37 yards (length of the string)
a = 32 yards (distance from where the kite is tied to the ground to the edge of the pond)
b = height of the kite above the edge of the pond (which we need to find)
Now, plug the values into the Pythagorean theorem:
37^2 = 32^2 + b^2
1369 = 1024 + b^2
Subtract 1024 from both sides:
b^2 = 345
Now, take the square root of both sides to solve for b:
b = √345
= 18.57 yards
The kite is approximately 18.57 yards high above the edge of the pond.
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Find the slope of the line shown below
The slope of the line which passes through points (-2, 1) and (0, -3) is calculated as: m = -2.
How to Find the Slope of a Line?In order to find the slope of the line given in the graph, pick two points on the line, then plug in their coordinates into the slope formula given as:
Slope (m) = change in y / change in x = y2 - y1 / x2 - x1
We have:
(-2, 1) = (x1, y1)
(0, -3) = (x2, y2)
Plug in the values:
Slope (m) = (-3 - 1) / (0 - (-2))
m = -4 / 2
Slope of the line (m) = -2
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The slope of the line represented by the graph is equal to -2.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Slope (m) = (-3 - 3)/(0 + 3)
Slope (m) = (-6)/(3)
Slope (m) = -2.
Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to -2.
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The slope of the line which passes through points (-2, 1) and (0, -3) is calculated as: m = -2.
How to Find the Slope of a Line?In order to find the slope of the line given in the graph, pick two points on the line, then plug in their coordinates into the slope formula given as:
Slope (m) = change in y / change in x = y2 - y1 / x2 - x1
We have:
(-2, 1) = (x1, y1)
(0, -3) = (x2, y2)
Plug in the values:
Slope (m) = (-3 - 1) / (0 - (-2))
m = -4 / 2
Slope of the line (m) = -2
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The slope of the line represented by the graph is equal to -2.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Slope (m) = (-3 - 3)/(0 + 3)
Slope (m) = (-6)/(3)
Slope (m) = -2.
Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to -2.
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what expression is equivalent to 91 plus 39?
Answer: 130
Step-by-step explanation:
The problem is asking for an expression that is equivalent to the addition of 91 and 39. An expression is a combination of numbers, variables, and mathematical operations that does not have an equal sign. In this case, the expression we are looking for should evaluate to the same value as the sum of 91 and 39, which is 130.
To obtain this expression, we simply add 91 and 39, since the sum of these two numbers is equivalent to the expression we are looking for. Adding 91 and 39, we get:
91 + 39 = 130
Therefore, the expression that is equivalent to 91 plus 39 is simply 130.
Please give Brainliest! Thanks and have a good rest of your day!
Break-Even Sales
BeerBev, Inc., reported the following operating information for a recent year (in millions):
Sales $6,512
Cost of goods sold $1,628
Gross profit $4,884
Marketing, general, and admin. expenses 592
Income from operations $ 4,292
Assume that BeerBev sold 37 million barrels of beer during the year, that variable costs were 75% of the cost of goods sold and 50% of marketing, general and administration expenses, and that the remaining costs are fixed. For the following year, assume that BeerBev expects pricing, variable costs per barrel, and fixed costs to remain constant, except that new distribution and general office facilities are expected to increase fixed costs by $21.09 million.
a. Compute the break-even sales (in barrels) for the current year. Round your answer to two decimal places. Enter your answers in millions.
The break even sales for the current year using the contribution per unit is 5.27.
The formula to find the break even sales is,
Break even sales = Fixed costs / Contribution per unit
Now,
Contribution per unit = Sales price per unit - Variable cost per unit.
Sales price = $6,512
Variable cost = (75% × cost of goods sold) + (50% × marketing, general and administration expenses)
= (75% × $1,628) + (50% × $592)
= $1517
Contribution margin = $6,512 - $1517 = $4995
Contribution per unit = $4995 / 37 = $135 per million
Fixed costs = (25% × cost of goods sold) + (50% × marketing, general and administration expenses)
= $703
Break even sales = 703 / 135 = 5.21
Hence the break even sales is 5.27.
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y<-4x-2 choose the graph that best models the inequality
Answer:the upper right one( the dash line that hit -2
Step-by-step explanation:
i need the answer to 1 over 3
Answer:
1 over 3 would juts be 1/3
160/30000 simplified
Answer:160/30000 simplified would be 2/375
Step-by-step explanation:
Exact Form:
[tex]\frac{2}{375}[/tex]
Decimal Form:
0.0053
EASY POINTS!
On a map, two cities are 2.8 inches apart. The map has a scale of 1 inch to 25 miles. How far apart, in inches, would the same two cities be on a map that has a scale of 1 inch to 40 miles? Show your work!
Answer:
1.75 inches (pls give brainliest lol!)
Step-by-step explanation:
Let's use a proportion to solve the problem:
On the first map, 2.8 inches represents 25 miles:
2.8 / 1 = 25 / x
Simplifying the equation, we get:
x = 25(2.8)/1 = 70
Therefore, the distance between the two cities in the first map is 70 miles.
Now, let's find the distance between the same two cities on the second map, which has a scale of 1 inch to 40 miles:
We want to find how many inches on the second map represent 70 miles. Let's call this value y.
1 / 40 = y / 70
Solving for y, we get:
y = 70/40 = 1.75
Therefore, the two cities would be 1.75 inches apart on the second map with the 1 inch to 40 miles scale.
The two buses drove towards each other at constant speeds. The first left NY at 11AM and arrived in Boston at 4 PM, and the second left Boston at 12 PM and arrived in NY at 5 PM. What time did they meet?
The two buses meet at the same time they left their respective cities, so they meet at 11 AM in NY.
Since the two buses are traveling towards each other at constant speeds, we can use the formula for finding the time two objects meet when traveling at constant speeds in opposite directions:
t = (d2 - d1)/(v1 + v2)
Where t is the time they meet, d1 is the distance the first bus travels, d2 is the distance the second bus travels, v1 is the speed of the first bus, and v2 is the speed of the second bus.
In this case, d1 is the distance between NY and Boston (approx. 200 miles), d2 is the distance between Boston and NY (also approx. 200 miles), v1 is the speed of the first bus (200 miles in 5 hours, or 40 miles/hour), and v2 is the speed of the second bus (200 miles in 5 hours, or 40 miles/hour).
Plugging these values into the formula, we get:
t = (200 - 200)/(40 + 40)
t = 0/80
t = 0
Hence, the two buses meet at the same time they left their respective cities, so they meet at 11 AM in NY.
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3.25x×400=2.50x+600 solve to determine when costs are equal
Okay, let's solve this step-by-step:
3.25x×400=2.50x+600
1300x = 1500
x = 500
So when x = 500, the costs are equal.
Suppose that the polynomial function f is defined as follows.
The zeros of f according to their multiplicity are:
Zero of multiplicity 1: x = -8, x = -3, x = 0, x = 9
Zero of multiplicity 2: None
Zero of multiplicity 3: None
Here,
We have,
The zeros of a polynomial function are the values of x that make the function equal to zero. The multiplicity of a zero is the number of times it appears as a factor in the polynomial.
In the given function f(x), the zeros are the values of x that make the function equal to zero.
We can find these values by setting the function equal to zero and solving for x.
f(x) = 7x(x-9)(x+8)^2(x+3) = 0
Therefore, the zeros of f(x) are x = -8, x = -3, x = 0, and x = 9.
To determine the multiplicity of each zero, we can look at the degree to which the corresponding factor appears in the polynomial.
For example, x = -8 is a zero of multiplicity 2 because it appears as a factor twice in the function, as (x+8)^2.
Similarly, x = -3, x = 0, and x = 9 are zeros of multiplicity 1 because they each appear as a factor once in the function.
There are no zeros of multiplicity 3 or higher in this function, so we can list "None" for those categories.
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The city of Raleigh has 9200 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 350 randomly selected registered voters was conducted. 109 said they'd vote for Brown, 235 said they'd vote for Feliz, and 6 were undecided. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. Note: The proportion should be a fraction or decimal, not a percent.
That this is just an estimate of the true proportion of all voters who would vote for Brown, based on the sample of 350 voters surveyed. The true proportion could be different, due to sampling variability.
What is Statistic?
A statistic is a numerical measure that summarizes some aspect of a dataset. It is a way to describe a sample of data in a concise and meaningful way. Common examples of statistics include measures of central tendency such as the mean, median, and mode, as well as measures of variability such as the range, standard deviation, and variance.
The sample statistic for the proportion of voters surveyed who said they'd vote for Brown is the sample proportion, which is the number of voters who said they'd vote for Brown divided by the total number of voters surveyed:
Number of votes who said they'd vote for brown
total number of surveyed
= 109/350
=0.31
Therefore, based on the sample of 350 voters surveyed.
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What values of y and z make
The values of y and z that make the triangles to be congruent are 13 each
Calculating the values of y and zFrom the question, we have the following parameters that can be used in our computation:
The triangles
For the two triangles to be congruent, the following equations must be true
2y = y + 13
y + 5z - 20 = 2y + z + 19
When the above equations are evaluated, we have
y = 13
Next, we have
4z = y + 39
So, we have
4z = 13 + 39
Add and divide by 4
z = 13
Hence, the values of y and z are 13
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Ken volunteers 1hr25min each day. How many hours of volunteering is completed in 4 weeks? Enter a mixed number.
He completed volunteering in 39 hours 40 minutes in 4 weeks
How to determine this
If Ken volunteers 1 hr 25 mins each day
i.e 1 hr 25 mins = 1 days
By converting 1 hr 25 mins to mins
When 60 mins = 1 hr
1 hr 25 mins = 60 + 25 = 85 mins
How many hours of volunteering is completed in 4 weeks
Let x represent the numbers of hours
i.e x = 4 weeks
By converting 4 weeks to days
When 7 days = 1 week
4 weeks = 4 * 7 days
= 28 days
So, when 85 mins = 1 day
x mins = 28 days
x = 28 days * 85 mins/1 day
x = 2380 mins
By converting it back to hour
When 60 mins = 1 hour
2380 mins = x
x = 2380/60 hour
x = 39 hours 40 mins
Therefore, the hours that can be completed in 4 weeks is 39 hours 40 minutes
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definition of a tangent?
Answer:
A tangent is a line that touches the curve or a circle at a point..
tion 9, 2.2.5 The histogram to the right represents the weights (in pounds) of members of a certain high-school math team. How many team members are included in the histogram? he histogram represents 20 math team members. www 4- 2- 0- Points: 0 of 1 110 120 130 140 150 160 170
Based on the information provided in the question, we can conclude that the histogram represents 20 math team members.
[tex]\huge{\colorbox{black}{\textcolor{lime}{\textsf{\textbf{I\:hope\:this\:helps\:!}}}}}[/tex]
[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{blue}{\small\texttt{If you have any further questions,}}[/tex] [tex]\textcolor{blue}{\small{\texttt{feel free to ask!}}}[/tex]
♥️ [tex]{\underline{\underline{\texttt{\large{\color{hotpink}{Sumit\:\:Roy\:\:(:\:\:}}}}}}\\[/tex]
Point P is shown on the number line below. The distance between Point Q and Point P is 6 1/2 uhits. Which number
could represent Point Q?
The number that could represent point Q is to be considered as the option c. 2 1/2.
How to solveCalculation of the number:
Since
p = -4
q could be 6.5 units to the right or to the left of point p.
So, to the right, it should be like
=p + q
= -4 + 6.5
= 2.5
Hence, The number that could represent point Q is to be considered as option c. 2 1/2.
In mathematics, a tool known as a number line offers a graphical representation of numerical values arranged in sequential order from left to right with zero located in the center. This instrument is frequently applied throughout mathematical fields when interpreting negative and positive numbers along with fractions and decimals.
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Find the value of x. Write your answer in simplest form.
Answer:
[tex]x = \frac{9}{ \sqrt{2} } = \frac{9 \sqrt{2} }{2} [/tex]
please help me i will give brainiest to whoever answers the questions thank you
PLEASE HELP please help thank you please hurry fast i will give brainiest
Answer:
3) The graph that has three x-intercepts
9) Plot the points on the graphing calculator, and then generate a linear regression equation. That equation is:
y = 2.857x - 1.4286
The closest equation is y = 3x - 2. That equation best represents the regression line for this data.
z = 3x + y solve for x
Answer:
x = (y-z)/3
Step-by-step explanation:
z = 3x + y
3x = z - y
x = (z - y)/3
The accompany data represent the percentages of teenagers in various countries that have used certain drugs. Complete parts (a) through (c) below.
Country - A B C D E F G H I J K
Drug 1, x - 23 17 41 5 38 18 23 5 8 54 35
Other Drug - 3 2 21 2 15 9 15 2 2 32 25
The coefficient of determination is: 88%
How to solveThe following table shows the calculations:
X Y X^2 Y^2 XY
22 3 484 9 66
17 4 289 16 68
41 21 1681 441 861
5 1 25 1 5
36 16 1296 256 576
19 7 361 49 133
24 14 576 196 336
6 4 36 16 24
8 2 64 4 16
52 32 2704 1024 1664
35 23 1225 529 805
Total 265 127 8741 2541 4554
Sample size: n=11
Now,
Syy=1074.72727Sxx= 2356.90909Sxy = 1494.454545(a)
The coefficient of correlation is :
r=[tex]\frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}=0.94[/tex]
(b)
The slope of the regression equation is 0.63
S.
and intercept of the equation will be
[tex]b_{0}=\frac{1}{n}(\sum y - b_{1} \sum x)=-3.729965\approx -3.73[/tex]
So the regression equation will be
y'=-3.73+0.63*x
(c)
The coefficient of determination is: 88%
Regression is a statistical analytical method that investigates correlations between two or more variables. Its widespread usage stems from its ability to forecast or assess the value of one contingent variable using one or many independently varying variables.
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A rectangle's base is 3 in shorter than five times its height. The rectangle's area is 68 in?. Find this rectangle's dimensions.
The rectangle's height is 2 in, and the rectangle's base is 5 x 2+ 3 = 30 in, whose area is given as 68in².
What is rectangle?It has two pairs of equal-length sides that are at right angles to each other. It is the most common type of quadrilateral, and it can be found in everyday objects like windows, doors, and tabletops.
To solve this problem, we need to use the formula for the area of a rectangle (A = l x w), where A is the area, l is the length, and w is the width. We also know that the base is 3 inches shorter than 5 times the height. Therefore, we can set up the equation to solve for the height and the base of the rectangle as follows:
A = l x w
A = (h + 3) x (5h)
A = 5h² + 3h
5h² + 3h = 68
h= -2 (as height can not be in negative)
h= 2
By using the quadratic formula, we can solve for the height, h, which is equal to 2.
Therefore, the rectangle's height is 2 in, and the rectangle's base is 5 x 2+ 3 = 30 in.
This problem was solved by using the quadratic equation to solve for the height of the rectangle, which was then used to solve for the base.
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Find the area of the circle. Round your answer to the nearest tenth. Use 3.14 or 22
area: about
mm²
9 mm
for π.
Answer:
254.34
Step-by-step explanation:
πr^2
3.14*81
254.34
Find the angle of depression from the top of a lighthouse 400 feet above water level to the water line of a ship 18,410 ft offshore? Round your answer to the nearest hundredth of a degree.
To find the angle of depression, we can use the tangent function in trigonometry. In this situation, we have a right triangle where the height (opposite side) is 400 feet, and the distance (adjacent side) is 18,410 feet.
tan(angle) = opposite / adjacent
tan(angle) = 400 / 18,410
Now, we'll use the arctangent (inverse tangent) function to find the angle:
angle = arctan(400 / 18,410)
angle ≈ 1.25 degrees
The angle of depression from the top of the lighthouse to the waterline of the ship is approximately 1.25 degrees, rounded to the nearest hundredth of a degree.