URGENT!!!!! Examine the graph of the function What is the initial value of the function?
Enter your answer as a number, like this: 42
Answers
The answer of the given question based graph of function on finding the initial value of the function the answer is the initial value of the function is 2.
What is Graph?A graph is visual representation of data that displays relationship between variables. It consists of points or vertices connected by lines or arcs that represent relationships between variables. Graphs can be used to represent various types of data, like numerical, categorical, and ordinal data.
Graph are commonly used in mathematics, science, engineering, and social sciences to help people understand complex data and relationships. Different types of graphs like bar graphs, line graphs, scatter plots, pie charts, and histograms. Graphs are powerful tool for data analysis and visualization, and they can help people identify patterns, trends, and outliers in data.
If the function intersects both the x-axis and y-axis at the point (2,4), then the function can be written in the form:
y = a(x - 2)(x - 4)
where a is some constant.
To find the value of a, we can use the fact that the function passes through the point (0,2). Substituting x = 0 and y = 2 into the equation above, we get:
2 = a(0 - 2)(0 - 4)
2 = 8a
Solving for a, we get:
a = 2/8 = 1/4
Therefore, the function is:
y = (1/4)(x - 2)(x - 4)
To find the initial value of the function, we need to determine the value of the function when x is equal to zero. Substituting x = 0 into the equation above, we get:
y = (1/4)(0 - 2)(0 - 4)
y = (1/4)(8)
y = 2
Therefore, initial value of function is 2.
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Related Questions
Suppose a product's revenue function is given by R(q) = - 7q + 600qr. Find an expression for the marginal revenue function, simplify it, and record your result in the box below. Be sure to use the proper variable in your answer. (Use the preview button to check your syntax before submitting your answer.) Answer: MR(q) =
Answers
The expression for the marginal revenue function is MR(q) = 600r - 7.
The given product's revenue function is R(q) = - 7q + 600qr.
To find an expression for the marginal revenue function, we can use the following steps:
Step 1: Take the first derivative of the revenue function with respect to q to obtain the marginal revenue function MR(q).
Step 2: Simplify the expression for MR(q) to record the final result.
In other words, the marginal revenue function MR(q) is the derivative of the revenue function R(q) with respect to q. Here, R(q) = - 7q + 600qr.
So, we have to differentiate R(q) with respect to q to get MR(q).
The derivative of - 7q with respect to q is - 7.
The derivative of 600qr with respect to q is 600r because the derivative of q with respect to q is 1.
MR(q) = dR(q) / dq
= (d/dq)(- 7q + 600r)
= (- 7) + (600r)
= 600r - 7
The equation that represents the marginal revenue function is MR(q) = 600r - 7.
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A greengrocer buys fruit and vegetables from the market and sells them at a 25% mark up. On one particular moring her fruit and vegetables cost her €500. If she sells all of her produce, find:
A) her profit
B) her total income
Answers
Answer: Below :)
Step-by-step explanation:
A) To find the profit, we first need to calculate the cost of the produce plus the 25% markup.
The markup is 25% of the cost, which is 0.25 * 500 = €125.
So the total cost of the produce plus markup is €500 + €125 = €625.
Now, if the greengrocer sells all the produce, the total revenue will be 100% plus the 25% markup, which is 125% of the original cost.
125% of €500 is 1.25 * 500 = €625, which is the same as the cost plus markup.
Therefore, the profit is the markup, which is €125.
B) To find the total income, we add the profit to the total cost:
Total income = €500 + €125 = €625
Answer:
A) €125
B) €625
The equation y = 8x represents the
relationship between the amount of
time Shanay takes to weave thread
into fabric and the number of rows.
How long will it take Shanay to weave
72 rows of fabric at this constant rate?
Answers
X=9
It will take 9
Megan's standard pay is £17.70 per hour. She gets paid 1.5 times this rate for working overtime. How much will Megan get paid for working 11 hours of overtime? Give your answer to the nearest pound.
Answers
Answer:
Step-by-step explanation:
Overtime Rate = [tex]17.70 \times 1\frac{1}{2}[/tex]
[tex]= 17.70 \times \frac{3}{2}[/tex]
[tex]=\frac{53.10}{2}[/tex]
[tex]=\pounds26.55[/tex]
Pay [tex]=11*26.55=\pounds 292.05[/tex] (I assume you can use a calculator for this)
Solution: [tex]\pounds 292[/tex]
A certain small country has $10 billion in paper currency in circulation, and each day $50 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Since both old bills and new bills will come into the banks while the new currency is gradually introduced, we will need to solve a differential equation to track the amount of new currency in circulation at a given time. Let x (t) denote the amount of new currency, in billions of $, in circulation after t days. We've shown that new currency is introduced at the rate 10 - x (t) / 10 0.05, which simplifies to 0.005 (10 - x (t)). This justifies that x (t) satisfies the differential equation dx / dt = 0.005 (10 - x). (a) Solve the differential equation to find x (t). (b) At what time t will new bills make up 90% of the currency in circulation?
Answers
(a) The solution to the differential equation isx(t) = 10(1 - e^(-0.005t))
To solve the differential equation dx/dt = 0.005(10 - x), we can use separation of variables:
dx / (10 - x) = 0.005 dt
Integrating both sides:
-ln|10 - x| = 0.005t + C
where C is the constant of integration. Solving for x:
|10 - x| = e^(-0.005t - C)
Since x cannot be negative, we can drop the absolute value sign and solve for C using the initial condition that x(0) = 0:
C = -ln(10)
Therefore, the solution to the differential equation is:
x(t) = 10 - e^(-0.005t - ln(10))
Simplifying:
x(t) = 10(1 - e^(-0.005t))
(b) New bills will make up 90% of the currency in circulation after approximately 461 days.
We want to find the value of t such that x(t) = 0.9(10) = 9. Plugging this into our solution from part (a):
9 = 10(1 - e^(-0.005t))
Dividing both sides by 10 and taking the natural logarithm:
ln(0.1) = -0.005t
Solving for t:
t = 200 ln(10) = 460.51
Therefore, new bills will make up 90% of the currency in circulation after approximately 461 days.
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There are 30 students in Mr. Hall class. 1/3 of the students are traveling somewhere this summer. Of those traveling, 1/5 are going out of the country. How many students are traveling out of the country?
Answers
The number of students traveling are 2 students out of the 30 who are traveling out of the country this summer. If 1/3 of the students are traveling somewhere this summer, then we can calculate the number of students who are traveling by multiplying the total number of students by 1/3:
Number of students traveling = 30 x 1/3 = 10
Now, we need to find out how many of these 10 students are traveling out of the country. We know that 1/5 of the students who are traveling are going out of the country, so we can find the number of students who are traveling out of the country by multiplying the total number of traveling students by 1/5:
Number of students traveling out of the country = 10 x 1/5 = 2
Therefore, there are 2 students out of the 30 who are traveling out of the country this summer.
It's important to note that fractions can be converted to decimals or percentages to make them easier to work with. For example, 1/3 can be written as 0.33 or 33%, and 1/5 can be written as 0.20 or 20%. This can be particularly useful when dealing with more complex problems or when working with larger numbers.
In summary, by using the information given, we can determine that out of the 30 students in Mr. Hall's class, 10 are traveling somewhere this summer, and out of those 10 students, 2 are going out of the country. This type of problem-solving helps build math skills that are applicable in real-world scenarios, such as budgeting and planning for travel.
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Change 0.182 0.005 0.050 0.174 Table 10-3. Regression results for predicting depression at wave 2 Predictor Variable b Beta P R? Depression Score Wave 1 0.267 0.231 0.000 0.182 Sociodemographic Age -0.014 -0.024 0.538 0.187 Sex 0.165 0.034 0.370 Psychologic Health Neuroticism, wave 1 0.067 0.077 0.056 0.0237 Past history of depression 0.320 0.136 0.000 Physical Health ADL, wave 1 -0.154 0.103 0.033 0.411 ADL, Wave 2 0.275 0.283 0.012 ADL?, wave 2 -0.013 --0.150 0.076 Number of current 0.115 0.117 0.009 symptoms, wave 2 Number of medical 0.309 0.226 0.000 conditions, wave 2 BP, systolic, wave 2 -0.010 -0.092 0.010 Global health rating 0.284 0079 0.028 change Sensory impairment -0.045 -0.064 0.073 change Social support inactivity Social support-friends, -1.650 -0.095 0.015 0.442 wave 2 Social support-visits, -1.229 -0.087 0.032 wave 2 Activity level, wave 2 0.061 0.095 0.025 Services (community residents 0.207 0.135 0.001 0.438° only), wave 2 Abhreviation: BP = blood pressure 0.031 0.015€ Based on above MLRA summary Table, which of following independent variables is the strongest predictor (or factor)?
Number of medical conditions, wave 2
Number of current symptoms, wave 2
Global health rating change
Past history of depression
ADL, wave 2
Answers
The regression result of 0.320, the beta of 0.136, and the p-value of 0.000.
The strongest predictor in the MLRA summary Table is past history of depression. This is shown by the regression result of 0.320, the beta of 0.136, and the p-value of 0.000. This means that past history of depression has a strong and statistically significant influence on predicting depression at wave 2.
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Expand and simplify (3x - 1)(9x² + 3x + 1)
Answers
Write the linear equation of a line going through (-2,7) with a y-intercept of -3.
Answers
Answer:
y = -5x - 3
Step-by-step explanation:
A linear equation is y = mx + b
m = the slope
b = y-intercept
We know
Points (-2,7) (0,-3)
Slope = rise/run or (y2 - y1) / (x2 - x1)
We see the y decrease by 10 and the x increase by 2, so the slope is
m = -10/2 = -5
Y-intercept is located at (0, -3)
So, the equation is y = -5x - 3
y = -5x - 3.
Step by step explanation:
We can use the point-slope form of a linear equation to find the equation of the line passing through the point (-2,7) with a y-intercept of -3.
Point-slope form of a linear equation: y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is the given point on the line.
Since the y-intercept is -3, we know that the point (0,-3) is also on the line. Using the two points (-2,7) and (0,-3), we can find the slope of the line:
slope = (y2 - y1) / (x2 - x1)
slope = (-3 - 7) / (0 - (-2))
slope = -10 / 2
slope = -5
Now we can plug in the values for the slope and the point (-2,7) into the point-slope form:
y - 7 = -5(x - (-2))
Simplifying and solving for y, we get:
y - 7 = -5x - 10
y = -5x - 3
Therefore, the equation of the line passing through the point (-2,7) with a y-intercept of -3 is y = -5x - 3.
please help ill give brainliest to the first correct answer.
i really dont understand this question
Answers
The required time is mathematically given as
t-150 minutes.
This is further explained below.
What is the time?We know that the volume of the prism is given by.
[tex]\text{Volume}=\text{(Base Area)}\times\text{height}[/tex]
[tex]\text{Base Area}=\dfrac{1}{2}\times(1.4+0.6)\times2[/tex]
[tex]\text{Base Area}=2\ \text{m}^2[/tex]
Now,
[tex]\text{Volume}=2\times1=2\ \text{m}^3[/tex]
Given that there is a twenty percent drop in the level of the pond during the first thirty minutes.
Because of this, the volume increases.
[tex]\text{Volume}=2\times0.8=1.6\ \text{m}^3[/tex]
Now, the rate of emptying the tank is,
[tex]=\dfrac{2-1.6}{30} =\dfrac{1}{75} \ \text{m}^3/ \text{min}[/tex]
In conclusion, We also know that,
$$
[tex]\text{time}=\dfrac{\text{volume}}{\text{rate}}[/tex]
[tex]\text{time}=\dfrac{2}{\frac{1}{75} } =150 \ \text{min}[/tex]
Therefore, Colin must wait for the pond to drain for a total of 150 minutes.
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Identify and name congruent triangles
Answers
The answers are a) ASA congruence rule b) SSS congruence rule c) it is not necessary congruent.
What is Congruence ?Congruent refers to having the same height and shape. Congruent therefore involves comparing two numbers, and equivalent denotes the equality of two expressions. Therefore, to state two line segments are congruent implies that the two lines have equal measures.
According to question:a) ∠GIH is corresponding to ∠LJK
GH = KL
∠IHG = ∠KLJ
By ASA congruence rule
ΔGIH ≅ ΔJKL
b) AB = DF
AC = DE
BC = EF
By SSS congruence rule
ΔABC ≅ ΔDEF
c) Two Corresponding sides are congruent, which is not enough to make them congruent.
So, it is not necessary congruent.
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hihihihihihihihihihihihihihihihihi
Answers
The coordinates below represent points that were translated.Draw a line to connect the coordinates with the correct description and algebraic representation of the translation.
Answers
(x-11, y+14) = (-4-7, 7+7) = (-11,14) which matches the new coordinates T(-11,14).
The coordinates' meaning is unclear?In this sense, coordinates are the points where a grid system intersects. GPS coordinates are typically created by combining latitude and longitude. The distance of north and the south from the equator, which is 0 degrees iof north and south, is measured by lines of latitude.
COORDINATES DESCRIPTION ALGEBRAIC REPRESENTATION8. T (-4,7) 7 units right, 7 units up (x-11, y+14)
9. U (3,-4) 7 units left, 7 units up (x+7, y+7)
10. V (-2,-10) 7 units right, 7 units down (x+7, y-7)
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Write a formula for f(t) as a sum of Heaviside functions. Type uc for the Heaviside function that jumps at c (don't type uc(t) ). F(t) = t, 0 ≤ t ≤ 3 2t−3, 3 < t ≤ 4 5, 4 < t
Answers
The formula for f(t) as a sum of Heaviside functions is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4).
To express f(t) as a sum of Heaviside functions, we break down the function into its respective intervals and use the unit step function or Heaviside function to represent the function in each interval.
f(t) = t, 0 ≤ t ≤ 3
f(t) = 2t - 3, 3 < t ≤ 4
f(t) = 5, 4 < t
Using the Heaviside function uc for the jump at c, we can represent each interval as follows:
f(t) = tuc(t) - tuc(t-3), 0 ≤ t ≤ 3
f(t) = (2t-3)uc(t-3) - (2t-3)uc(t-4), 3 < t ≤ 4
f(t) = 5uc(t-4), 4 < t
Therefore, the formula is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4)
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Write the percent as a decimal.
95%
Answers
Answer:
9.5 decimal
espero y te ayude
BP = FC + VCM
The fixed costs associated with the fundraiser include: one-time charges of art ($45), screen and set-up ($60),
and advertising ($50 for a newspaper ad). In addition, the unit cost of the sweatshirt will be $16.50 per sweatshirt, with an additional charge of $.50 per shirt for shipping and individual plastic wrap. You plan to sell the sweatshirts for a retail price of $22.
A. Calculate breakeven in units.
B.calculate breakeven in dollars
Answers
1. The breakeven in units equals 31 units.
2. The dollar amount to breakeven is
What is the breakeven in units?The variable cost per unit includes the cost of the sweatshirt ($16.50) and the additional charge for shipping and plastic wrap ($0.50), so the total variable cost per unit is:
= $16.50 + $0.50
= $17.00
The contribution margin per unit is:
= 22.00 - $17.00
= $5.00
The fixed costs include the one-time charges of art ($45), screen and set-up ($60), and advertising ($50), so the total fixed costs are:
= $45 + $60 + $50
= $155
Using the breakeven formula, we can calculate the number of units required to break even:
= Fixed costs / Contribution margin per unit
= $155 / $5.00
= 31 units
What is the breakeven in dollars?To calculate the breakeven in dollars, we need to multiply the breakeven in units by the selling price per unit:
The breakeven in dollars equals to:
= Breakeven in units x Selling price per unit
= 31 x $22.00
= $682.00
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The Book Nook makes four times as much revenue on paperback books as on hardcover books. If last month's sales totaled $124,300, how much was sold of each type book?
Answers
The revenue from hardcover books was $24,860 and the revenue from paperback books was $99,440.
How much was sold of each type book?Let's assume the revenue from hardcover books as "x" dollars.
Then, the revenue from paperback books will be 4 times the revenue from hardcover books, i.e., 4x dollars.
The total revenue is given as $124,300, so we can set up the following equation:
x + 4x = 124300
Simplifying the above equation, we get:
5x = 124300
x = 24860
Therefore, the revenue from hardcover books was $24,860 and the revenue from paperback books was 4 times that amount, i.e., $99,440.
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use the y-and -x intercept to write the equation of the line y intercept (0,6), x intercept (-2,0)
Answers
Answer:
3x -y = -6
Step-by-step explanation:
You want the equation of the line with intercepts (0, 6) and (-2, 0).
Intercept formThe equation of the line with x-intercept 'a' and y-intercept 'b' is ...
x/a +y/b = 1
For the given intercepts, the equation is ...
x/(-2) +y/6 = 1
Standard formIn standard form, we want the leading coefficient positive and the integer coefficients mutually prime. We can get there by multiplying by -6:
3x -y = -6
__
Additional comment
You can get slope-intercept form by solving for y, or you can recognize that ...
slope = rise/run = -(y-intercept)/(x-intercept) = -6/-2 = 3
Since you already know the y-intercept, you can write the slope-intercept equation as ...
y = 3x +6
There are perhaps a dozen or more forms of the equation for a line. The "intercept form" equation is one of the more useful ones.
ASA, SSS, SAS
Define each postulate and give a well written and visual example of each term.
Include as much detail as possible
Answers
Answer:
In geometry, postulates are statements that are accepted as true without proof. The three postulates for congruent triangles are ASA, SSS, and SAS. These postulates are used to prove that two triangles are congruent.
ASA Postulate:
ASA stands for "Angle, Side, Angle." This postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Visual example:
In the above image, ΔABC and ΔDEF have ∠A ≅ ∠D, ∠B ≅ ∠E, and AB ≅ DE. Therefore, we can conclude that ΔABC ≅ ΔDEF by ASA postulate.
SSS Postulate:
SSS stands for "Side, Side, Side." This postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Visual example:
In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and AC ≅ DF. Therefore, we can conclude that ΔABC ≅ ΔDEF by SSS postulate.
SAS Postulate:
SAS stands for "Side, Angle, Side." This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Visual example:
In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and ∠B ≅ ∠E. Therefore, we can conclude that ΔABC ≅ ΔDEF by SAS postulate.
Overall, the ASA, SSS, and SAS postulates are important tools in proving the congruence of triangles in geometry. They allow us to make logical deductions about the properties of triangles based on their corresponding angles and sides.
Answer:
They are different because ASA means that the two triangles have two angles and the side between the angles congruent. SAS means that two sides and the angle in between them are congruent
Step-by-step explanation:
and sss If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.
Elena and Jada were racing on their bikes. Elena started 15 meters ahead of Jada. Elena biked at a rate of 20 meters per second. Jada biked at a rate of 22 meters per second. Let x represent time in seconds and y represent distance in meters. After how many seconds will Jada pass Elena?
Answers
Jada overtakes Elena after 7.5 seconds.
The set of equations that best captures the scenario is =y=15+20x.
Let's establish a coordinate system with Elena's starting point as the origin. Elena's separation from the origin at time x is given by: y=15+20x
y1 = 15 + 20x
Jada's distance from the origin at time x is determined similarly by:
y2 = 22x
Finding the moment x at which Jada overtakes Elena and their distances from the origin are equal is our goal.
y1 = y2
With the formulas for y1 and y2 substituted, we obtain:
15 + 20x = 22x
When we simplify this equation, we obtain:
2x = 15
x = 7.5
Jada therefore overtakes Elena after 7.5 seconds.
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Stanley is making trail mix out of 10 bags of nuts and 20 bags of dried fruits. He want each new portion of trail mix to be identical, containing the same combination of dried fruits with no bags left over. What is the greatest number of portions of trail mix Stanley can make?
Answers
To solve this problem, we can use the Greatest Common Factor (GCF) of 10 and 20.
The GCF is the largest number that divides evenly into both 10 and 20. To find the GCF, we can use a factor tree.
We start with 10 and 20 as our starting numbers.
10 = 2 * 5
20 = 2 * 2 * 5
We can see that both 10 and 20 have a factor of 2 and a factor of 5. The Greatest Common Factor between 10 and 20 is 2 * 5, or 10.
Therefore, the greatest number of portions of trail mix Stanley can make is 10.
Benito made a wooden box to grow herbs on his patio. The box is 16 inches wide, 12 inches tall, and 28 inches long. He plans to fill the box exactly two-thirds full with potting soil. What volume of soil does Benito need? I know how to do this I just need to know if the two-thirds part is trying to throw me off
Answers
To fill the wooden box with potting soil precisely up to two-thirds of its capacity, Benito requires a volume of 3,584 cubic inches.
The volume of soil that Benito needs to fill the box two-thirds full can be calculated by finding two-thirds of the total volume of the box.
The volume of the box can be calculated by multiplying the width, height, and length:
16 inches (width) x 12 inches (height) x 28 inches (length) = 5,376 cubic inches.
Two-thirds of this volume can be found by multiplying the total volume by 2/3:
5,376 cubic inches x 2/3 = 3,584 cubic inches.
Therefore, Benito needs 3,584 cubic inches of potting soil to fill the box exactly two-thirds full.
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List all prime numbers in the 2023 February calendar
Answers
1,2,3,5,7,11, 13,17,19,23 and 29, that is 11 in all.
Answer:
6 29 25
Step-by-step explanation:
those are the prime numbers on the 2023 feb calendar
A line passes through the point (-4,4) and has a slope of -3
Answers
4y+3x=0
explanation:
please give me brainliest I only need 2 more
Someone please help me ASAP!! It’s due today!! Show work please! I will mark brainliest if it’s done correctly
Answers
Answer:
D
Step-by-step explanation:
First set up the fraction [tex]\frac{9}{40}[/tex] , and next divide 9 ÷ 40 = 0.225. Lastly, multiply 0.225 × 100 = 22.5%.
Hope this helps.
3) Jiya walks 6 km due east and then 8 km due north. How far is she from her
starting place?
6 km
8 km
Answers
Answer:
10km
Step-by-step explanation:
Pythagoras
Formula=[tex]a^2+b^2=c^2[/tex]
[tex]6^{2} +8^{2} =c^2\\c^2=100\\c=\sqrt{100} \\c=10km[/tex]
X^2=8^2+6^2
Suppose you have a certain amount of money in a savings account that earns compound monthly interest, and you want to calculate the amount that you will have after a specific number of months. The formula is as follows: f=p*(1 + i)^t f is the future value of the account after the specified time period. p is the present value of the account. i is the monthly interest rate. t is the number of months. Write a program that takes the account's present value, monthly interest rate, and the number of months that the money will be left in the account as three inputs from the user. The program should pass these values to a function that returns the future value of the account, after the specified number of months. the program should print the account's future value. SAMPLE RUN #2: python3 FutureValue.py None Show Highlighted Only Interactive Session Hide Invisibles Highlight: Enter current bank. balance: 35.72 Enter.interest rate:0 Enter the amount of time that passes: 100 35.7
Answers
Answer:
Step-by-step explanation:
Hi there! Just multiply by x and find the value of f=p. Good luck!
How much greater is 0.05723 then 0.005?
Answers
0.05723 is 0.05223 greater than 0.005.
What is greater than?"Greater than" is a comparison term used to indicate that one quantity or value is larger or more than another quantity or value. It is represented mathematically by the symbol ">".
What is lesser than?"Lesser than" is a comparison term used to indicate that one quantity or value is smaller or less than another quantity or value. It is represented mathematically by the symbol "<".
In the given question,
To find out how much greater 0.05723 is than 0.005, we can subtract 0.005 from 0.05723:0.05723 - 0.005 = 0.05223
Therefore, 0.05723 is 0.05223 greater than 0.005.
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2x+2y= 24
x=3y
What is the value of x+y? I WILL MARK BRAINLIEST AND GIVE 20 POINTS
Answers
Answer:
x + y = 12
Step-by-step explanation:
Pre-SolvingWe are given the following system of equations:
2x + 2y =24
x = 3y
We want to find the value of x + y.
SolvingWe first need to find the values of x and y, which we will do by solving the system.
We can solve this system by substitution.
We know that x = 3y, so we can substitute 3y as x in 2x+2y=24.
This gives us:
2(3y) + 2y = 24
Multiply.
6y + 2y = 24
Add the terms together.
8y = 24
Divide both sides by 8.
y = 3
We found the y value, now let's find the value of x.
The second equation is x=3y, so if we plug the value of y in there, we can find the value of x.
Substitute 3 as y.
x = 3(3) = 9
The value of x is 9.
So, to find x+y, we substitute the values we found.
x + y = 3 + 9 = 12
from a survey involving 1,000 university students, a market research company found that 750 students owned laptops, 450 owned cars, and 350 owned cars and laptops. if a university student is selected at random, what is the (empirical) probability that
Answers
The probability that a student selected randomly owns either a laptop or a car is 85%.
Given a survey with a total of 1000 students, the following data was obtained: 750 students own laptops450 students own cars350 students own laptops and cars a university student is selected at random, what is the (empirical) probability that the student owns either a laptop or a car?
For two events A and B, the union of A and B is the probability that event A or event B occurs. It is the addition of the probabilities of each event minus the intersection of the two events. So in this case, the probability of a student owning either a laptop or a car is P(A∪B) = P(A) + P(B) - P(A∩B) where:
P(A) = probability of owning a laptop = 750/1000 = 0.75
P(B) = probability of owning a car = 450/1000 = 0.45
P(A∩B) = probability of owning both a laptop and a car = 350/1000 = 0.35
Now, substituting values into the formula:
P(A∪B) = 0.75 + 0.45 - 0.35= 0.85
Therefore, the probability that a university student selected randomly owns either a laptop or a car is 85%.
To learn more about probability refer :
https://brainly.com/question/22544647
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