Final answer:
A negative y-intercept in a real-world context indicates that the system or condition being measured starts below the baseline or has a deficit to begin with. It can represent an initial loss in economics, such as starting with debt or needing initial investment. The slope of the line is critical to understanding how changes in one variable affect another.
Explanation:
A negative y-intercept in a real-world application can have various implications depending on the context. In many scientific experiments, the y-intercept represents the baseline level of the system without any experimental conditions applied. If the y-intercept is negative, this might indicate that in the absence of a certain factor (represented by the x-variable), the system has a deficit or a reduction in the measured quantity. For instance, if we are plotting a graph of growth over time, a negative y-intercept could imply that there was an initial debt or loss before measurements began.
When it comes to economics and data models, a negative y-intercept on a graph could represent a starting deficit. For example, a company might have initial losses (negative y-intercept) that it seeks to overcome as production (x-variable) increases. Supply and demand models, cost projections, and similar economic graphs can also have negative y-intercepts indicating starting positions below zero on the graph—such as starting with a debt or having to invest before seeing any return.
The y-intercept and the slope (m-term) together specify a particular line on a graph that can offer a reasonable approximation of real-world data. Economists find the slope particularly useful as it shows the relationship between two variables, like how a change in price affects the quantity supplied.
the quotient of a and c is 8. The product of a and c is 2. The quotient of a and b is -16. The product of a and b is -1. The quotient of b and c is -0.5. What is value of a,b, and c?
To find the values of a, b, and c, we can use the given information and solve the system of equations.
Explanation:To find the values of a, b, and c, we can use the given information and solve the system of equations.
From the first two statements, we have a/c = 8 and a*c = 2. This allows us to solve for a and c.
Similarly, from the next two statements, we have a/b = -16 and a*b = -1. Using these equations, we can find the values of a and b.
Finally, the last statement gives us b/c = -0.5, and we can use this equation to find the value of c.
Substituting the appropriate values for a, b, and c, we find that a = 1, b = 0.0211, and c = -0.0211.
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A marble is drawn at random from the bag shown below. The bag contains 3 green, 4 yellow, 5 blue, and 8 pink marbles.What is P(not pink)?
Answer: [tex]\dfrac{3}{5}[/tex]
Step-by-step explanation:
Given : The number of pink marbles in bag= 8
Total number of marbles in bag= [tex]4+5+8+3=20[/tex]
Now, the number of marbles that are not pink =[tex]20-8=12[/tex]
We know that the formula to find the probability is :-
[tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
Similarly, [tex]\text{P(not pink)}=\dfrac{12}{20}=\dfrac{3}{5}[/tex]
You have 4 dimes, 5 quarters, and 3 pennies in your pocket. What is the probability of reaching in and randomly picking out a dime or a quarter? Express your answer as a fraction in lowest terms.
The probability of picking a dime or a quarter is 3/4
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given, you have 4 dimes, 5 quarters, and 3 pennies in your pocket.
There are a total of 4 + 5 + 3 = 12 coins in your pocket.
The probability of picking a dime or a quarter can be calculated as the sum of the probability of picking a dime and the probability of picking a quarter. Since the coins are selected randomly, each coin has an equal chance of being picked.
The probability of picking a dime is 4/12 or 1/3, since there are 4 dimes in the pocket out of a total of 12 coins.
The probability of picking a quarter is 5/12, since there are 5 quarters in the pocket out of a total of 12 coins.
Therefore, the probability of picking a dime or a quarter is:
P(dime or quarter) = P(dime) + P(quarter)
P(dime or quarter) = 4/12 + 5/12
P(dime or quarter) = 9/12
P(dime or quarter) = 3/4
So the probability of picking a dime or a quarter is 3/4, or three-fourths.
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Use doubles to find the sum of 7+8
With a speed of 55 mph, a driver drives through a tunnel in 1 minute. How long would it take him to get through the same tunnel with a speed of 45 mph?
what is 29.5 multiplied 2.6
I need to know what does untethers mean
You have $12 to buy five goldfish for your new fish tank. Write and solve an inequality that represents that prices you can pay per fish.
The prices you can pay per fish can be represented by the inequality 5x ≤ 12. After solving the inequality, the maximum price you can pay per fish is $2.40.
Explanation:To write the inequality that represents the prices you can pay per fish, let's assume that the price of each goldfish is 'x' dollars. Since you have $12 in total, the inequality can be written as:
5x ≤ 12
To solve this inequality, divide both sides by 5:
x ≤ 2.4
Therefore, you can pay at most $2.40 per fish.
1/20=0.05. Which calculation is NOT a way to find 14/20?
a. 0.5+0.05
b. 0.75−0.05
c. 14÷20
d. 14·0.05
The calculation that is NOT a relevant way to find the value of 14/20 is given by option a: 0.5 + 0.05.
Let's find the value of 14/20 first:
To find 14/20, divide 14 by 20:
14 ÷ 20 = 0.7
Now, let's check each calculation:
a. 0.5 + 0.05 = 0.55 (Not relevant to finding 14/20)
b. 0.75 - 0.05 = 0.7 (Relevant, as this gives us 14/20)
c. 14 ÷ 20 = 0.7 (Relevant, as this is the correct calculation for 14/20)
d. 14 × 0.05 = 0.7 (Relevant to finding 14/20)
Therefore, the calculation that is NOT a way to find 14/20 is option a: 0.5 + 0.05.
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solve the equation 20x-5y=10 for y
Sofia wants to place a sticker 2 ½ inches long in the center of a switch box that is 3 ¾ inches wide. About how far from the edge will she place the sticker?
The total charge on 7 particles is −42 units. All the particles have the same charge.
What is the charge on each particle? (1 point)
6 units
5 units
−5 units
−6 units
Your answer would be -6! -42= -6 divided by 7 or 7 X -6= -42
find −3(2.5−k)+0.5(7+8k)
zack made this table for his survey? grape 16, orange 10, berry 9, apple 12 how many votes were cast?
Three hikers equally shared gallon of water. Explain how you would use an area model to find the amount of water each hiker drank.
Answer:
Draw a square and shade half of it. Then draw 2 lines to divide the square into 3 equal parts. There will be one shaded piece in each group, and there are 6 pieces total, so the answer is 1
6
of a gallon.
Step-by-step explanation:
0.009842 in scientific notation
Idk what the properties are I need help
Why do you subtract exponents when dividing powers with the same base
Answer:
[tex]\displaystyle\frac{x^r}{x^s} = x^{r-s}[/tex]
Step-by-step explanation:
The quotient rule of exponential power states that:
[tex]\displaystyle\frac{x^r}{x^s} = x^{r-s}[/tex]
This can be easily understood with the help of an example:[tex]\displaystyle\frac{x^4}{x^2} = \displaystyle\frac{x\times x\times x\times x}{x\times x} = x^2 = x^{4-2}[/tex]
Basically, this quotient rule helps us to reducing the fractions. Since the numerator and the denominator is same as we have same base, we could simply subtract the powers to get the answer as illustrated in the above example.
When dividing powers with the same base, subtracting exponents simplifies the expression due to the quotient of powers rule is [tex]a^m / a^n = a^{(m - n).[/tex]
When dividing powers with the same base, subtract the exponents because of the properties of exponents.
The rule is known as the "quotient of powers" rule, and it states that when you divide two powers with the same base,
subtract the exponents to simplify the expression.
The rule can be stated as follows:
[tex]a^m / a^n = a^{(m - n).[/tex]
Here's why this rule works,
Let's say you have a number 'a' raised to two exponents 'm' and 'n':
[tex]a^m[/tex]= a × a × a ×... (m times)
[tex]a^n[/tex] = a × a × a × ... (n times)
Now, to divide these two powers, cancel out the common factors:
[tex]a^m / a^n[/tex] = (a × a × a ×... ... × a) / (a × a × a ×...... × a)
In the numerator and denominator, there are 'm' and 'n' occurrences of 'a', respectively.
Since we are dividing, we can cancel out 'n' occurrences of 'a' from the numerator and denominator:
[tex]a^m / a^n[/tex] = (a × a × a ×... ... × a) / (a × a × a ×...... × a)
= [tex]a^{(m - n)[/tex]
Therefore, when divide powers with the same base, subtract the exponents to simplify the expression and apply this property of exponents.
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does the point given below occur on the line shown. Can you show the work please
n the figure, 2004-02-04-06-00_files/i0250000.jpg. If the ratio of the perimeter of to that of is 3:2 and the sum of the perimeters of the two triangles is 110, find the perimeter of each triangle.
A.
perimeter of = 66
perimeter of = 44
B.
perimeter of = 73
perimeter of = 37
C.
perimeter of = 37
perimeter of = 73
D.
perimeter of = 44
perimeter of = 66
Answer:
Perimeter of triangle 1 = p1 = 66
Perimeter of triangle 2 = p2 = 44
Add. Simplify the answer to lowest terms before entering the numerator and denominator in their boxes. 11/16 + 3/16
Answer:
The answer is 7/8.
Step-by-step explanation:
If you add 11/16 to 3/16, you'll get 14/16. 14/16 has two numbers that are divisible by 2, so when you divide 14/16 by 2 you'll get 7/8 which is 14/16 in a simplified form. 7 is prime and you can't divide it down any more, but 8 i'snt the same way. The rule is, whatever you do to one side, you have to do to the other. You can divide 8, but not 7; therefore, you cannot simplify the fraction any further.
To add fractions with the same denominator, simply add the numerators together, while keeping the denominator the same.
Explanation:To add fractions with the same denominator, simply add the numerators together, while keeping the denominator the same. In this case, we have 11/16 + 3/16. The denominators are already the same, so we can add the numerators: 11 + 3 = 14. The fraction 14/16 cannot be simplified further.
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90 points!! Forreal!
What is the justification for each step in the solution of the equation?
−2(x−1)+12=4x−6
Select from the drop-down menus to correctly justify each step
-2(x-1)+12=4x-6 - (GIVEN)
-2+2+12=4x-6 - ______ ?
-2x+14=4x-6 - (COMBINE LIKE TERMS)
-2x=4x-20 - ________ ?
-6x=-20 - (ADDITON OR SUBTRACTION OF EQUALITY)
x=20/6 - _____ ?
x=10/3 - (SIMPLIFY)
Distributive Property
Addition or Subtraction Property of Equality
Multiplication or Division Property of Equality
Find the average rate of change of a function that contains the points (-2,3) and (2,5).
A. -2
B. 1/2
C. -1/2
D. 2
A translation of trapezoid PQRS (blue) to trapezoid P'Q'R'S' (green) is shown, where the location of Q' is the origin. The coordinates of point R' are
On USATestprep the answer is C) (c-a,-b)
The coordinates of point R' are (-c, b-d).
What is the translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.
Given that, a translation of trapezoid PQRS (blue) to trapezoid P'Q'R'S' (green).
Translation rules:
When the shape is moved down by k units, then replace y with y - k.
So, the coordinates of point R' are (-c, b-d)
Therefore, the coordinates of point R' are (-c, b-d).
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What is 1920 divided by 12
A computer store bought a program at a cost of 20$ and sold it at a selling price of 24$ find the percent markup
$14.30 watch ; 6 3/4% sales tax
You borrowed $25 from your mom to buy close a week later you repaid her $13 write an expression to show how much money you owe
What's 140,250 rounded to the nearest 100,000
During a day a student spends 7 hours sleeping, ¹/4 of the day studying and of the time travelling. What fraction of the day is left for other things?
Answer:
[tex]\dfrac{5}{24}[/tex]
Step-by-step explanation:
Time Spent Sleeping=7 hoursTime Spent Studying=[tex]\frac{1}{4}[/tex] of the dayTime Spent Travelling=[tex]\frac{1}{4}[/tex] of the dayThere are 24 hours in a day, therefore:
Time Spent Studying=[tex]\frac{1}{4}[/tex] X 24 =6 HoursTime Spent Travelling=[tex]\frac{1}{4}[/tex] X 24 =6 HoursThe total hour used for sleeping, studying and travelling=7+6+6=19 hours
Hours used for other things=24-19=5 hours
Therefore, the fraction of the day used for other things=[tex]\dfrac{5}{24}[/tex]